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    <title>Ecdysone coordinates plastic growth with robust pattern in the developing wing</title>
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      <article itemscope="" itemtype="http://schema.org/Article" data-itemscope="root">
        <h1 itemprop="headline">Ecdysone coordinates plastic growth with robust pattern in the
          developing wing</h1>
        <meta itemprop="image"
          content="https://via.placeholder.com/1200x714/dbdbdb/4a4a4a.png?text=Ecdysone%20coordinates%20plastic%20growth%20with%20robust%20pattern%20in%20the%20developing%20wing">
        <ol data-itemprop="authors">
          <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
            <meta itemprop="name" content="André Nogueira Alves"><span
              data-itemprop="givenNames"><span itemprop="givenName">André</span></span><span
              data-itemprop="familyNames"><span itemprop="familyName">Nogueira</span><span
                itemprop="familyName">Alves</span></span><span data-itemprop="affiliations"><a
                itemprop="affiliation" href="#author-organization-1">1</a><a itemprop="affiliation"
                href="#author-organization-2">2</a></span>
          </li>
          <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
            <meta itemprop="name" content="Marisa Mateus Oliveira"><span
              data-itemprop="givenNames"><span itemprop="givenName">Marisa</span><span
                itemprop="givenName">Mateus</span></span><span data-itemprop="familyNames"><span
                itemprop="familyName">Oliveira</span></span><span data-itemprop="affiliations"><a
                itemprop="affiliation" href="#author-organization-1">1</a></span>
          </li>
          <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
            <meta itemprop="name" content="Takashi Koyama"><span data-itemprop="givenNames"><span
                itemprop="givenName">Takashi</span></span><span data-itemprop="familyNames"><span
                itemprop="familyName">Koyama</span></span><span data-itemprop="affiliations"><a
                itemprop="affiliation" href="#author-organization-1">1</a><a itemprop="affiliation"
                href="#author-organization-3">3</a></span>
          </li>
          <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
            <meta itemprop="name" content="Alexander Shingleton"><span
              data-itemprop="givenNames"><span itemprop="givenName">Alexander</span></span><span
              data-itemprop="familyNames"><span itemprop="familyName">Shingleton</span></span><span
              data-itemprop="emails"><a itemprop="email"
                href="mailto:ashingle@uic.edu">ashingle@uic.edu</a></span><span
              data-itemprop="affiliations"><a itemprop="affiliation"
                href="#author-organization-4">4</a></span>
          </li>
          <li itemscope="" itemtype="http://schema.org/Person" itemprop="author">
            <meta itemprop="name" content="Christen Kerry Mirth"><span
              data-itemprop="givenNames"><span itemprop="givenName">Christen</span><span
                itemprop="givenName">Kerry</span></span><span data-itemprop="familyNames"><span
                itemprop="familyName">Mirth</span></span><span data-itemprop="emails"><a
                itemprop="email"
                href="mailto:christen.mirth@monash.edu">christen.mirth@monash.edu</a></span><span
              data-itemprop="affiliations"><a itemprop="affiliation"
                href="#author-organization-1">1</a><a itemprop="affiliation"
                href="#author-organization-2">2</a></span>
          </li>
        </ol>
        <ol data-itemprop="affiliations">
          <li itemscope="" itemtype="http://schema.org/Organization" itemid="#author-organization-1"
            id="author-organization-1"><span itemprop="name">Oeiras</span><address itemscope=""
              itemtype="http://schema.org/PostalAddress" itemprop="address"><span
                itemprop="addressCountry">Portugal</span></address></li>
          <li itemscope="" itemtype="http://schema.org/Organization" itemid="#author-organization-2"
            id="author-organization-2"><span itemprop="name">Melbourne</span><address itemscope=""
              itemtype="http://schema.org/PostalAddress" itemprop="address"><span
                itemprop="addressCountry">Australia</span></address></li>
          <li itemscope="" itemtype="http://schema.org/Organization" itemid="#author-organization-3"
            id="author-organization-3"><span itemprop="name">Copenhagen</span><address itemscope=""
              itemtype="http://schema.org/PostalAddress" itemprop="address"><span
                itemprop="addressCountry">Denmark</span></address></li>
          <li itemscope="" itemtype="http://schema.org/Organization" itemid="#author-organization-4"
            id="author-organization-4"><span itemprop="name">Chicago</span><address itemscope=""
              itemtype="http://schema.org/PostalAddress" itemprop="address"><span
                itemprop="addressCountry">United States</span></address></li>
        </ol><span itemscope="" itemtype="http://schema.org/Organization" itemprop="publisher">
          <meta itemprop="name" content="Unknown"><span itemscope=""
            itemtype="http://schema.org/ImageObject" itemprop="logo">
            <meta itemprop="url"
              content="https://via.placeholder.com/600x60/dbdbdb/4a4a4a.png?text=Unknown">
          </span>
        </span><time itemprop="datePublished" datetime="2022-03-09">2022-03-09</time>
        <ul data-itemprop="genre">
          <li itemprop="genre">Research Article</li>
        </ul>
        <ul data-itemprop="about">
          <li itemscope="" itemtype="http://schema.org/DefinedTerm" itemprop="about"><span
              itemprop="name">Developmental Biology</span></li>
          <li itemscope="" itemtype="http://schema.org/DefinedTerm" itemprop="about"><span
              itemprop="name">Evolutionary Biology</span></li>
        </ul>
        <ul data-itemprop="keywords">
          <li itemprop="keywords">phenotypic plasticity</li>
          <li itemprop="keywords">developmental robustness</li>
          <li itemprop="keywords">growth rates</li>
          <li itemprop="keywords">patterning rates</li>
          <li itemprop="keywords">wing disc</li>
          <li itemprop="keywords">D. melanogaster</li>
        </ul>
        <ul data-itemprop="identifiers">
          <li itemscope="" itemtype="http://schema.org/PropertyValue" itemprop="identifier">
            <meta itemprop="propertyID"
              content="https://registry.identifiers.org/registry/publisher-id"><span
              itemprop="name">publisher-id</span><span itemprop="value"
              data-itemtype="http://schema.org/Number">72666</span>
          </li>
          <li itemscope="" itemtype="http://schema.org/PropertyValue" itemprop="identifier">
            <meta itemprop="propertyID" content="https://registry.identifiers.org/registry/doi">
            <span itemprop="name">doi</span><span itemprop="value">10.7554/eLife.72666</span>
          </li>
          <li itemscope="" itemtype="http://schema.org/PropertyValue" itemprop="identifier">
            <meta itemprop="propertyID"
              content="https://registry.identifiers.org/registry/elocation-id"><span
              itemprop="name">elocation-id</span><span itemprop="value">e72666</span>
          </li>
        </ul>
        <section data-itemprop="description">
          <h2 data-itemtype="http://schema.stenci.la/Heading">Abstract</h2>
          <meta itemprop="description"
            content="Animals develop in unpredictable, variable environments. In response to environmental change, some aspects of development adjust to generate plastic phenotypes. Other aspects of development, however, are buffered against environmental change to produce robust phenotypes. How organ development is coordinated to accommodate both plastic and robust developmental responses is poorly understood. Here, we demonstrate that the steroid hormone ecdysone coordinates both plasticity of organ size and robustness of organ pattern in the developing wings of the fruit fly  Drosophila melanogaster . Using fed and starved larvae that lack prothoracic glands, which synthesize ecdysone, we show that nutrition regulates growth both via ecdysone and via an ecdysone-independent mechanism, while nutrition regulates patterning only via ecdysone. We then demonstrate that growth shows a graded response to ecdysone concentration, while patterning shows a threshold response. Collectively, these data support a model where nutritionally regulated ecdysone fluctuations confer plasticity by regulating disc growth in response to basal ecdysone levels and confer robustness by initiating patterning only once ecdysone peaks exceed a threshold concentration. This could represent a generalizable mechanism through which hormones coordinate plastic growth with robust patterning in the face of environmental change.">
          <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Animals develop in
            unpredictable, variable environments. In response to environmental change, some aspects
            of development adjust to generate plastic phenotypes. Other aspects of development,
            however, are buffered against environmental change to produce robust phenotypes. How
            organ development is coordinated to accommodate both plastic and robust developmental
            responses is poorly understood. Here, we demonstrate that the steroid hormone ecdysone
            coordinates both plasticity of organ size and robustness of organ pattern in the
            developing wings of the fruit fly <em itemscope=""
              itemtype="http://schema.stenci.la/Emphasis">Drosophila melanogaster</em>. Using fed
            and starved larvae that lack prothoracic glands, which synthesize ecdysone, we show that
            nutrition regulates growth both via ecdysone and via an ecdysone-independent mechanism,
            while nutrition regulates patterning only via ecdysone. We then demonstrate that growth
            shows a graded response to ecdysone concentration, while patterning shows a threshold
            response. Collectively, these data support a model where nutritionally regulated
            ecdysone fluctuations confer plasticity by regulating disc growth in response to basal
            ecdysone levels and confer robustness by initiating patterning only once ecdysone peaks
            exceed a threshold concentration. This could represent a generalizable mechanism through
            which hormones coordinate plastic growth with robust patterning in the face of
            environmental change.</p>
        </section>
        <h2 itemscope="" itemtype="http://schema.stenci.la/Heading" id="introduction">Introduction
        </h2>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Developing animals respond to
          changes in their environment in a multitude of ways, for example, altering how long and
          how fast they grow, the time it takes them to mature, and their reproductive output <span
            itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib62"><span>62</span><span>Nylin
                  and Gotthard</span><span>1998</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib86"><span>86</span><span>West-Eberhard</span><span>1989</span></a></cite></span>.
          Other aspects of their phenotype, however, must be unresponsive to environmental change to
          ensure that they function correctly regardless of environmental conditions. This presents
          a particular problem for morphological traits of developing animals. For any given trait,
          some aspects, such as final organ size, vary with changes in the environment, a phenomenon
          termed plasticity <span itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib4"><span>4</span><span>Beldade et
                  al.</span><span>2011</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib40"><span>40</span><span>Koyama
                  et al.</span><span>2013</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib75"><span>75</span><span>Shingleton</span><span>2010</span></a></cite><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib53"><span>53</span><span>Mirth and
                  Shingleton</span><span>2019</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib60"><span>60</span><span>Nijhout
                  et al.</span><span>2017</span></a></cite></span>. Other aspects, like patterning
          the cell types within an organ necessary for it to function, remain constant across
          environmental conditions and are thus termed robust <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib53"><span>53</span><span>Mirth
                  and Shingleton</span><span>2019</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib60"><span>60</span><span>Nijhout
                  et al.</span><span>2017</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib27"><span>27</span><span>Félix
                  and Barkoulas</span><span>2015</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib26"><span>26</span><span>Félix
                  and Wagner</span><span>2008</span></a></cite></span>. For many organs, growth and
          patterning occur at the same time during development, and may even be regulated by the
          same hormones <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib53"><span>53</span><span>Mirth and
                Shingleton</span><span>2019</span></a></cite>. How then do organs achieve plasticity
          in size while maintaining the robustness of pattern?</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">If we want to extract general
          principles of how organisms regulate their development in variable environments, we need
          to understand how developmental processes unfold over time. Several recent studies that
          have applied systems approaches to development offer excellent examples, frequently
          employing methods to quantify how gene expression patterns change over time. These studies
          have used the dynamic changes in expression patterns to uncover the rules governing how
          insects build their segments <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib78"><span>78</span><span>Surkova
                  et al.</span><span>2009</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib79"><span>79</span><span>Surkova
                  et al.</span><span>2009</span></a></cite></span>, how the gene regulatory network
          underlying segmentation evolves <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib12"><span>12</span><span>Clark</span><span>2017</span></a></cite><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib11"><span>11</span><span>Clark and
                  Akam</span><span>2016</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib13"><span>13</span><span>Clark
                  and Peel</span><span>2018</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib18"><span>18</span><span>Crombach
                  et al.</span><span>2016</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib82"><span>82</span><span>Verd et
                  al.</span><span>2018</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib87"><span>87</span><span>Wotton
                  et al.</span><span>2015</span></a></cite></span>, how morphogen gradients scale
          across organs and bodies <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib90"><span>90</span><span>Zhou et
                  al.</span><span>2012</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib1"><span>1</span><span>Almuedo-Castillo et
                  al.</span><span>2018</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib91"><span>91</span><span>Zhu et
                  al.</span><span>2020</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib72"><span>72</span><span>Schwank
                  et al.</span><span>2011</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib84"><span>84</span><span>Wartlick
                  et al.</span><span>2011</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib35"><span>35</span><span>Hamaratoglu et
                  al.</span><span>2011</span></a></cite></span>, how sensory organs are positioned
          within epithelia <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib17"><span>17</span><span>Corson et al.</span><span>2017</span></a></cite>,
          and how somites and digits form in vertebrates <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib69"><span>69</span><span>Raspopovic et
                  al.</span><span>2014</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib24"><span>24</span><span>Dubrulle
                  et al.</span><span>2001</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib3"><span>3</span><span>Baker et
                  al.</span><span>2006</span></a></cite></span>. The power of these approaches is
          that they provide a framework for understanding how genes interact within a network to
          generate a pattern that can be applied across a variety of contexts.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The success of these studies
          is, in part, due to the fact that the gene regulatory networks underlying each of these
          processes have been well described in their respective developmental contexts. In
          contrast, the gene regulatory networks governing growth and patterning at later stages of
          development, even at later stages of embryonic development, are not as well resolved. If
          we further complicate this by comparing development across environmental conditions and
          even across traits, approaches that rely on understanding the configuration of gene
          regulatory networks become much more difficult to implement.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Nevertheless, we can still use
          the principle of comparing the dynamics of developmental processes across environments to
          gain useful insights into the relationship between plasticity and robustness. Many types
          of environmental conditions impact organ development to induce changes in body and organ
          size. Malnutrition or starvation reduces growth rates in all animals, resulting in smaller
          body and organ sizes <span itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib58"><span>58</span><span>Nijhout</span><span>2003</span></a></cite><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib59"><span>59</span><span>Nijhout et
                  al.</span><span>2014</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib51"><span>51</span><span>Mirth
                  and Shingleton</span><span>2012</span></a></cite></span>. Similarly, changing
          temperature can alter animal growth. In insect species, rearing animals in warmer
          conditions results in smaller adult body sizes when compared to animals reared under
          cooler conditions <span itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib2"><span>2</span><span>Azevedo et
                  al.</span><span>2002</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib20"><span>20</span><span>David et
                  al.</span><span>1994</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib28"><span>28</span><span>French
                  et al.</span><span>1998</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib39"><span>39</span><span>James et
                  al.</span><span>1997</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib68"><span>68</span><span>Partridge et
                  al.</span><span>1994</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib34"><span>34</span><span>Grunert
                  et al.</span><span>2015</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib70"><span>70</span><span>Reynolds
                  and Nottingham</span><span>1985</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib81"><span>81</span><span>Thomas</span><span>1993</span></a></cite></span>.
          Other factors like oxygen availability and the presence of toxic or noxious compounds also
          act to alter animal sizes <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib8"><span>8</span><span>Callier
                  and Nijhout</span><span>2011</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib9"><span>9</span><span>Callier et
                  al.</span><span>2013</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib31"><span>31</span><span>Glendinning</span><span>2003</span></a></cite></span>.
          Examining how organ growth and patterning progress across these environmental conditions
          helps us to understand how these two processes are coordinated.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">We already have some
          understanding of the mechanisms that regulate growth and patterning in response to
          changing environmental conditions. The genetic mechanisms underlying plasticity in growth
          are best elucidated in insects. In insects, changes in available nutrition affect the
          synthesis and secretion of the conserved insulin-like peptides <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib88"><span>88</span><span>Wu and
                  Brown</span><span>2006</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib6"><span>6</span><span>Brogiolo
                  et al.</span><span>2001</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib38"><span>38</span><span>Ikeya et
                  al.</span><span>2002</span></a></cite></span>. Insulin-like peptides bind to the
          insulin receptor in target tissues and activate the insulin signalling cascade, ultimately
          leading to increased growth <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib6"><span>6</span><span>Brogiolo
                  et al.</span><span>2001</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib10"><span>10</span><span>Chen et
                  al.</span><span>1996</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib89"><span>89</span><span>Yenush
                  et al.</span><span>1996</span></a></cite></span>. Starvation reduces the
          concentration of insulin-like peptides in the hemolymph, or insect blood, and the
          resulting decrease in insulin signalling causes organs to grow more slowly <span
            itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib38"><span>38</span><span>Ikeya et
                  al.</span><span>2002</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib30"><span>30</span><span>Géminard
                  et al.</span><span>2009</span></a></cite></span>.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">While changes in insulin
          signalling are known to affect organ size, they have little effect on organ pattern <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib85"><span>85</span><span>Weinkove and
                Leevers</span><span>2000</span></a></cite>. However, studies in the fruit fly <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">Drosophila melanogaster</em>
          have shown that, at least in this insect, insulin acts to control the synthesis of a
          second developmental hormone, the steroid hormone ecdysone <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib7"><span>7</span><span>Caldwell
                  et al.</span><span>2005</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib16"><span>16</span><span>Colombani et
                  al.</span><span>2012</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib49"><span>49</span><span>Mirth et
                  al.</span><span>2005</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib41"><span>41</span><span>Koyama
                  et al.</span><span>2014</span></a></cite></span>. Most of the body and organ
          growth in <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">D.
            melanogaster</em> occurs in the third, and final, larval instar, after which the animal
          initiates metamorphosis at pupariation. Either starving or reducing insulin signalling
          early in the third instar delays the timing of ecdysone synthesis, thereby prolonging the
          length of the third instar and the time it takes to metamorphose <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib7"><span>7</span><span>Caldwell
                  et al.</span><span>2005</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib16"><span>16</span><span>Colombani et
                  al.</span><span>2012</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib49"><span>49</span><span>Mirth et
                  al.</span><span>2005</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib41"><span>41</span><span>Koyama
                  et al.</span><span>2014</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib73"><span>73</span><span>Shingleton et
                  al.</span><span>2005</span></a></cite></span>.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">In addition to its effects on
          developmental time, ecdysone controls the growth of the developing adult organs <span
            itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib76"><span>76</span><span>Stieper
                  et al.</span><span>2008</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib36"><span>36</span><span>Herboso
                  et al.</span><span>2015</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib32"><span>32</span><span>Gokhale
                  et al.</span><span>2016</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib25"><span>25</span><span>Dye et
                  al.</span><span>2017</span></a></cite></span>. In <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">D. melanogaster</em> larvae, many of the
          adult organs form and grow inside the larvae as pouches of cells called imaginal discs. If
          ecdysone synthesis is reduced or if the glands that produce ecdysone, the prothoracic
          glands (PG), are ablated, these imaginal discs grow at greatly reduced rates <span
            itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib36"><span>36</span><span>Herboso
                  et al.</span><span>2015</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib50"><span>50</span><span>Mirth et
                  al.</span><span>2009</span></a></cite></span>.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Ecdysone signalling also
          regulates organ patterning. Reducing ecdysone signalling in either the wing imaginal disc
          or the developing ovary causes substantial delays in their patterning <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib36"><span>36</span><span>Herboso
                  et al.</span><span>2015</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib50"><span>50</span><span>Mirth et
                  al.</span><span>2009</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib47"><span>47</span><span>Mendes
                  and Mirth</span><span>2016</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib29"><span>29</span><span>Gancz et
                  al.</span><span>2011</span></a></cite></span>. In the wing disc, reducing ecdysone
          signalling stalls the progression of patterning of sensory bristles <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib36"><span>36</span><span>Herboso
                  et al.</span><span>2015</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib50"><span>50</span><span>Mirth et
                  al.</span><span>2009</span></a></cite></span>. Similarly, in the ovary terminal
          filament cell specification and the rate of terminal filament addition both require
          ecdysone to progress normally <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib47"><span>47</span><span>Mendes
                  and Mirth</span><span>2016</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib29"><span>29</span><span>Gancz et
                  al.</span><span>2011</span></a></cite></span>. Given its role in both the
          patterning and the growth of imaginal discs and ovaries, ecdysone is potentially a key
          coordinator of plastic growth and robust pattern.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Characterizing organ growth
          rates is experimentally straightforward, requiring only accurate measurement of changes in
          organ size over time. To quantify the progression of organ patterning, however, requires
          developing a staging scheme. We previously developed such a scheme for the wing imaginal
          disc in <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">D. melanogaster</em>.
          This scheme makes use of the dynamic changes in expression from the moult to the third
          instar to pupariation of up to seven patterning-gene products in the developing wing <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib64"><span>64</span><span>Oliveira et al.</span><span>2014</span></a></cite>.
          Two of these patterning-gene products, Achaete and Senseless, can be classed into seven
          different stages throughout third-instar development (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib64"><span>64</span><span>Oliveira
                et al.</span><span>2014</span></a></cite>, <a href="#fig1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1A</a>), providing us with the ability to
          quantify the progression of wing disc pattern over a variety of conditions. In short, by
          describing patterning on a near-continuous scale, our scheme not only allows us to
          determine under what conditions patterning is initiated, but also the rate at which it
          progresses.</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig1" title="Figure 1.">
          <label data-itemprop="label">Figure 1.</label><img
            src="index.html.media/elife-72666-fig1-v2.jpg" alt="" itemscope=""
            itemtype="http://schema.org/ImageObject">
          <figcaption>
            <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="quantitative-assessments-of-the-progression-of-patterning-allow-us-to-test-hypotheses-about-the-relationship-between-the-size-and-patterning-stage-of-the-developing-wing">
              Quantitative assessments of the progression of patterning allow us to test hypotheses
              about the relationship between the size and patterning stage of the developing wing.
            </h3>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) The staging scheme developed
              by <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                  href="#bib64"><span>64</span><span>Oliveira et
                    al.</span><span>2014</span></a></cite> to quantify the progression of Achaete
              and Senseless pattern. The pattern elements shown in orange are diagnostic for each
              stage, which is indicated by the number beside the disc. (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">B–D</strong>) The relationship between
              wing disc size and patterning stage (represented as wing discs progressing through a
              series of colours) if (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">B</strong>) Hypothesis 1: wing discs grow
              first and then initiate pattern; (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">C</strong>) Hypothesis 2: wing disc
              patterning is regulated by wing disc size (arrows); and (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">D</strong>) Hypothesis 3: wing disc
              pattern and growth are regulated at least partially independently.</p>
          </figcaption>
        </figure>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The ability to simultaneously
          quantify both organ growth and pattern allows us to generate, and test, hypotheses
          regarding how ecdysone coordinates plastic growth with robust patterning. One hypothesis
          is that growth and patterning occur at different times, with ecdysone driving growth first
          then pattern later, or vice versa <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib53"><span>53</span><span>Mirth and
                Shingleton</span><span>2019</span></a></cite>. If this were true, we would expect to
          identify an interval where ecdysone concentrations primarily affected growth and a second
          interval where they affected mostly pattern (<a href="#fig1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1B</a>). There is some precedence for
          this idea; most of the patterning in the wing discs and ovaries of <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">D. melanogaster</em> occurs 15 hr after the
          moult to the third larval instar <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib47"><span>47</span><span>Mendes and
                Mirth</span><span>2016</span></a></cite>. Similarly, wing discs are known to grow
          faster in the early part of the third instar and slow their growth in the mid-to-late
          third instar <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib74"><span>74</span><span>Shingleton et
                al.</span><span>2008</span></a></cite>. As a second hypothesis, ecdysone could
          coordinate plastic growth with robust pattern if the impacts of ecdysone on one of these
          processes depended on its effects on the other. For example, morphogens are known to
          regulate both growth and patterning of the wing. If ecdysone controlled the action of
          morphogens, we would expect the progression of patterning to be tightly coupled to growth
          over time, with different aspects of patterning being initiated at different disc sizes
          (<a href="#fig1" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 1C</a>).
          Finally, a third hypothesis is that ecdysone regulates the growth and patterning of the
          wing discs independently, and that each process responds in a qualitatively and
          quantitatively different manner to ecdysone <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib53"><span>53</span><span>Mirth and
                Shingleton</span><span>2019</span></a></cite>. As an example of this, we might see
          that growth rates increase in a graded response to increasing ecdysone while patterning
          shows threshold responses, or vice versa. If this were the case, we would expect that
          growth and the progression of pattern would be uncoupled over time (<a href="#fig1"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 1D</a>).</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Here, we test these hypotheses
          of whether and how ecdysone co-regulates plastic growth and robust pattern in wing
          imaginal discs in <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">D.
            melanogaster</em>. We blocked the production of ecdysone by genetically ablating the PG
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib36"><span>36</span><span>Herboso et al.</span><span>2015</span></a></cite>
          and quantified the effects on growth and patterning rates throughout the third instar. We
          then manipulated the rate of ecdysone synthesis by up- or down-regulating the activity of
          the insulin-signalling pathway in the PG <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib49"><span>49</span><span>Mirth et
                  al.</span><span>2005</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib41"><span>41</span><span>Koyama
                  et al.</span><span>2014</span></a></cite></span> to test how this alters the
          relationship between disc size and disc pattern. Finally, we tested our hypotheses about
          how a single steroid can regulate both plastic growth and robust patterning by conducting
          dose-response experiments under two nutritional conditions. These studies provide a
          foundation for a broader understanding of how developmental hormones coordinate both
          plastic and robust responses across varying environmental conditions during animal
          development.</p>
        <h2 itemscope="" itemtype="http://schema.stenci.la/Heading" id="results">Results</h2>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="ecdysone-is-necessary-for-the-progression-of-growth-and-patterning">Ecdysone is
          necessary for the progression of growth and patterning</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To understand how ecdysone
          affects the dynamics of growth and patterning, we needed to be able to precisely
          manipulate ecdysone concentrations. For this reason, we made use of a technique we
          developed previously to genetically ablate the PGs (referred to as PGX) <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib36"><span>36</span><span>Herboso et
                al.</span><span>2015</span></a></cite>. This technique pairs the
          temperature-sensitive repressor of GAL4, GAL80<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">ts</sup>, with a PG-specific GAL4 (<em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">phm-GAL4</em>) to drive an
          apoptosis-inducing gene (<em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">UAS-GRIM</em>). GAL80<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">ts</sup> is active at 17°C, where it
          represses GAL4 action, but inactive above 25°C, which allows <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">phm-GAL4</em> to drive expression of <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">UAS-GRIM</em> and ablate the PG
          <span itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib45"><span>45</span><span>McGuire
                  et al.</span><span>2003</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib46"><span>46</span><span>McGuire
                  et al.</span><span>2004</span></a></cite></span>. Because ecdysone is required at
          every moult, we reared larvae from egg to the third larval instar (L3) at 17°C to repress
          GAL4, then shifted the larvae to 29°C at the moult to the third instar to generate PGX
          larvae.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">PGX larvae had significantly
          reduced ecdysteroid titres than control genotypes (<a href="#fig2s1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 2—figure supplement 1</a>). This method
          of reducing ecdysteroid concentration in the larvae allows us to examine how reducing
          ecdysone titres affects disc size and pattern in third-instar wing imaginal discs and
          manipulate ecdysone concentrations by adding it back in specific concentrations to the
          food <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib36"><span>36</span><span>Herboso et al.</span><span>2015</span></a></cite>.
          For simplicity, all the data from the two control strains (either the <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">phm-GAL4; GAL80ts</em> or <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">UAS-GRIM</em> parental strain crossed to
          w<sup itemscope="" itemtype="http://schema.stenci.la/Superscript"><span
              data-itemtype="http://schema.org/Number">1118</span></sup>) were pooled in all
          analyses.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Insect wing discs show damped
          exponential, or fast-then-slow, growth dynamics <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib74"><span>74</span><span>Shingleton et
                  al.</span><span>2008</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib57"><span>57</span><span>Nijhout
                  and Wheeler</span><span>1996</span></a></cite></span>. These types of growth
          dynamics have frequently been modelled using a Gompertz function, which assumes that
          exponential growth rates slow down with time. The growth of wing discs from control and
          PGX larvae shows the same pattern, with a Gompertz function providing a significantly
          better fit to the relationship between log disc size and time than a linear function
          (ANOVA, linear vs. Gompertz model, n &gt; 93, <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">F</em> &gt; 65, p&lt;0.001 for discs from
          both PGX and control larvae). Growth of the discs, however, followed a significantly
          different trajectory in PGX versus control larvae (<a href="#fig2" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 2</a>, <a href="#supp1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 1a</a>). In control larvae,
          discs continue to grow until 42 hr after ecdysis to the third instar (AEL3) when the
          larvae pupariate. In contrast, the wing imaginal discs of the PGX larvae grow at slower
          rates between 0 and 25 hr AEL3 (<a href="#fig2" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 2</a>, <a href="#supp1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>a) and stop growing at
          approximately 25 hr AEL3 at a significantly smaller size. This is despite the fact that
          PGX larvae do not pupariate, and so disc growth is not truncated by metamorphosis.</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig2" title="Figure 2.">
          <label data-itemprop="label">Figure 2.</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 28
#&#39; @height 20

# Packages
library(&quot;ggplot2&quot;)
library(&quot;lme4&quot;)
library(&quot;nlme&quot;)
library(&quot;deSolve&quot;)
library(&quot;MASS&quot;)
library(&quot;gdata&quot;)
library(&quot;gtools&quot;)
library(&quot;plyr&quot;)
library(&quot;dplyr&quot;)
library(&quot;nlstools&quot;)
library(&quot;tibble&quot;)
library(&quot;gridExtra&quot;)
library(&quot;grid&quot;)
library(&quot;car&quot;)
library(&quot;mosaic&quot;)
library(&quot;cowplot&quot;)
library(&quot;readr&quot;)
library(&quot;emmeans&quot;)
library(&quot;multcomp&quot;)
library(&quot;multcompView&quot;)
library(&quot;broom&quot;)
library(&quot;drc&quot;)

# Import data
PGXdata &lt;- read_csv(&quot;PGXdata.csv&quot;, col_types = cols(X1 = col_skip()))
PGXrescue &lt;- read_csv(&quot;PGXrescue.csv&quot;, col_types = cols(X1 = col_skip()))
PGX.starved &lt;- read_csv(&quot;PGX.starved.csv&quot;, col_types = cols(X1 = col_skip()))
Pattern_Size&lt;-read_csv(&quot;Pattern_Size.csv&quot;, col_types = cols(X1 = col_skip()))
PGX_E&lt;-read_csv(&quot;PGX_E.csv&quot;, col_types = cols(X1 = col_skip()))
ecdysone.titres &lt;- read_csv(&quot;EcdysoneQuantifications.csv&quot;, col_types = cols(X1 = col_skip()))


# We first explore how ablation of the PG affects growth and patterning of the wing imaginal discs. We will pool the control data, and remove Sens (Senseless) data since this is from the same disc as the Ac (Achaete) data.
dt &lt;- PGXdata %&gt;% filter(gene.product != &quot;sens&quot;)  %&gt;% mutate(Group = derivedFactor(
						&quot;Control&quot;=(genotype == &quot;w_Grim&quot; | genotype == &quot;PG_w&quot;),
						&quot;Exp&quot;=(genotype == &quot;PGX&quot;),
						.method=&quot;first&quot;))

PGX.lm&lt;-lm(logdisc.area~timepoint, data=subset(dt, genotype==&quot;PGX&quot;))
PGX.nls&lt;- nls(logdisc.area ~ SSgompertz(timepoint, Asym, b2, b3), data=subset(dt, genotype==&quot;PGX&quot;))
#anova(PGX.nls,PGX.lm)
#coef(PGX.nls)
#confint2(PGX.nls)

control.lm&lt;-lm(logdisc.area~timepoint, data=subset(dt, genotype==&quot;w_Grim&quot; |genotype==&quot;PG_w&quot; ))
control.nls&lt;- nls(logdisc.area ~ SSgompertz(timepoint, Asym, b2, b3), data=subset(dt, genotype==&quot;w_Grim&quot;|genotype==&quot;PG_w&quot;))
#anova(control.nls,control.lm)
#coef(control.nls)
#confint2(control.nls)

PGX_all&lt;- nls(logdisc.area ~ SSgompertz(timepoint, Asym, b2, b3), data=dt,start = list(Asym = rep(10, 1), b2 = rep(0.1, 1), b3 = rep(0.9, 1)))
#coef(PGX_all)

PGX_group&lt;- nls(logdisc.area ~ SSgompertz(timepoint, Asym[Group], b2[Group], b3[Group]), data=dt,start = list(Asym = rep(10, 2), b2 = rep(0.1, 2), b3 = rep(0.9, 2)))
#coef(PGX_group)
#confint(PGX_group, level = 1-(0.05/1))
#anova(PGX_all,PGX_group)

#WHich Paramaters are Different?
PGX_group_dropAsym&lt;- nls(logdisc.area ~ SSgompertz(timepoint, Asym, b2[Group], b3[Group]), data=dt,start = list(Asym = rep(10, 1), b2 = rep(0.1, 2), b3 = rep(0.9, 2)))

PGX_group_dropb2&lt;- nls(logdisc.area ~ SSgompertz(timepoint, Asym[Group], b2, b3[Group]), data=dt,start = list(Asym = rep(10, 2), b2 = rep(0.1, 1), b3 = rep(0.9, 2)))

PGX_group_dropb3&lt;- nls(logdisc.area ~ SSgompertz(timepoint, Asym[Group], b2[Group], b3), data=dt,start = list(Asym = rep(10, 2), b2 = rep(0.1, 2), b3 = rep(0.9, 1)))

#anova(PGX_group,PGX_group_dropAsym)
#anova(PGX_group,PGX_group_dropb2)
#anova(PGX_group,PGX_group_dropb3)

# Plot
ggplot(data=dt,aes(x=timepoint,y=logdisc.area, color = Group))+
  xlab(&quot;Time (hours after L3 moult)&quot;)+
ylab(&quot;ln Disc Size (nm2)&quot;)+
theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=20), axis.title.y=element_text(size=20), 
        axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
 theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
 scale_y_continuous(breaks = c(9, 9.5, 10, 10.5, 11, 11.5))+
geom_smooth(method = &quot;nls&quot;, formula = y ~ SSgompertz(x, phi1, phi2, phi3), se = FALSE, size = 1)+
  geom_point(position = position_jitter(width = 0, height = 0.3), alpha = 0.5, size = 3)+
  #ggtitle(&quot;Figure 1&quot;)+
  #scale_color_brewer(palette = &quot;Set2&quot;, labels = c(&quot;Control&quot;, &quot;PGX&quot;))
  scale_colour_manual(values=c(&quot;grey50&quot;, &quot;#b2182b&quot;), labels = c(&quot;Control&quot;, &quot;PGX&quot;))+
  scale_fill_manual(values=c(&quot;grey50&quot;, &quot;#b2182b&quot;), labels = c(&quot;Control&quot;, &quot;PGX&quot;))</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h4 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="growth-rates-of-wing-discs-are-reduced-in-larvae-with-genetically-ablated-prothoracic-glands-pgx-versus-control-larvae">
              Growth rates of wing discs are reduced in larvae with genetically ablated prothoracic
              glands (PGX) versus control larvae.</h4>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Curves are Gompertz
              functions of disc size against time (hours after the third larval instar (L3) moult).
              Parameters for the curves are significantly different between PGX and control (<a
                href="#supp1" itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary
                file 1</a>a). Control genotypes are the pooled results from both parental controls
              (either the <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">phm-GAL4;
                GAL80ts,</em> or <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">UAS-GRIM</em> parental strain crossed to
              w<sup itemscope="" itemtype="http://schema.stenci.la/Superscript"><span
                  data-itemtype="http://schema.org/Number">1118</span></sup>). Each point represents
              the size of an individual wing disc. N<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">PGX</sub> = 95, N<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">Control</sub> = 125 across all time
              points.</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig2s1"
          title="Figure 2—figure supplement 1."><label data-itemprop="label">Figure 2—figure
            supplement 1.</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 28
#&#39; @height 20
# Titrating Ecdysone

## Ecdysone in Food and Hemolymph
#First calculate ecdysone levels as pg per mg of larvae or as pg per larvae
ecdysone.titres &lt;-ecdysone.titres %&gt;% mutate(pg_mg_larvae = Ecdysone.concentration.real/weight, pg_L3 = Ecdysone.concentration.real/sample)

ecdysone.titres &lt;- ecdysone.titres %&gt;% mutate(Group = derivedFactor(
         &quot;Control&quot; = (genotype == &quot;w_Grim&quot; |  genotype == &quot;PG_w&quot;),
         &quot;PGX&quot; = (genotype == &quot;PGX&quot;)))

#look at titres with 0 20E and fully fed

ecdysone.model.mg0&lt;-lm(pg_L3 ~ Group, data= subset(ecdysone.titres, D20E == 0 &amp; food == &quot;Fed&quot;)) 
#Anova(ecdysone.model.mg0)
#summary(ecdysone.model.mg0)

means.20Ecompare &lt;- emmeans(ecdysone.model.mg0, ~ Group)
#multcomp::cld(means.20Ecompare)

ggplot(data= subset(ecdysone.titres, D20E == 0 &amp; food == &quot;Fed&quot;), aes(x= Group, y= pg_L3, colour = Group, fill = Group))+ 
xlab(&quot;Genotype&quot;)+
ylab(&quot;Ecdysteroid titre \n (pg/larva)&quot;)+
theme_bw()+
theme(panel.grid=element_blank(), axis.title.x=element_text(size=24), axis.title.y=element_text(size=24), axis.text.y=element_text(size=20), axis.text.x=element_text(size=20), panel.background = element_rect(colour = &quot;black&quot;), legend.title=element_blank(), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=24))+ 
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+theme(strip.text.x = element_text(size = 16))+
 #scale_y_continuous(limits=c(10,28))+
 #scale_x_continuous(limits=c(1.4,2.2))+
scale_colour_manual(values=c(&quot;grey50&quot;, &quot;#b2182b&quot;))+
scale_fill_manual(values=c(&quot;grey50&quot;, &quot;#b2182b&quot;))+
geom_point(size=5, alpha=0.7)+
geom_violin(alpha = 0.5) +
geom_blank()</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h4 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="ecdysteroid-titres-in-genetically-ablated-prothoracic-glands-pgx-and-control-larvae">
              Ecdysteroid titres in genetically ablated prothoracic glands (PGX) and control larvae.
            </h4>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Newly ecdysed larvae were
              placed on sucrose/yeast diets. Ecdysteroid titres in control (phm&gt; + and +
              &gt;grim) are significantly higher ecdysteroid titres than PGX larvae, as determined
              by linear models and pairwise comparisons of the means (F-value<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">1, 13</sub> = 10.75, p-value=0.006,
              N<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">control</sub> = 10,
              N<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">PGX</sub> = 5). Data
              is plotted with violin plots, and the individual replicates (five per genotype) are
              included as points overlaying the violin plots.</p>
          </figcaption>
        </figure>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">We next explored how the loss
          of ecdysone affected the progression of wing patterning. We used the staging scheme that
          we previously devised in <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib64"><span>64</span><span>Oliveira et al.</span><span>2014</span></a></cite>
          to quantify the progression of wing disc patterning in PGX and control larvae. We selected
          two gene-products from this scheme, Achaete and Senseless, as they each progress through
          seven stages throughout the third instar. Further we can stain for both antigens in the
          same discs, which allowed us to compare disc size, Achaete stage, and Senseless stage in
          the same sample.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The progression of Achaete
          patterning was best fit by a Gompertz function for discs from both PGX and control larvae
          (ANOVA, linear versus Gompertz model, n &gt; 48, <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">F</em> &gt; 10.4, p=0.002) <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib64"><span>64</span><span>Oliveira et al.</span><span>2014</span></a></cite>
          and was significantly affected by reduced ecdysone titres in PGX larvae. In control
          larvae, the wing discs progressed to Achaete stage 6 or 7 out of seven stages by 42 hr
          AEL3, while in PGX larvae, discs of the same age had not passed Achaete stage 3, and had
          not matured past Achaete stage 5 by 92 hr AEL3 (<a href="#fig3" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 3A</a>, <a href="#supp1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>b). The progression of
          Senseless patterning was best fit by a linear model, but again was significantly affected
          by reduced ecdysone titres. In control larvae, most discs had progressed to Senseless
          stage 6 out of seven stages by 42 hr AEL3, while no disc progressed past Senseless stage 2
          by 92 hr AEL3 (<a href="#fig3" itemscope="" itemtype="http://schema.stenci.la/Link">Figure
            3B</a>, <a href="#supp1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>c).</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig3" title="Figure 3.">
          <label data-itemprop="label">Figure 3.</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 28
#&#39; @height 20
# Next we will look at how patterning of Achaete and Senseless is affected by ablation of the PG. We will look at Achaete patterning first, then Senseless patterning

dt &lt;- PGXdata %&gt;% filter(gene.product == &quot;ac&quot;) %&gt;% mutate(Group = derivedFactor(
						&quot;Control&quot;=(genotype == &quot;w_Grim&quot; | genotype == &quot;PG_w&quot;),
						&quot;Exp&quot;=(genotype == &quot;PGX&quot;),
						.method=&quot;first&quot;))

Controlachaete.lm &lt;- lm(gene.stage ~ timepoint, data = subset(dt, gene.product == &quot;ac&quot; &amp; Group==&quot;Control&quot;))
Controlachaete.nls = nls(gene.stage ~ SSgompertz(timepoint, Asym, b2, b3), data = subset(dt, gene.product == &quot;ac&quot;&amp; Group==&quot;Control&quot;))
#anova(Controlachaete.nls,Controlachaete.lm)

PGXachaete.lm &lt;- lm(gene.stage ~ timepoint, data = subset(dt, gene.product == &quot;ac&quot; &amp; Group==&quot;Exp&quot;))
PGXachaete.nls = nls(gene.stage ~ SSgompertz(timepoint, Asym, b2, b3), data = subset(dt, gene.product == &quot;ac&quot;&amp; Group==&quot;Exp&quot;))
#anova(PGXachaete.nls,PGXachaete.lm)

# Now we can test whether the Gompertz curve is significantly different between control and PGX larvae.

PGXAchaete.nls_single = nls(gene.stage ~ SSgompertz(timepoint, Asym, b2, b3), data = dt)

PGXAchaete.nls_group = nls(gene.stage ~ SSgompertz(timepoint, Asym[Group], b2[Group], b3[Group]), data = dt, start = list(Asym = rep(8, 2), b2 = rep(2, 2), b3 = rep(0.97, 2)))

#anova(PGXAchaete.nls_single, PGXAchaete.nls_group)
#coef(PGXAchaete.nls_group)
#confint2(PGXAchaete.nls_group)



# Which Parameter is Different?

PGXAchaete_group_dropAsym&lt;- nls(gene.stage ~ SSgompertz(timepoint, Asym, b2[Group], b3[Group]), data=dt,start = list(Asym = rep(4, 1), b2 = rep(1, 2), b3 = rep(0.9, 2)))

PGXAchaete_group_dropb2&lt;- nls(gene.stage ~ SSgompertz(timepoint, Asym[Group], b2, b3[Group]), data=dt,start = list(Asym = rep(4, 2), b2 = rep(1, 1), b3 = rep(0.9, 2)))

PGXAchaete_group_dropb3&lt;- nls(gene.stage ~ SSgompertz(timepoint, Asym[Group], b2[Group], b3), data=dt,start = list(Asym = rep(4, 2), b2 = rep(1, 2), b3 = rep(0.9, 1)))

#anova(PGXAchaete.nls_group,PGXAchaete_group_dropAsym)
#anova(PGXAchaete.nls_group,PGXAchaete_group_dropb2)
#anova(PGXAchaete.nls_group,PGXAchaete_group_dropb3)


# Now plotting the two curves, the difference is clear.

Figure_3A &lt;- ggplot(data = dt, aes(x = timepoint, y = gene.stage, color = Group, fill = Group))+ 
xlab(&quot;Time (hours after L3 moult)&quot;)+
ylab(&quot;Achaete Stage&quot;)+
theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=20), axis.title.y=element_text(size=20), 
        axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
 theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
 scale_y_continuous(breaks = c(1, 2, 3, 4, 5, 6, 7))+
geom_smooth(method = &quot;nls&quot;, formula = y ~ SSgompertz(x, phi1, phi2, phi3), se = FALSE, size = 1)+ 
  geom_point(position = position_jitter(width = 0, height = 0.3), alpha = 0.5, size = 3)+
#ggtitle(&quot;Figure 2A&quot;)+ 
#scale_color_brewer(palette = &quot;Set2&quot;, labels = c(&quot;Control&quot;, &quot;PGX&quot;))
  scale_colour_manual(values=c(&quot;grey50&quot;, &quot;#b2182b&quot;), labels = c(&quot;Control&quot;, &quot;PGX&quot;))+
  scale_fill_manual(values=c(&quot;grey20&quot;, &quot;#b2182b&quot;), labels = c(&quot;Control&quot;, &quot;PGX&quot;))


# Now we will do the same for Senseless patterning, which is best fit with a linear function. Indeed a Gompertz function cant be fit for the PGX data.

dt &lt;- PGXdata %&gt;% filter(gene.product == &quot;sens&quot;) %&gt;% mutate(Group = derivedFactor(
						&quot;Control&quot;=(genotype == &quot;w_Grim&quot; | genotype == &quot;PG_w&quot;),
						&quot;Exp&quot;=(genotype == &quot;PGX&quot;),
						.method=&quot;first&quot;))

PGXsens.lm&lt;- lm(gene.stage ~ timepoint, data = subset(dt, Group == &quot;Exp&quot;))
#PGXsens.nls = nls(gene.stage ~ SSgompertz(timepoint, Asym, b2, b3), data = subset(dt, Group == &quot;Exp&quot;))

# Wont fit

Controlsens.lm&lt;- lm(gene.stage ~ timepoint, data = subset(dt, Group == &quot;Control&quot;))
Controlsens.nls = nls(gene.stage ~ SSgompertz(timepoint, Asym, b2, b3), data = subset(dt, Group == &quot;Control&quot;))

#anova(Controlsens.nls,Controlsens.lm)

# We can fit a Gompertz function to the control data, and it provides a better fit, but to allow comparison between control and experimental we will use a linear function for both.

PGXSens.lm_group &lt;- lm(gene.stage ~ timepoint * Group, data = dt)
#summary(PGXSens.lm_group)
#coef(PGXSens.lm_group)
#confint(PGXSens.lm_group)
#Anova(PGXSens.lm_group, type=&quot;III&quot;)

# Now we can plot the data
Figure_3B &lt;- ggplot(data = dt, aes(x = timepoint, y = gene.stage, colour = Group, fill = Group))+ 
xlab(&quot;Time (hours after L3 moult)&quot;)+
ylab(&quot;Senseless Stage&quot;)+
theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=20), axis.title.y=element_text(size=20), 
        axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
 theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
 scale_y_continuous(breaks = c(1, 2, 3, 4, 5, 6, 7))+
  geom_point(position = position_jitter(width = 0, height = 0.3), alpha = 0.5, size = 3)+
geom_smooth(method = &quot;lm&quot;, formula = y ~ x, se = FALSE, size = 1)+ 
#ggtitle(&quot;Figure 2B&quot;)+ 
#scale_color_brewer(palette = &quot;Set2&quot;, labels = c(&quot;Control&quot;, &quot;PGX&quot;))
  scale_colour_manual(values=c(&quot;grey50&quot;, &quot;#b2182b&quot;), labels = c(&quot;Control&quot;, &quot;PGX&quot;))+
  scale_fill_manual(values=c(&quot;grey50&quot;, &quot;#b2182b&quot;), labels = c(&quot;Control&quot;, &quot;PGX&quot;))

# Plot 3A and B
Figure_3ANoL &lt;- Figure_3A + theme(legend.position=&#39;none&#39;,axis.title.x=element_text(size=15), axis.title.y=element_text(size=15),axis.text.y=element_text(size=10), axis.text.x=element_text(size=10))
Figure_3BNoL &lt;- Figure_3B + theme(legend.position=&#39;none&#39;,axis.title.x=element_text(size=15), axis.title.y=element_text(size=15),axis.text.y=element_text(size=10), axis.text.x=element_text(size=10))
legend &lt;- get_legend(Figure_3A)
ggdraw(plot_grid(plot_grid(Figure_3ANoL, Figure_3BNoL, ncol=2, align=&#39;h&#39;),
                 plot_grid(NULL, legend, ncol=1), rel_widths=c(1, 0.2))) +
  draw_plot_label(c(&quot;A&quot;, &quot;B&quot;), c(0, 0.41), c(1, 1), size = 20)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h4 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="achaete-and-senseless-patterning-of-wing-discs-is-delayed-in-larvae-with-genetically-ablated-prothoracic-glands-pgx-versus-control-larvae">
              Achaete and Senseless patterning of wing discs is delayed in larvae with genetically
              ablated prothoracic glands (PGX) versus control larvae.</h4>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) Curves are Gompertz functions
              of Achaete stage against time (hours after the third instar (L3) moult). Parameters
              for the curves are significantly different between PGX and control (<a href="#supp1"
                itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>b).
              (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>) Lines are
              linear regression of Senseless stage against time (hours after the L3 moult).
              Parameters for the lines are significantly different between PGX and control (<a
                href="#supp1" itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary
                file 1</a>c). Control genotypes are the pooled results from both parental controls
              (either the <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">phm-GAL4;
                GAL80ts,</em> or <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">UAS-GRIM</em> parental strain crossed to
              w<sup itemscope="" itemtype="http://schema.stenci.la/Superscript"><span
                  data-itemtype="http://schema.org/Number">1118</span></sup>). For Achaete: N<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">PGX</sub> = 50, N<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">Control</sub> = 61, for
              Senseless: N<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">PGX</sub> =
              52, N<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">Control</sub> = 54
              across all time points.</p>
          </figcaption>
        </figure>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">We found no evidence of
          temporal separation between wing disc growth and the progression of pattern (compare <a
            href="#fig2" itemscope="" itemtype="http://schema.stenci.la/Link">Figures 2</a> and <a
            href="#fig3" itemscope="" itemtype="http://schema.stenci.la/Link"><span
              data-itemtype="http://schema.org/Number">3</span></a>). Both growth and patterning
          progressed at steady rates throughout most of the third instar in control larvae, slowing
          down only at the later stages of development. Thus, the hypothesis that ecdysone
          coordinates plastic growth with robust pattern by acting on each process at different
          times (<a href="#fig1" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 1B</a>;
          Hypothesis 1) is not correct.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To confirm that reduced
          ecdysone titres were responsible for delayed patterning, and not a systemic response to
          the death of the glands, we performed a second experiment where we added either the active
          form of ecdysone, 20-hydroxyecdysone (20E), or ethanol (the carrier) back to the food. PGX
          and control larvae were transferred onto either 20E or ethanol food and allowed to feed
          for 42 hr, after which we dissected their wing discs and examined their size and pattern.
          On the control (ethanol) food, wing discs from PGX larvae were smaller (<a href="#fig4"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 4A</a>, <a href="#supp1"
            itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>d) and
          showed reduced patterning for both Achaete (<a href="#fig4" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 4B</a>, <a href="#supp1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>d) and Senseless (<a
            href="#fig4" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 4C</a>, <a
            href="#supp1" itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file
            1</a>d) when compared to control genotypes. Adding 0.15 mg of 20E/mg food fully restored
          disc size, and Achaete and Senseless pattern, such that they were indistinguishable from
          control genotypes fed on 20E-treated food.</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig4" title="Figure 4.">
          <label data-itemprop="label">Figure 4.</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 28
#&#39; @height 20
# To demonstrate that it is the lack of ecysone that is suppressing growth and patterning rather than a systemic repsonse to death of the PG, we can add ecdysone back in.

dt &lt;- PGXrescue %&gt;% mutate(Group = derivedFactor(
						&quot;Control&quot;=(genotype == &quot;w_Grim&quot; | genotype == &quot;PG_w&quot;),
						&quot;Exp&quot;=(genotype == &quot;PGX&quot;),
						.method=&quot;first&quot;))


PGXrescueSize &lt;- lm(logdisc.area ~  Group * medium, data = dt)
#summary(PGXrescueSize)
#Anova(PGXrescueSize)
emmeans.size &lt;- emmeans(PGXrescueSize, ~ Group * medium)
#CLD(emmeans.size)

PGXrescueAchaete &lt;- lm(Ac.stage ~  Group * medium, data = dt)
#summary(PGXrescueAchaete)
#Anova(PGXrescueAchaete)
emmeans.Achaete &lt;- emmeans(PGXrescueAchaete, ~ Group * medium)
#CLD(emmeans.Achaete)

PGXrescueSens &lt;- lm(Sens.stage ~  Group * medium, data = dt)
#summary(PGXrescueSens)
#Anova(PGXrescueSens)
emmeans.Sens &lt;- emmeans(PGXrescueSens, ~ Group * medium)
#CLD(emmeans.Sens)

dt &lt;- PGXrescue %&gt;% mutate(Group = derivedFactor(
						&quot;Control&quot;=(genotype == &quot;w_Grim&quot; | genotype == &quot;PG_w&quot;),
						&quot;PGX&quot;=(genotype == &quot;PGX&quot;),
						.method=&quot;first&quot;))


#dt$Group&lt;-factor(dt$Group,level=c(&quot;Control&quot;, &quot;Exp&quot;))
dt$medium&lt;-factor(dt$medium,level=c(&quot;ethanol&quot;, &quot;20E&quot;))

detach(&quot;package:plyr&quot;, unload = TRUE)

#THE FOLLOWING CODE WILL RETURN AN ERROR IF plyr IS ATTACHED DUE TO A CONFLICT BETWEEN plyr AND dplyr

labeldat = dt %&gt;%
     group_by(Group, medium) %&gt;%
     summarize(ypos = max(logdisc.area) + .1 ) %&gt;% mutate(Group_med = paste(Group, medium, sep = &quot;_&quot;) , sig_level = derivedFactor(
       &quot;A&quot; = ((Group == &quot;Control&quot; &amp; medium  == &quot;ethanol&quot;) | (Group == &quot;PGX&quot; &amp; medium  == &quot;20E&quot;)),
       &quot;B&quot; = (Group == &quot;Control&quot; &amp; medium  == &quot;20E&quot;),
       &quot;C&quot; = (Group == &quot;PGX&quot; &amp; medium  == &quot;ethanol&quot;),
						.method=&quot;first&quot;))

Figure_4A&lt;-ggplot(aes(y = logdisc.area, x = Group, fill = medium), data = dt) +
   geom_violin(aes(fill=medium), alpha = 0.5, position = position_dodge(width = 0.7)) +
  geom_point(aes(colour = medium),position=position_jitterdodge(jitter.width = 0.1, dodge=0.7), size=1)+
ylab(&quot;ln Disc Size (nm2)&quot;)+
xlab(&quot;&quot;)+
theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=10), axis.text.x=element_text(face=&quot;italic&quot;,size=15), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(size=15))+
 theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+ 
  coord_cartesian(ylim=c(9.5,12))+
#ggtitle(&quot;Figure 3A&quot;)+ 
 scale_colour_manual(values=c(&quot;grey50&quot;, &quot;#1793bd&quot;), labels = c(&quot;Ethanol&quot;, &quot;Ecdysone&quot;))+
  scale_fill_manual(values=c(&quot;grey50&quot;, &quot;#1793bd&quot;), labels = c(&quot;Ethanol&quot;, &quot;Ecdysone&quot;))+
  geom_text(data = labeldat, aes(label = sig_level, y = ypos), position = position_dodge(width = .7), show.legend = FALSE )


labeldat &lt;- dt %&gt;% 
     group_by(Group, medium) %&gt;% summarise(ypos =  (max(Ac.stage) + 0.1)) %&gt;%
      mutate(Group_med = paste(Group, medium, sep = &quot;_&quot;) , sig_level = derivedFactor(
       &quot;A&quot; = ((Group == &quot;Control&quot; &amp; medium  == &quot;ethanol&quot;) | (Group == &quot;Control&quot; &amp; medium  == &quot;20E&quot;) | (Group == &quot;PGX&quot; &amp; medium  == &quot;20E&quot;)),
       &quot;B&quot; = (Group == &quot;PGX&quot; &amp; medium  == &quot;ethanol&quot;),
						.method=&quot;first&quot;))

Figure_4B&lt;-ggplot(aes(y = Ac.stage, x = Group, fill = medium), data = dt)  +
   geom_violin(aes(fill=medium), alpha = 0.5, position = position_dodge(width = 0.7)) +
  geom_point(aes(colour = medium),position=position_jitterdodge(jitter.width = 0.1, dodge=0.7), size=1)+
ylab(&quot;Achaete Stage&quot;)+
xlab(&quot;&quot;)+
theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=10), axis.text.x=element_text(face=&quot;italic&quot;,size=15), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(size=15))+
 theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+ 
  coord_cartesian(ylim=c(0.5,7.5))+
   scale_y_continuous(breaks = c(1, 2, 3, 4, 5, 6, 7))+
#ggtitle(&quot;Figure 3B&quot;)+ 
 scale_colour_manual(values=c(&quot;grey50&quot;, &quot;#1793bd&quot;), labels = c(&quot;Ethanol&quot;, &quot;Ecdysone&quot;))+
  scale_fill_manual(values=c(&quot;grey50&quot;, &quot;#1793bd&quot;), labels = c(&quot;Ethanol&quot;, &quot;Ecdysone&quot;))+
  geom_text(data = labeldat, aes(label = sig_level, y = c(7.3, 7.3, 5.3, 7.3)), position = position_dodge(width = .7), show.legend = FALSE )


labeldat &lt;- dt %&gt;% 
     group_by(Group, medium) %&gt;% summarise(ypos =  (max(Sens.stage) + 0.1)) %&gt;%
      mutate(Group_med = paste(Group, medium, sep = &quot;_&quot;) , sig_level = derivedFactor(
       &quot;A&quot; = (Group == &quot;Control&quot; &amp; medium  == &quot;ethanol&quot;),
       &quot;B&quot; = ((Group == &quot;Control&quot; &amp; medium  == &quot;20E&quot;) | (Group == &quot;PGX&quot; &amp; medium  == &quot;20E&quot;)),
       &quot;C&quot; = (Group == &quot;PGX&quot; &amp; medium  == &quot;ethanol&quot;),
						.method=&quot;first&quot;))

Figure_4C&lt;-ggplot(aes(y = Sens.stage, x = Group, fill = medium), data = dt)  +
   geom_violin(aes(fill=medium), alpha = 0.5, position = position_dodge(width = 0.7)) +
  geom_point(aes(colour = medium),position=position_jitterdodge(jitter.width = 0.1, dodge=0.7), size=1)+
ylab(&quot;Senseless Stage&quot;)+
xlab(&quot;&quot;)+
theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=10), axis.text.x=element_text(face=&quot;italic&quot;,size=15), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(size=15))+
 theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
  coord_cartesian(ylim=c(0.5,7.5))+
   scale_y_continuous(breaks = c(1, 2, 3, 4, 5, 6, 7))+
#ggtitle(&quot;Figure 3C&quot;)+ 
 scale_colour_manual(values=c(&quot;grey50&quot;, &quot;#1793bd&quot;), labels = c(&quot;Ethanol&quot;, &quot;Ecdysone&quot;))+
  scale_fill_manual(values=c(&quot;grey50&quot;, &quot;#1793bd&quot;), labels = c(&quot;Ethanol&quot;, &quot;Ecdysone&quot;))+
  geom_text(data = labeldat, aes(label = sig_level, y = c(7.3, 7.3, 2.3, 7.3)), position = position_dodge(width = .7), show.legend = FALSE )

Figure_4ANoL &lt;- Figure_4A + theme(legend.position=&#39;none&#39;)
Figure_4BNoL &lt;- Figure_4B + theme(legend.position=&#39;none&#39;)
Figure_4CNoL &lt;- Figure_4C + theme(legend.position=&#39;none&#39;)
legend &lt;- get_legend(Figure_4A)
ggdraw() +
  draw_plot(Figure_4ANoL, 0.05, 0.5, 0.45, 0.5) +
  draw_plot(Figure_4BNoL, 0.05, 0, 0.45, 0.5) +
  draw_plot(Figure_4CNoL, 0.55, 0, 0.45, 0.5) +
  draw_plot(legend, 0.5, 0.5, 0.45, 0.5) +
  draw_plot_label(c(&quot;A&quot;, &quot;B&quot;, &quot;C&quot;), c(0, 0, 0.5), c(1, 0.5, 0.5), size = 20)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h4 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="supplementing-genetically-ablated-prothoracic-gland-pgx-larvae-with-20-hydroxyecdysone-20e-rescues-wing-disc-growth-a-and-achaete-b-and-senseless-c-patterning">
              Supplementing genetically ablated prothoracic gland (PGX) larvae with
              20-hydroxyecdysone (20E) rescues wing disc growth (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>), and Achaete (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>) and Senseless
              (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">C</strong>)
              patterning.</h4>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Both the control and PGX
              larvae were exposed to 20E-treated food (0.15 mg/mg of food) or ethanol-treated food
              (which contains the same volume of ethanol) at 0 hr after the third instar moult. Wing
              discs were removed at 42 hr after the third instar moult. Control genotypes are the
              pooled results from both parental controls (either the <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">phm-GAL4; GAL80ts,</em> or <em
                itemscope="" itemtype="http://schema.stenci.la/Emphasis">UAS-GRIM</em> parental
              strain crossed to w<sup itemscope=""
                itemtype="http://schema.stenci.la/Superscript"><span
                  data-itemtype="http://schema.org/Number">1118</span></sup>). Treatments marked
              with different letters are significantly different (Tukey’s HSD, p&lt;0.05, for ANOVA
              see <a href="#supp1" itemscope=""
                itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>d). Data were
              plotted using violin plots with individual wing discs displayed over the plots. N<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">PGX + ethanol</sub> = 21,
              N<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">PGX + 20E</sub> = 23,
              N<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">Control +
                ethanol</sub> = 43, N<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">Control + 20E</sub> = 42.</p>
          </figcaption>
        </figure>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Collectively, these data
          indicate that ecdysone is necessary for the normal progression of growth and patterning in
          wing imaginal discs. The loss of ecdysone has a more potent effect on patterning, however,
          which is effectively shutdown in PGX larvae, than on disc growth, which continues, albeit
          at a slower rate, for the first 24 hr of the third instar in PGX larvae.</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="ecdysone-rescues-patterning-and-some-growth-in-wing-discs-of-yeast-starved-larvae">
          Ecdysone rescues patterning and some growth in wing discs of yeast-starved larvae</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The observation that ecdysone
          is necessary to drive both normal growth and patterning suggests that it may play a role
          in coordinating growth and patterning across environmental conditions. However, to do so
          it must lie downstream of the physiological mechanisms that sense and respond to
          environmental change. As discussed above, ecdysone synthesis is regulated by the activity
          of the insulin-signalling pathway, which is in turn regulated by nutrition. Starving
          larvae of yeast early in the third instar both suppress insulin signalling and inhibit
          growth and patterning of organs <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib50"><span>50</span><span>Mirth et
                  al.</span><span>2009</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib47"><span>47</span><span>Mendes
                  and Mirth</span><span>2016</span></a></cite></span>. We explored whether ecdysone
          was able to rescue some of this inhibition by transferring larvae immediately after the
          moult to 1% sucrose food that contained either 20E or ethanol and comparing their growth
          and patterning after 24 hr to wing discs from larvae fed on normal food. Both the PGX and
          control genotype failed to grow and pattern on the 1% sucrose with ethanol (<a
            href="#fig5" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 5A–C</a>, <a
            href="#supp1" itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file
            1</a>e). Adding 20E to the 1% sucrose food rescued Achaete and Senseless patterning in
          both the control and the PGX larvae to levels seen in fed controls (<a href="#fig5"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 5B</a>, <a href="#supp1"
            itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>e). 20E
          also partially rescued disc growth in PGX larvae, although not to the levels of the fed
          controls (<a href="#fig5" itemscope="" itemtype="http://schema.stenci.la/Link">Figure
            5A</a>). Collectively, these data suggest that the effect of nutrition on growth and
          patterning is at least partially mediated through ecdysone.</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig5" title="Figure 5.">
          <label data-itemprop="label">Figure 5.</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 28
#&#39; @height 20
dt &lt;- PGX.starved %&gt;% mutate(Group = derivedFactor(
						&quot;Control&quot;=(genotype == &quot;w_Grim&quot; | genotype == &quot;PG_w&quot;),
						&quot;Exp&quot;=(genotype == &quot;PGX&quot;),
						.method=&quot;first&quot;))



PGXStarvedSize &lt;- lm(logdisc.area ~  Group * medium, data = subset(dt, gene.product == &quot;ac&quot;))
#summary(PGXStarvedSize)
#Anova(PGXStarvedSize, type=&quot;III&quot;)
emmeans.size &lt;- emmeans(PGXStarvedSize, ~ Group * medium)
#CLD(emmeans.size)

PGXStarvedAchaete &lt;- lm(gene.stage ~  Group * medium, data = subset(dt, gene.product == &quot;ac&quot;))
#summary(PGXStarvedAchaete)
emmeans.Ac &lt;- emmeans(PGXStarvedAchaete, ~ Group * medium)
#CLD(emmeans.Ac)

PGXStarvedSens &lt;-lm(gene.stage ~  Group * medium, data = subset(dt, gene.product == &quot;sens&quot;))
#summary(PGXStarvedSens)
#Anova(PGXStarvedSens, type=&quot;III&quot;)
emmeans.Sens &lt;- emmeans(PGXStarvedSens, ~ Group * medium)
#CLD(emmeans.Sens)

dt &lt;- PGX.starved %&gt;% mutate(Group = derivedFactor(
						&quot;Control&quot;=(genotype == &quot;w_Grim&quot; | genotype == &quot;PG_w&quot;),
						&quot;PGX&quot;=(genotype == &quot;PGX&quot;),
						.method=&quot;first&quot;))



dtA&lt;-subset(dt, gene.product==&quot;ac&quot;)


 
labeldat = dtA %&gt;%
     group_by(Group, medium) %&gt;%
     summarize(ypos = max(logdisc.area) + .1 ) %&gt;% mutate(Group_med = paste(Group, medium, sep = &quot;_&quot;) , sig_level = derivedFactor(
       &quot;A&quot; = ((Group == &quot;Control&quot; &amp; medium  == &quot;1ethanol&quot;) | (Group == &quot;PGX&quot; &amp; medium  == &quot;1ethanol&quot;)),
       &quot;B&quot; = (Group == &quot;Control&quot; &amp; medium  == &quot;20E&quot;),
       &quot;C&quot; = ((Group == &quot;PGX&quot; &amp; medium  == &quot;20E&quot;) | (Group == &quot;PGX&quot; &amp; medium  == &quot;normal.food&quot;)),
       &quot;D&quot; = (Group == &quot;Control&quot; &amp; medium  == &quot;normal.food&quot;),
						.method=&quot;first&quot;))

Figure_5A&lt;-ggplot(aes(y = logdisc.area, x = Group, fill = medium), data = dtA)+
  geom_violin(aes(fill=medium), alpha = 0.5, position = position_dodge(width = 0.6)) +
  geom_point(aes(colour = medium),position=position_jitterdodge(jitter.width = 0.1, dodge=0.6), size=1)+
ylab(&quot;ln Disc Size (nm2)&quot;)+
xlab(&quot;&quot;)+
theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=10), axis.text.x=element_text(face=&quot;italic&quot;,size=15), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(size=15))+
 theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+ 
  coord_cartesian(ylim=c(8.5,11.5))+
#ggtitle(&quot;Figure 4A&quot;)+ 
scale_colour_manual(values=c(&quot;#a6e1f5&quot;, &quot;#1793bd&quot;, &quot;grey50&quot;), labels = c(&quot;Starved + Ethanol&quot;, &quot;Starved + Ecdysone&quot;, &quot;Fed&quot;))+
  scale_fill_manual(values=c(&quot;#a6e1f5&quot;, &quot;#1793bd&quot;, &quot;grey50&quot;), labels = c(&quot;Starved + Ethanol&quot;, &quot;Starved + Ecdysone&quot;, &quot;Fed&quot;))+
  geom_text(data = labeldat, aes(label = sig_level, y = ypos), position = position_dodge(width = .6), show.legend = FALSE )

labeldat &lt;- dtA %&gt;% 
     group_by(Group, medium) %&gt;% summarise(ypos =  (max(gene.stage) + 0.2)) %&gt;%
      mutate(Group_med = paste(Group, medium, sep = &quot;_&quot;) , sig_level = derivedFactor(
       &quot;A&quot; = ((Group == &quot;Control&quot; &amp; medium  == &quot;1ethanol&quot;) | (Group == &quot;PGX&quot; &amp; medium  == &quot;1ethanol&quot;)),
       &quot;B&quot; = (Group == &quot;PGX&quot; &amp; medium  == &quot;normal.food&quot;),
       &quot;C&quot; = (Group == &quot;Control&quot; &amp; medium  == &quot;20E&quot;),
       &quot;CD&quot; = (Group == &quot;Control&quot; &amp; medium  == &quot;normal.food&quot;),
       &quot;D&quot; = (Group == &quot;PGX&quot; &amp; medium  == &quot;20E&quot;),
						.method=&quot;first&quot;))

Figure_5B&lt;-ggplot(aes(y = gene.stage, x = Group, fill = medium), data = dtA)   +
  geom_violin(aes(fill=medium), alpha = 0.5, position = position_dodge(width = 0.6)) +
  geom_point(aes(colour = medium),position=position_jitterdodge(jitter.width = 0.1, dodge=0.6), size=1)+
ylab(&quot;Achaete Stage&quot;)+
xlab(&quot;&quot;)+
theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=10), axis.text.x=element_text(face=&quot;italic&quot;,size=15), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(size=15))+
 theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
  coord_cartesian(ylim=c(0.5,7))+
  scale_y_continuous(breaks = c(1, 2, 3, 4, 5, 6, 7))+
#ggtitle(&quot;Figure 4B&quot;)+ 
scale_colour_manual(values=c(&quot;#a6e1f5&quot;, &quot;#1793bd&quot;, &quot;grey50&quot;), labels = c(&quot;Starved + Ethanol&quot;, &quot;Starved + Ecdysone&quot;, &quot;Fed&quot;))+
  scale_fill_manual(values=c(&quot;#a6e1f5&quot;, &quot;#1793bd&quot;, &quot;grey50&quot;), labels = c(&quot;Starved + Ethanol&quot;, &quot;Starved + Ecdysone&quot;, &quot;Fed&quot;))+
  geom_text(data = labeldat, aes(label = sig_level, y = ypos), position = position_dodge(width = .6), show.legend = FALSE )

dtS&lt;-subset(dt, gene.product==&quot;sens&quot;)

labeldat &lt;- dtS %&gt;% 
     group_by(Group, medium) %&gt;% summarise(ypos =  (max(gene.stage) + 0.2)) %&gt;%
      mutate(Group_med = paste(Group, medium, sep = &quot;_&quot;) , sig_level = derivedFactor(
       &quot;A&quot; = ((Group == &quot;Control&quot; &amp; medium  == &quot;1ethanol&quot;) | (Group == &quot;PGX&quot; &amp; medium  == &quot;1ethanol&quot;) | (Group == &quot;PGX&quot; &amp; medium  == &quot;normal.food&quot;)),
       &quot;B&quot; = (Group == &quot;Control&quot; &amp; medium  == &quot;20E&quot;),
       &quot;C&quot; = (Group == &quot;Control&quot; &amp; medium  == &quot;normal.food&quot;) | (Group == &quot;PGX&quot; &amp; medium  == &quot;20E&quot;),
						.method=&quot;first&quot;))


Figure_5C&lt;-ggplot(aes(y = gene.stage, x = Group, fill = medium), data = dtS)+
  geom_violin(aes(fill=medium), alpha = 0.5, position = position_dodge(width = 0.6)) +
  geom_point(aes(colour = medium),position=position_jitterdodge(jitter.width = 0.1, dodge=0.6), size=1)+
ylab(&quot;Senseless Stage&quot;)+
xlab(&quot;&quot;)+
theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=10), axis.text.x=element_text(face=&quot;italic&quot;,size=15), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(size=15))+
 theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
  coord_cartesian(ylim=c(0.5,6))+
 coord_cartesian(ylim=c(0.5,7))+
  scale_y_continuous(breaks = c(1, 2, 3, 4, 5, 6, 7))+
#ggtitle(&quot;Figure 4B&quot;)+ 
scale_colour_manual(values=c(&quot;#a6e1f5&quot;, &quot;#1793bd&quot;, &quot;grey50&quot;), labels = c(&quot;Starved\n+ Ethanol&quot;, &quot;Starved\n+ Ecdysone&quot;, &quot;Fed&quot;))+
  scale_fill_manual(values=c(&quot;#a6e1f5&quot;, &quot;#1793bd&quot;, &quot;grey50&quot;), labels = c(&quot;Starved\n+ Ethanol&quot;, &quot;Starved\n+ Ecdysone&quot;, &quot;Fed&quot;))+
  geom_text(data = labeldat, aes(label = sig_level, y = ypos), position = position_dodge(width = .6), show.legend = FALSE )

Figure_5ANoL &lt;- Figure_5A + theme(legend.position=&#39;none&#39;)
Figure_5BNoL &lt;- Figure_5B + theme(legend.position=&#39;none&#39;)
Figure_5CNoL &lt;- Figure_5C + theme(legend.position=&#39;none&#39;)
legend &lt;- get_legend(Figure_5A)
ggdraw() +
  draw_plot(Figure_5ANoL, 0.05, 0.5, 0.45, 0.5) +
  draw_plot(Figure_5BNoL, 0.05, 0, 0.45, 0.5) +
  draw_plot(Figure_5CNoL, 0.55, 0, 0.45, 0.5) +
  draw_plot(legend, 0.5, 0.5, 0.45, 0.5) +
  draw_plot_label(c(&quot;A&quot;, &quot;B&quot;, &quot;C&quot;), c(0, 0, 0.5), c(1, 0.5, 0.5), size = 20)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h4 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="supplementing-genetically-ablated-prothoracic-gland-pgx-larvae-with-20-hydroxyecdysone-20e-is-able-to-partially-rescue-the-effect-of-yeast-starvation-on-a-wing-discs-growth-and-fully-rescue-b-achaete-and-c-senseless-patterning">
              Supplementing genetically ablated prothoracic gland (PGX) larvae with
              20-hydroxyecdysone (20E) is able to partially rescue the effect of yeast starvation on
              (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">A</strong>) wing discs
              growth, and fully rescue (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">B</strong>) Achaete and (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">C</strong>) Senseless
              patterning.</h4>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Both the control and PGX
              larvae were exposed from 0 hr after the third instar moult to one of three food types:
              (1) starved + 20 E – starvation medium containing 1% sucrose and 1% agar laced with
              20E (0.15 mg/mg of food), (2) starved + ethanol – starvation medium treated with the
              same volume of ethanol, or (3) fed – normal fly food. Wing discs were removed at 24 hr
              after the third instar moult. Control genotypes are the pooled results from both
              parental controls (the <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">UAS-GRIM</em> parental strain crossed to
              w<sup itemscope="" itemtype="http://schema.stenci.la/Superscript"><span
                  data-itemtype="http://schema.org/Number">1118</span></sup>). Treatments marked
              with different letters are significantly different (Tukey’s HSD, p&lt;0.05, for ANOVA
              see <a href="#supp1" itemscope=""
                itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>e). Data were
              plotted using violin plots with individual wing discs displayed over the plots. N<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">PGX + starved -
                ethanol</sub> = 23, N<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">PGX + starved - 20E</sub> = 22, N<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">PGX + fed</sub> = 26,
              N<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">Control +
                starved-ethanol</sub> = 28, N<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">Control + starved-20E</sub> = 22, N<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">Control + fed</sub> = 27.
            </p>
          </figcaption>
        </figure>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">An important aspect of these
          data is that in PGX larvae either supplementing the 1% sucrose food with 20E or feeding
          them on normal food both rescued wing disc growth (<a href="#fig5" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 5A</a>), albeit incompletely. This
          suggests that nutrition can drive growth through mechanisms independent of ecdysone, and
          vice versa. In contrast, nutrition alone only marginally promoted Achaete and Senseless
          patterning in starved PGX larvae, while 20E alone completely restored patterning. Further,
          even early patterning did not progress in PGX larvae (<a href="#fig3" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 3</a>). Thus, the effect of nutrition on
          patterning appears to be wholly mediated by ecdysone, while the effect of nutrition on
          growth appears to be partially mediated by ecdysone and partially through another
          independent mechanism. Ecdysone-independent growth appears to occur early in the third
          larval instar, however, since disc growth in PGX and control larvae is more or less the
          same in the first 12 hr after ecdysis to L3 (<a href="#fig2" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 2</a>).</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="ecdysone-drives-growth-and-patterning-independently">Ecdysone drives growth and
          patterning independently</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The data above suggest a model
          of growth and patterning, where both ecdysone and nutrition can drive growth, but where
          patterning is driven by ecdysone. We next focused on exploring how ecdysone regulates both
          growth and patterning. Patterning genes, particularly morphogens, are known to regulate
          growth, so one hypothesis is that ecdysone promotes patterning, which in turn promotes the
          ecdysone-driven component of disc growth. A second related hypothesis is that
          ecdysone-driven growth is necessary to promote patterning. Under either of these
          hypotheses, because the mechanisms regulating patterning and growth are interdependent, we
          would expect that changes in ecdysone levels would not change the relationship between
          disc size and disc pattern. An alternative hypothesis, therefore, is that ecdysone
          promotes growth and patterning through at least partially independent mechanisms. Under
          this hypothesis, the relationship between size and patterning may change at different
          levels of ecdysone.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To distinguish between these
          two hypotheses, we increased or decreased the activity of the insulin-signalling pathway
          in the PG, which is known to increase or decrease the level of circulating ecdysone,
          respectively <span itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib7"><span>7</span><span>Caldwell et
                  al.</span><span>2005</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib41"><span>41</span><span>Koyama
                  et al.</span><span>2014</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib15"><span>15</span><span>Colombani et
                  al.</span><span>2005</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib49"><span>49</span><span>Mirth et
                  al.</span><span>2005</span></a></cite></span>. We then looked at how these
          manipulations affected the relationship between disc size and disc pattern, again focusing
          on Achaete and Senseless patterning. We increased insulin signalling in the PG by
          overexpressing InR (<em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">phm&gt;InR</em>) and reduced insulin
          signalling by overexpressing the negative regulator of insulin signalling PTEN (<em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">P0206&gt;PTEN</em>).</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">We found that a linear model is
          sufficient to capture the relationship between disc size and Achaete stage when we either
          increase (<em itemscope="" itemtype="http://schema.stenci.la/Emphasis">phm&gt;InR</em>:
          AIC<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">linear</sub> – AIC<sub
            itemscope="" itemtype="http://schema.stenci.la/Subscript">logistic</sub> = 22, ANOVA,
          <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">F</em><sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript">(25,27)</sub> = 1.71, p=0.2018) or decrease
          ecdysone synthesis rates (<em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">P0206&gt;PTEN</em>). Changing ecdysone
          levels, however, significantly changed the parameters of the linear model and altered the
          relationship between disc size and Achaete pattern. Specifically, increasing ecdysone
          level shifted the relationship so that later stages of Achaete patterning occurred in
          smaller discs (<a href="#fig6" itemscope="" itemtype="http://schema.stenci.la/Link">Figure
            6A</a>, <a href="#supp1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>f).</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig6" title="Figure 6.">
          <label data-itemprop="label">Figure 6.</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 28
#&#39; @height 20
# Relationship Between Size and Pattern
# We first need to set up the data tables

dt &lt;- Pattern_Size %&gt;% filter(gene.product == &quot;Ac&quot; |gene.product == &quot;Sens&quot;) %&gt;% mutate(umdata = 1000000 * disc.area, logdisc.area = log(umdata))

dt&lt;- dt %&gt;% filter(genotype == &quot;phm.InR&quot; | genotype == &quot;InRcontrol&quot;|genotype == &quot;P0206.PTEN&quot; | genotype == &quot;PTENcontrol&quot;)

dt &lt;- dt%&gt;% mutate(Group = derivedFactor(
						&quot;phm.InR&quot;=(genotype == &quot;phm.InR&quot;),
						&quot;Control&quot;=(genotype == &quot;InRcontrol&quot;| genotype == &quot;PTENcontrol&quot;),
						&quot;P0206.PTEN&quot;=(genotype == &quot;P0206.PTEN&quot;),
						.method=&quot;first&quot;))

dt$genotype&lt;-drop.levels(dt$genotype)

## Senseless
### Stats
# We first to test whether a threshold or linear function is the best fit for the data. The threshold function is a 4 parameter logistic. The parameterization we are using is A+(B-A)/(1+exp((xmid-input)/scal)), where A is minimum, B is maximum, xmid is the inflection point and scal is (1/scal), where scal is the logistic growth rate, or the steepness of the curve.

##all data
Allsens.rate &lt;- lm(gene.stage ~ logdisc.area, data = subset(dt, gene.product == &quot;Sens&quot;))
Allsens.threshold &lt;-  nls(gene.stage ~ SSfpl(logdisc.area, A,B,xmid,scal), data = subset(dt, gene.product == &quot;Sens&quot;))
#anova(Allsens.threshold, Allsens.rate)
#AIC(Allsens.threshold, Allsens.rate)

##InR Control
InRcontrolsens.rate &lt;- lm(gene.stage ~ logdisc.area, data = subset(dt, gene.product == &quot;Sens&quot; &amp; genotype == &quot;InRcontrol&quot;))
InRcontrolsens.threshold &lt;-  nls(gene.stage ~ SSfpl(logdisc.area, A,B,xmid,scal), data = subset(dt, gene.product == &quot;Sens&quot; &amp; genotype == &quot;InRcontrol&quot;))
#anova(InRcontrolsens.threshold, InRcontrolsens.rate)
#AIC(InRcontrolsens.threshold, InRcontrolsens.rate)

##phm&gt;InR
phmInRsens.rate &lt;- lm(gene.stage ~ logdisc.area, data = subset(dt, gene.product == &quot;Sens&quot; &amp; genotype == &quot;phm.InR&quot;))

phmInRsens.threshold &lt;-  nls(gene.stage ~ SSfpl(logdisc.area, A,B,xmid,scal), data = subset(dt, gene.product == &quot;Sens&quot; &amp; genotype == &quot;phm.InR&quot;))

#anova(phmInRsens.threshold, phmInRsens.rate)
#AIC(phmInRsens.threshold, phmInRsens.rate)

##PTEN Control
PTENcontrolsens.rate  &lt;- lm(gene.stage ~ logdisc.area, data = subset(dt, gene.product == &quot;Sens&quot; &amp; genotype == &quot;PTENcontrol&quot;))

PTENcontrolsens.threshold &lt;-  nls(gene.stage ~ SSfpl(logdisc.area, A,B,xmid,scal), data = subset(dt, gene.product == &quot;Sens&quot; &amp; genotype == &quot;PTENcontrol&quot;))

#anova(PTENcontrolsens.threshold, PTENcontrolsens.rate)
#AIC(PTENcontrolsens.threshold, PTENcontrolsens.rate)

##P0206&gt;PTEN
P0206PTENsens.rate  &lt;- lm(gene.stage ~ logdisc.area, data = subset(dt, gene.product == &quot;Sens&quot; &amp; genotype == &quot;P0206.PTEN&quot;))


P0206PTENsens.threshold &lt;-  nls(gene.stage ~ SSfpl(logdisc.area, A,B,xmid,scal), data = subset(dt, gene.product == &quot;Sens&quot; &amp; genotype == &quot;P0206.PTEN&quot;))


#anova(P0206PTENsens.threshold, P0206PTENsens.rate)
#AIC(P0206PTENsens.threshold, P0206PTENsens.rate)

#Senseless is best fit with a threshold function.

#Now we can test whether the parameters of the model change with changes in ecdysone.
#(For the parameters, 1 = phm.InR, 2 = Control, 3 = P0206.PTEN)

# Is there a difference between groups across all parameters?
Sens.threshold_single &lt;-  nls(gene.stage ~ SSfpl(logdisc.area, A,B,xmid,scal), data = subset(dt, gene.product == &quot;Sens&quot;),  start = list(A = rep(0.9, 1), B = rep(8, 1), xmid = rep(11, 1), scal=rep(0.5, 1)))
#summary(Sens.threshold_single)

model.drm3 &lt;- drm (gene.stage ~ logdisc.area, data = subset(dt, gene.product == &quot;Sens&quot;), fct = LL.4())

Sens.threshold_group &lt;-  nls(gene.stage ~ SSfpl(logdisc.area, A[Group],B[Group],xmid[Group],scal[Group]), data = subset(dt, gene.product == &quot;Sens&quot;),  start = list(A = rep(1, 3), B = rep(7, 3), xmid = rep(11, 3), scal=rep(0.3, 3)))
#coef(Sens.threshold_group)
#confint2(Sens.threshold_group, level=(1-(0.05/3)))

#anova(Sens.threshold_group,Sens.threshold_single)

#Which parameter?

Sens.threshold_groupdropA &lt;-  nls(gene.stage ~ SSfpl(logdisc.area, A,B[Group],xmid[Group],scal[Group]), data = subset(dt, gene.product == &quot;Sens&quot;),  start = list(A = rep(1, 1), B = rep(7, 3), xmid = rep(11, 3), scal=rep(0.3, 3)))

Sens.threshold_groupdropB &lt;-  nls(gene.stage ~ SSfpl(logdisc.area, A[Group],B,xmid[Group],scal[Group]), data = subset(dt, gene.product == &quot;Sens&quot;),  start = list(A = rep(1, 3), B = rep(7, 1), xmid = rep(11, 3), scal=rep(0.3, 3)))

Sens.threshold_groupdropxmid &lt;-  nls(gene.stage ~ SSfpl(logdisc.area, A[Group],B[Group],xmid,scal[Group]), data = subset(dt, gene.product == &quot;Sens&quot;),  start = list(A = rep(1, 3), B = rep(7, 3), xmid = rep(11, 1), scal=rep(0.3, 3)))

Sens.threshold_groupdropscal &lt;-  nls(gene.stage ~ SSfpl(logdisc.area, A[Group],B[Group],xmid[Group],scal), data = subset(dt, gene.product == &quot;Sens&quot;),  start = list(A = rep(1, 3), B = rep(7,3), xmid = rep(11, 3), scal=rep(0.3, 1)))

#anova(Sens.threshold_group,Sens.threshold_groupdropA)
#anova(Sens.threshold_group,Sens.threshold_groupdropB)
#anova(Sens.threshold_group,Sens.threshold_groupdropxmid)
#anova(Sens.threshold_group,Sens.threshold_groupdropscal)

Figure_6B &lt;- ggplot(data = subset(dt, gene.product == &quot;Sens&quot;), aes(x = logdisc.area, y = gene.stage, colour = Group, fill = Group))+ 
xlab(&quot;ln Disc Size (nm2)&quot;)+
ylab(&quot;Senseless Stage&quot;)+
theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=10), axis.text.x=element_text(size=10), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
   scale_y_continuous(limits = c(1,7.5),breaks = c(1, 2, 3, 4, 5, 6, 7))+
  scale_x_continuous(breaks = c(8, 9, 10, 11, 12))+
geom_point(size = 3, shape = 16, alpha = 0.5)+ 
  geom_smooth(method = &quot;nls&quot;, formula = y ~ SSfpl(x, A, B, xmid, scal), se = FALSE, size = 1)+
#ggtitle(&quot;Figure 5A&quot;)+ 
#scale_color_brewer(palette = &quot;Set2&quot;)
scale_colour_manual(values=c(&quot;#1793bd&quot;, &quot;grey50&quot;, &quot;#f0853e&quot;), labels = c(&quot;phm&gt;InR&quot;, &quot;Control&quot;, &quot;P0206&gt;PTEN&quot;))+
  scale_fill_manual(values=c(&quot;#1793bd&quot;, &quot;grey50&quot;, &quot;#f0853e&quot;), labels = c(&quot;phm&gt;InR&quot;, &quot;Control&quot;, &quot;P0206&gt;PTEN&quot;))

## Achaete
### Stats

#Now do the same with Achaete:
##all data
Allac.rate &lt;- lm(gene.stage ~ logdisc.area, data = subset(dt, gene.product == &quot;Ac&quot;))
Allac.threshold &lt;-  nls(gene.stage ~ SSfpl(logdisc.area, A,B,xmid,scal), data = subset(dt, gene.product == &quot;Ac&quot;))
#anova(Allac.threshold, Allac.rate)
#AIC(Allac.threshold, Allac.rate)

##InR Control
InRcontrolachaete.rate &lt;- lm(gene.stage ~ logdisc.area, data = subset(dt, gene.product == &quot;Ac&quot; &amp; genotype == &quot;InRcontrol&quot;))


InRcontrolachaete.threshold &lt;-  nls(gene.stage ~ SSfpl(logdisc.area, A,B,xmid,scal), data = subset(dt, gene.product == &quot;Ac&quot; &amp; genotype == &quot;InRcontrol&quot;))


#anova(InRcontrolachaete.threshold, InRcontrolachaete.rate)
#AIC(InRcontrolachaete.threshold, InRcontrolachaete.rate)

##phm&gt;InR
phmInRachaete.rate &lt;- lm(gene.stage ~ logdisc.area, data = subset(dt, gene.product == &quot;Ac&quot; &amp; genotype == &quot;phm.InR&quot;))


phmInRachaete.threshold &lt;-  nls(gene.stage ~ SSfpl(logdisc.area, A,B,xmid,scal), data = subset(dt, gene.product == &quot;Ac&quot; &amp; genotype == &quot;phm.InR&quot;))

#anova(phmInRachaete.threshold, phmInRachaete.rate)
#AIC(phmInRachaete.threshold, phmInRachaete.rate)


##PTEN Control
PTENcontrolachaete.rate  &lt;- lm(gene.stage ~ logdisc.area, data = subset(dt, gene.product == &quot;Ac&quot; &amp; genotype == &quot;PTENcontrol&quot;))


PTENcontrolachaete.threshold &lt;-  nls(gene.stage ~ SSfpl(logdisc.area, A,B,xmid,scal), data = subset(dt, gene.product == &quot;Ac&quot; &amp; genotype == &quot;PTENcontrol&quot;))


#anova(PTENcontrolachaete.threshold, PTENcontrolachaete.rate)
#AIC(PTENcontrolachaete.threshold, PTENcontrolachaete.rate)

##P0206&gt;PTEN
P0206PTENachaete.rate  &lt;- lm(gene.stage ~ logdisc.area, data = subset(dt, gene.product == &quot;Ac&quot; &amp; genotype == &quot;P0206.PTEN&quot;))

#P0206PTENachaete.threshold &lt;-  nls(gene.stage ~ SSfpl(logdisc.area, A,B,xmid,scal), data = subset(dt, gene.product == &quot;Ac&quot; &amp; genotype == &quot;P0206.PTEN&quot;),start = list(A = rep(0.2, 1), B = rep(8, 1), xmid = rep(11, 1), scal=rep(0.8, 1)))

#Won&#39;t resolve

#So the linear fit is better for the experimental flies but the threshold is better for the controls. In order to compare we need to use a linear fit.

### test for differences between genotypes

AchaeteLinear&lt;-lm(gene.stage ~ Group*logdisc.area, data = subset(dt, gene.product == &quot;Ac&quot;))
#Anova(AchaeteLinear, type=&quot;III&quot;)
#coef(AchaeteLinear)
#confint(AchaeteLinear, level=(1-0.05/2))


# Test for pairwise differences
phmInRvC&lt;-lm(gene.stage ~ logdisc.area + Group, data = subset(dt, gene.product == &quot;Ac&quot; &amp; Group!=&quot;P0206.PTEN&quot;))
#Anova(AchaeteLinear, type=&quot;II&quot;)

P0206.PTENRvC&lt;-lm(gene.stage ~ logdisc.area*Group, data = subset(dt, gene.product == &quot;Ac&quot; &amp; Group!=&quot;phm.InR&quot;))
#Anova(AchaeteLinear, type=&quot;II&quot;)

#So there is a difference between genotype, but not between control and phm&gt;InR

Figure_6A &lt;-  ggplot(data = subset(dt, gene.product == &quot;Ac&quot;), aes(x = logdisc.area, y = gene.stage, colour = Group, fill = Group))+ 
xlab(&quot;ln Disc Size (nm2)&quot;)+
ylab(&quot;Achaete Stage&quot;)+
theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=10), axis.text.x=element_text(size=10), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
    scale_y_continuous(limits = c(1,7.5),breaks = c(1, 2, 3, 4, 5, 6, 7))+
  scale_x_continuous(breaks = c(8, 9, 10, 11, 12))+
  geom_point(size = 3, shape = 16, alpha = 0.5)+
geom_smooth(method = &quot;lm&quot;, formula = y ~ x, se = FALSE, size = 1)+
#ggtitle(&quot;Figure 5B&quot;)+ 
scale_colour_manual(values=c(&quot;#1793bd&quot;, &quot;grey50&quot;, &quot;#f0853e&quot;), labels = c(&quot;phm&gt;InR&quot;, &quot;Control&quot;, &quot;P0206&gt;PTEN&quot;))+
  scale_fill_manual(values=c(&quot;#1793bd&quot;, &quot;grey50&quot;, &quot;#f0853e&quot;), labels = c(&quot;phm&gt;InR&quot;, &quot;Control&quot;, &quot;P0206&gt;PTEN&quot;))

Figure_6ANoL &lt;- Figure_6A + theme(legend.position=&#39;none&#39;)
Figure_6BNoL &lt;- Figure_6B + theme(legend.position=&#39;none&#39;)
legend &lt;- get_legend(Figure_6B)

ggdraw(plot_grid(plot_grid(Figure_6ANoL, Figure_6BNoL,ncol=2, align=&#39;v&#39;),
                 plot_grid(NULL, legend, ncol=1), rel_widths=c(1, 0.3))) +
  draw_plot_label(c(&quot;A&quot;, &quot;B&quot;), c(0, 0.39), c(1, 1), size = 20)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h4 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="changing-rate-of-ecdysteroid-synthesis-changes-the-relationship-between-disc-pattern-and-disc-size-throughout-the-third-instar-larval-stage">
              Changing rate of ecdysteroid synthesis changes the relationship between disc pattern
              and disc size throughout the third-instar larval stage.</h4>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) The relationship between
              Achaete stage and disc size was fitted with a linear regression, the parameters of
              which are significantly different between genotypes (<a href="#supp1" itemscope=""
                itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>f). (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>) The relationship
              between Senseless stage and disc size was fitted with a four-parameter logistic
              regression, the parameters of which are significantly different between genotypes (<a
                href="#supp1" itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary
                file 1</a>g). We staged third instar larvae from the onset of the moult to the
              formation of white prepupae. The length of this developmental interval varied across
              genotypes. For control genotypes, we sampled larvae at 0, 10, 20, 30, 48, and 51 (InR
              control)/53 (PTEN control) hr after third instar ecdysis (AL3E). For phm&gt;InR, we
              sampled larvae at 0, 10, 20, 29, 30, and 36 hr AL3E. For P0206&gt;PTEN, we sampled
              larvae at 0, 10, 20, 30, 40, 60, 73, and 80 hr AL3E. The number of discs sampled for
              each genotype and patterning gene was: for Achaete: N<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">phm&gt;InR</sub> = 29, N<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">Control</sub> = 99, N<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">P0206&gt;PTEN</sub> = 40,
              for Senseless: N<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">phm&gt;InR</sub> = 29, N<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">Control</sub> = 99, N<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">P0206&gt;PTEN</sub> = 41.
            </p>
          </figcaption>
        </figure>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The relationship between
          Senseless pattern and disc size is best fit using a four-parameter logistic (threshold)
          function, which provides a significantly better fit to the data than a linear function
          (AIC<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">linear</sub> – AIC<sub
            itemscope="" itemtype="http://schema.stenci.la/Subscript">logistic</sub> = 32.2; ANOVA,
          <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">F</em><sub itemscope=""
            itemtype="http://schema.stenci.la/Subscript">(44,46)</sub> = 25.8, p&lt;0.001). Changing
          ecdysone levels significantly changed the parameters of the logistic model and altered the
          relationship between disc size and Senseless pattern (<a href="#fig6" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 6B</a>, <a href="#supp1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>g). Again, increasing
          ecdysone level shifted the relationship so that later stages of Senseless patterning
          occurred in smaller discs. Collectively, these data support the hypothesis that ecdysone
          acts on growth and patterning at least partially independently (<a href="#fig1"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 1D</a>; Hypothesis 3), and
          that patterning is not regulated by wing disc size (<a href="#fig1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 1C</a>; Hypothesis 2).</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="ecdysone-regulates-disc-growth-and-disc-patterning-through-different-mechanisms">
          Ecdysone regulates disc growth and disc patterning through different mechanisms</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The data above support a model
          whereby environmental signals act through ecdysone to co-regulate growth and patterning,
          generating organs of variable size but invariable pattern. Further, growth is also
          regulated by an ecdysone-independent mechanism, enabling similar progressions of pattern
          across discs of different sizes. An added nuance, however, is that ecdysone levels are not
          constant throughout development. Rather, the ecdysone titre fluctuates through a series of
          peaks throughout the third larval instar and the dynamics of these fluctuations are
          environmentally sensitive <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib83"><span>83</span><span>Warren et al.</span><span>2006</span></a></cite>.
          To gain further insight into how ecdysone co-regulates plasticity and robustness, we
          therefore explored which aspects of ecdysone dynamics regulate growth and patterning.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Two characteristics of ecdysone
          fluctuations appear to be important with respect to growth and patterning. First, the
          timing of the ecdysone peaks set the pace of development, initiating key developmental
          transitions such as larval wandering and pupariation <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib41"><span>41</span><span>Koyama
                  et al.</span><span>2014</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib49"><span>49</span><span>Mirth et
                  al.</span><span>2005</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib83"><span>83</span><span>Warren
                  et al.</span><span>2006</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib71"><span>71</span><span>Riddiford et
                  al.</span><span>1993</span></a></cite></span>. Second, the basal levels of
          ecdysone appear to regulate the rate of body growth, with an increase in basal level
          leading to a reduction in body growth <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib7"><span>7</span><span>Caldwell
                  et al.</span><span>2005</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib36"><span>36</span><span>Herboso
                  et al.</span><span>2015</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib15"><span>15</span><span>Colombani et
                  al.</span><span>2005</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib49"><span>49</span><span>Mirth et
                  al.</span><span>2005</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib52"><span>52</span><span>Mirth et
                  al.</span><span>2014</span></a></cite></span>. While several studies, including
          this one, have established that disc growth is positively regulated by ecdysone <span
            itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib36"><span>36</span><span>Herboso
                  et al.</span><span>2015</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib25"><span>25</span><span>Dye et
                  al.</span><span>2017</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib66"><span>66</span><span>Parker
                  and Shingleton</span><span>2011</span></a></cite></span>, whether disc growth is
          driven by basal levels or peaks of ecdysone is unknown.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">There are a number of
          hypotheses as to how ecdysone levels may drive patterning and growth. One hypothesis is
          that patterning and ecdysone-regulated disc growth show threshold responses, which are
          initiated once ecdysone rises above a certain level. This would manifest as low patterning
          and growth rates when ecdysteroid titres were sub-threshold, and a sharp, switch-like
          increase in patterning and growth rates after threshold ecdysone concentrations was
          reached. Alternatively, both may show a graded response, with patterning and growth rates
          increasing continuously with increasing ecdysteroid titres. Finally, disc patterning may
          show one type of response to ecdysone, while disc growth may show another. Separating
          these hypotheses requires the ability to titrate levels of ecdysone.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To do this, we reared PGX
          larvae on standard food supplemented with a range of 20E concentrations (0, 6.25, 12.5,
          25, 50, and 100 ng of ecdysone/mg of food). However, as noted above, disc growth early in
          the third larval instar is only moderately affected by ablation of the PG, potentially
          obfuscating the effects of supplemental 20Esupplemental 20E<a href="#supp1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 1E</a>. In contrast, discs
          from starved PGX larvae show no growth or patterning without supplemental 20E.supplemental
          20E <a href="#supp1" itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary
            file 1E</a> We therefore also reared PGX larvae either on standard food or on 20%
          sucrose/1% agar medium (from hereon referred to as ‘starved’ larvae) supplemented with a
          range of 20E concentrations. For both control genotypes and PGX larvae, increasing the
          concentration of 20E in the food increased ecdysteroids titres in the larvae (<a
            href="#fig7s1" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 7—figure
            supplement 1</a>, <a href="#supp1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>h).</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To quantify the effects of 20E
          concentration in the wing disc growth, we dissected discs at 5 hr intervals starting
          immediately after the moult to the third instar (0 hr AL3E) to 20 hr AL3E. Because male
          and female larvae show differences in wing disc growth <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib80"><span>80</span><span>Testa et
                al.</span><span>2013</span></a></cite>, we separated the sexes in this experiment
          and focused our analysis on female wing discs.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">As before, in both PGX and
          control larvae, wing disc growth was suppressed by starvation (<a href="#fig7s2"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 7—figure supplement 2</a>,
          <a href="#supp1" itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file
            1</a>i). To explore how disc size changed over time with increasing 20E concentration,
          we modelled the data using a second-order polynomial regression against time after third
          instar ecdysis. Increasing the concentration of supplemental 20E <a href="#supp1"
            itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file 1E</a>increased
          the disc growth rate in starved PGX larvae (<a href="#fig7" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 7A</a>, <a href="#supp1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>j). In contrast,
          increasing 20E concentrations had no effect on disc growth rate in fed PGX larvae (<a
            href="#fig7s3" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 7—figure
            supplement 3</a>, <a href="#supp1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>j). This confirms that
          the effect of nutrition on growth masks the effect of 20E early in the third larval instar
          and supports that hypothesis that disc growth during this period is primarily regulated by
          nutrition and only moderately regulated by ecdysone <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib74"><span>74</span><span>Shingleton
                et al.</span><span>2008</span></a></cite>.</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig7" title="Figure 7.">
          <label data-itemprop="label">Figure 7.</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 28
#&#39; @height 15
## Growth with Ecdysone
### Stats
PGX_E &lt;- PGX_E %&gt;% mutate(Group = derivedFactor(
						&quot;Control&quot;=(genotype == &quot;w_Grim&quot; | genotype == &quot;PG_w&quot;),
						&quot;Exp&quot;=(genotype == &quot;PGX&quot;),
						.method=&quot;first&quot;))
PGX_E$d20Ecat&lt;-as.factor(PGX_E$d20Ecat)
PGX_E$food&lt;-as.factor(PGX_E$food)

dt&lt;-subset(PGX_E, food==&quot;starved&quot; )
growth.starvedLM &lt;- lm(ln.disc.area ~ poly(timepoint, 2, raw = FALSE) * d20Ecat, data = dt)
#Anova(growth.starvedLM, Type = &quot;III&quot;)
growth.trends &lt;- emtrends(growth.starvedLM, ~ d20Ecat, var = &quot;timepoint&quot;, max.degree = 1)
# multcomp::cld(growth.trends)

coefs.growthstarved &lt;- tidy(growth.trends)
coefs.growthstarved$d20Ecat&lt;-as.numeric(as.character(coefs.growthstarved$d20Ecat))
names(coefs.growthstarved)[1]&lt;-&quot;d20E&quot;

dt&lt;-PGX_E[PGX_E$genotype==&quot;PGX&quot; &amp; PGX_E$food==&quot;fed&quot;,]
# Anova(lm(ln.disc.area~d20E*poly(timepoint, degree=2), data=dt), type=&quot;III&quot;)

# Starved

Figure_7A&lt;-ggplot(data=subset(PGX_E, genotype==&quot;PGX&quot; &amp; food==&quot;starved&quot;), aes(x=timepoint,y=ln.disc.area, color=d20Ecat))+
   ylim(9.5,10.6)+
    xlab(&quot;Time (hours after L3 moult)&quot;)+
 ylab(&quot;ln Disc Size (nm2)&quot;)+
   ggtitle(&quot;Starved - PGX&quot;)+
   geom_smooth(method=&quot;lm&quot;,formula=y~poly(x, degree=2),se=F)+
   geom_point(size = 5, shape = 16, alpha = 0.5)+
   theme_bw()+
 theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15),
         axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
 theme(legend.title=element_blank())+
  theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
   scale_colour_brewer(type=&#39;seq&#39;, palette=&#39;RdGy&#39;, labels = c(&quot;0 - A&quot;,&quot;6.25 - AB&quot;,&quot;12.5 - ABC&quot;,&quot;25 - ABC&quot;,&quot;50 - C&quot;,&quot;100 - BC&quot;))

# extract coefficients from emtrends
model.drm1 &lt;- drm (timepoint.trend ~ d20E, data = coefs.growthstarved, fct = MM.3())
model.drm2 &lt;- drm (timepoint.trend ~ d20E, data = coefs.growthstarved, fct = LL.3())
model.drm3 &lt;- drm (timepoint.trend ~ d20E, data = coefs.growthstarved, fct = LL.4())

#AIC(model.drm1, model.drm2, model.drm3)
#BIC(model.drm1, model.drm2, model.drm3)


###Michaelis Menten is the best fit
mml &lt;- data.frame(d20E = seq(0, max(coefs.growthstarved$d20E), length.out = 100))
mml$linear_growth &lt;- predict(model.drm1, newdata = mml)


 Figure_7B&lt;-ggplot(data=coefs.growthstarved, aes(x=d20E,y=timepoint.trend))+
    xlab(&quot;20E Concentration in Food (ng/ml)&quot;)+
 ylab(&quot;Disc linear growth rate&quot;)+
   scale_y_continuous(limits = c(0.02, 0.06), breaks = c(0.02, 0.03, 0.04, 0.05, 0.06))+
   ggtitle(&quot;Starved - PGX&quot;)+
   geom_line(data = mml, aes(x = d20E, y = linear_growth), colour = &quot;black&quot;, size = 2)+
   geom_point(size = 5, shape = 16)+
   theme_bw()+
 theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
         axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
 theme(legend.title=element_blank())+
  theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))
 
 ggdraw() +
   draw_plot(Figure_7A, 0, 0, 0.66, 1) +
   draw_plot(Figure_7B, 0.66, 0, 0.33, 1) +
   draw_plot_label(c(&quot;A&quot;, &quot;B&quot;), c(0, 0.65), c(1, 1), size = 20)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h4 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="effect-of-supplemental-20-hydroxyecdysone-20e-supplementary-file-1eon-growth-of-the-wing-imaginal-disc-in-starved-genetically-ablated-prothoracic-gland-pgx-larvae">
              Effect of supplemental 20-hydroxyecdysone (20E) <a href="#supp1" itemscope=""
                itemtype="http://schema.stenci.la/Link">Supplementary file 1E</a>on growth of the
              wing imaginal disc in starved genetically ablated prothoracic gland (PGX) larvae.</h4>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Growth was modelled as <em
                itemscope="" itemtype="http://schema.stenci.la/Emphasis">S</em> = <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">E + T + T</em><sup itemscope=""
                itemtype="http://schema.stenci.la/Superscript"><span
                  data-itemtype="http://schema.org/Number">2</span></sup><em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">+ E * T + E * T</em><sup itemscope=""
                itemtype="http://schema.stenci.la/Superscript"><span
                  data-itemtype="http://schema.org/Number">2</span></sup>, where <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">S</em> = disc size, <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">E</em> = 20E concentration, and <em
                itemscope="" itemtype="http://schema.stenci.la/Emphasis">T</em> = disc age. (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">A</strong>) There was a
              significant effect of <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">E</em> on the linear growth rate of the
              wing imaginal discs (<a href="#supp1" itemscope=""
                itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>j). Each point
              corresponds to a wing disc, N<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">PGX – starved</sub> = 409 (63–72 discs
              were sampled per treatment across all time points). 20E treatments that do not share a
              letter (see legend) are significantly different in patterning rates as determined by
              post-hoc test on the slopes (<a href="#supp1" itemscope=""
                itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>j). (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>) The linear growth
              rate of the wing disc was extracted from the growth model for each concentration of
              20E and modelled using a three-parameter Michaelis–Menten equation: <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">y = c + (d-c)/(_1 </em>+ (b/x<em
                itemscope="" itemtype="http://schema.stenci.la/Emphasis">)), where _c</em> is <em
                itemscope="" itemtype="http://schema.stenci.la/Emphasis">y</em> at <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">x</em> = 0<em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">, d</em> = <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">y[max]</em>, and <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">b</em> is <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">x</em> where <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">y</em> is halfway between <em
                itemscope="" itemtype="http://schema.stenci.la/Emphasis">c</em> and <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">d</em>. Linear growth rate increases
              steadily with ecdysone concentration in the food up until 25 ng of 20E/ml of food,
              after which growth rate increases more slowly with increasing 20E concentration.</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig7s1"
          title="Figure 7—figure supplement 1."><label data-itemprop="label">Figure 7—figure
            supplement 1.</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 28
#&#39; @height 20
ggplot(data= ecdysone.titres, aes(x= D20E, y= pg_L3, colour = food, fill = food, shape = food, linetype = food))+ 
xlab(&quot;20E Concentration in Food (ng/ml)&quot;)+
ylab(&quot;Ecdysteroid titre \n (pg/larva)&quot;)+
theme_bw()+
theme(panel.grid=element_blank(), axis.title.x=element_text(size=24), axis.title.y=element_text(size=24), axis.text.y=element_text(size=20), axis.text.x=element_text(size=20), panel.background = element_rect(colour = &quot;black&quot;), legend.title=element_blank(), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=24))+ 
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+theme(strip.text.x = element_text(size = 16))+
 #scale_y_continuous(limits=c(10,28))+
 #scale_x_continuous(limits=c(1.4,2.2))+
scale_colour_manual(values=c(&quot;#4a4534&quot;, &quot;#a19670&quot;), labels = c(&quot;fed&quot;, &quot;starved&quot;))+
scale_fill_manual(values=c(&quot;#4a4534&quot;, &quot;#a19670&quot;), labels = c(&quot;fed&quot;, &quot;starved&quot;))+
geom_point(size=5, alpha=0.7)+
  scale_shape_manual(values=c(16, 1), labels = c(&quot;fed&quot;, &quot;starved&quot;))+
  scale_linetype_manual(values = c(1,2), labels = c(&quot;fed&quot;, &quot;starved&quot;))+
geom_smooth(method=&quot;lm&quot;, formula = y ~ poly(x, 2, raw=TRUE), se=FALSE, size = 1) +
facet_grid(. ~ Group)+
geom_blank()</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h4 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="the-effects-of-20-hydroxyecdysone-20e-concentration-in-the-food-on-ecdysteroid-titres-in-control-and-genetically-ablated-prothoracic-gland-pgx-larvae">
              The effects of 20-hydroxyecdysone (20E) concentration in the food on ecdysteroid
              titres in control and genetically ablated prothoracic gland (PGX) larvae.</h4>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Newly ecdysed larvae were
              placed on sucrose/yeast (fed) or 20% sucrose/1% agar (starved) diets supplemented with
              a range of 20E concentrations for 20 hr. They were then transferred to the same diet
              without 20E and dyed with blue food colouring for 2 hr to eliminate residual 20E in
              the gut. Ecdysteroid titres in fed and starved control (phm&gt; + and + &gt;grim) and
              PGX larvae fed a range of 20E concentrations. There is a significant positive
              relationship between 20E concentration in the food and the concentration of
              ecdysteroids in the larvae, as indicated by a significant 20E term (<a href="#supp1"
                itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>h).
              Furthermore, starved larvae had higher ecdysone titres than fed larvae. Open and
              closed points represent the biological replicates, and solid and dashed lines are
              linear regressions. N<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">control - starved</sub> = 60, N<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">control - fed</sub> = 60,
              N<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">PGX - starved</sub> =
              30, N<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">PGX - fed</sub> =
              30 across all 20E concentrations.</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig7s2"
          title="Figure 7—figure supplement 2."><label data-itemprop="label">Figure 7—figure
            supplement 2.</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 28
#&#39; @height 20
## Growth w/o Ecdysone or Food
### Stats

#First we will test how ecdysone affects growth in discs from fed and starved PGX larvae without ecdysone. Quadratic function are best fit for growth across genotypes in fed conditions:

PGX_E &lt;- PGX_E %&gt;% mutate(Group = derivedFactor(
						&quot;Control&quot;=(genotype == &quot;w_Grim&quot; | genotype == &quot;PG_w&quot;),
						&quot;Exp&quot;=(genotype == &quot;PGX&quot;),
						.method=&quot;first&quot;))
PGX_E$d20Ecat&lt;-as.factor(PGX_E$d20Ecat)
PGX_E$food&lt;-as.factor(PGX_E$food)

dt&lt;-subset(PGX_E, food==&quot;fed&quot; &amp; d20E==0 )

PGX.lm&lt;-lm(ln.disc.area~timepoint, data=subset(dt, Group==&quot;Exp&quot;))
PGX.poly&lt;-lm(ln.disc.area~poly(timepoint, 2), data=subset(dt, genotype==&quot;PGX&quot;))
PGX.nls&lt;- nls(ln.disc.area ~ SSgompertz(timepoint, Asym, b2, b3), data=subset(dt, genotype==&quot;PGX&quot;))
#anova(PGX.nls,PGX.poly,PGX.lm)
#coef(PGX.poly)
#confint2(PGX.poly)
#summary(PGX.poly)

Control.lm&lt;-lm(ln.disc.area~timepoint, data=subset(dt, Group==&quot;Control&quot;))
Control.poly&lt;-lm(ln.disc.area~poly(timepoint, 2), data=subset(dt, Group==&quot;Control&quot;))
#Control.nls&lt;- nls(ln.disc.area ~ SSgompertz(timepoint, Asym, b2, b3), data=subset(dt, Group==&quot;Control&quot;))
#anova(Control.poly,Control.lm)
#coef(Control.poly)
#confint2(Control.poly)
#summary(Control.poly)

#Across genotypes, growth is suppressed in starvation conditions.

dt&lt;-subset(PGX_E, d20E==0 )
#Anova(lm&lt;-lm(ln.disc.area~Group*food*poly(timepoint, degree=2), data=dt), type=&quot;III&quot;)

#There is a difference in starvation-response among genotypes.
dt&lt;-subset(PGX_E, d20E==0 &amp; food==&quot;fed&quot; )
#Anova(lm&lt;-lm(ln.disc.area~Group*poly(timepoint, degree=2), data=dt), type=&quot;III&quot;)
#summary(lm(ln.disc.area~Group*poly(timepoint, degree=2), data=dt))[[4]]
#confint(lm(ln.disc.area~Group*poly(timepoint, degree=2), data=dt))

Sup_Figure_2A&lt;-ggplot(data=subset(PGX_E, Group==&quot;Exp&quot; &amp; d20Ecat ==&quot;0&quot;), aes(x=timepoint,y=ln.disc.area, colour = food, fill = food, linetype = food))+
  ylim(9.5,10.75)+
   xlab(&quot;Time (hours after L3 moult)&quot;)+
ylab(&quot;ln Disc Size (nm2)&quot;)+
  geom_smooth(method=&quot;lm&quot;,formula=y~poly(x,2),se=F)+
  geom_point(aes(shape = food), size = 3, alpha = 0.5)+
   ggtitle(&quot;PGX&quot;)+ 
  theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=10), axis.text.x=element_text(size=10), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
  scale_shape_manual(values=c(16, 1), labels = c(&quot;fed&quot;, &quot;starved&quot;))+
  scale_linetype_manual(values = c(1,2), labels = c(&quot;fed&quot;, &quot;starved&quot;))+
  scale_colour_manual(values=c(&quot;#b2182b&quot;, &quot;#FF6600&quot;))+
scale_fill_manual(values=c(&quot;#b2182b&quot;, &quot;#FF6600&quot;))


Sup_Figure_2B&lt;-ggplot(data=subset(PGX_E, Group==&quot;Control&quot; &amp; d20Ecat==&quot;0&quot;), aes(x=timepoint,y=ln.disc.area, colour = food, fill = food, linetype = food, shape = food))+
  ylim(9.5,10.75)+
   xlab(&quot;Time (hours after L3 moult)&quot;)+
ylab(&quot;ln Disc Size (nm2)&quot;)+
  geom_smooth(method=&quot;lm&quot;,formula=y~poly(x,2),se=F)+
  geom_point(aes(shape = food), size = 3, alpha = 0.5)+
   ggtitle(&quot;Control&quot;)+ 
  theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=10), axis.text.x=element_text(size=10), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
  scale_shape_manual(values=c(16, 1), labels = c(&quot;fed&quot;, &quot;starved&quot;))+
  scale_linetype_manual(values = c(1,2), labels = c(&quot;fed&quot;, &quot;starved&quot;))+
  scale_colour_manual(values=c(&quot;#4a4534&quot;, &quot;#a19670&quot;))+
scale_fill_manual(values=c(&quot;#4a4534&quot;, &quot;#a19670&quot;))


ggdraw(plot_grid(plot_grid(Sup_Figure_2A, Sup_Figure_2B,ncol=2, align=&#39;v&#39;))) +
  draw_plot_label(c(&quot;A&quot;, &quot;B&quot;), c(0, 0.5), c(1, 1), size = 20)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h4 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="wing-imaginal-disc-growth-is-suppressed-in-fed-genetically-ablated-prothoracic-gland-pgx-larvae-relative-to-controls-and-in-starved-larvae-of-both-genotypes">
              Wing imaginal disc growth is suppressed in fed genetically ablated prothoracic gland
              (PGX) larvae relative to controls and in starved larvae of both genotypes.</h4>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">PGX (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) and control (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>) larvae reared on
              sucrose/yeast (fed) or 20% sucrose/1% agar (starved) diets without 20E
              supplementation. Wing discs were sampled at 5 h intervals between 0-20 h after the
              moult to third instar. Wing disc growth was modelled as a quadratic, and there was a
              significant interaction between genotype (PGX vs. Control) and nutrition (fed vs.
              starved) on growth (<a href="#supp1" itemscope=""
                itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>i). Solid
              line/closed point = fed larvae, broken line/open point = starved larvae. Each point
              corresponds to a wing disc, N<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">PGX - starved</sub> = 67, N<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">PGX - fed</sub> = 74,
              N<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">control -
                starved</sub> = 118, N<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">control - fed</sub> = 151 across all
              time points.</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig7s3"
          title="Figure 7—figure supplement 3."><label data-itemprop="label">Figure 7—figure
            supplement 3.</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 28
#&#39; @height 20
ggplot(data=subset(PGX_E, genotype==&quot;PGX&quot; &amp; food==&quot;fed&quot;), aes(x=timepoint,y=ln.disc.area, color=d20Ecat))+
  ylim(9.5,10.75)+
   xlab(&quot;Time (hours after L3 moult)&quot;)+
ylab(&quot;ln Disc Size (nm2)&quot;)+
  geom_smooth(method=&quot;lm&quot;,formula=y~poly(x, degree=2),se=F)+
  geom_point(size = 5, shape = 16, alpha = 0.5)+
  theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
  scale_colour_brewer(type=&#39;seq&#39;, palette=&#39;RdGy&#39;)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h4 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="there-is-no-effect-of-supplemental-20-hydroxyecdysone-20e-supplementary-file-1eon-growth-of-the-wing-imaginal-disc-in-fed-genetically-ablated-prothoracic-gland-pgx-larvae">
              There is no effect of supplemental 20-hydroxyecdysone (20E) <a href="#supp1"
                itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file 1E</a>on
              growth of the wing imaginal disc in fed genetically ablated prothoracic gland (PGX)
              larvae.</h4>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Growth was modelled as <em
                itemscope="" itemtype="http://schema.stenci.la/Emphasis">S</em> = <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">E + T + T</em><sup itemscope=""
                itemtype="http://schema.stenci.la/Superscript"><span
                  data-itemtype="http://schema.org/Number">2</span></sup><em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">+ E * T + E * T</em><sup itemscope=""
                itemtype="http://schema.stenci.la/Superscript"><span
                  data-itemtype="http://schema.org/Number">2</span></sup>, where <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">S</em> = disc size, <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">E</em> = 20E concentration, and <em
                itemscope="" itemtype="http://schema.stenci.la/Emphasis">T</em> = disc age. There
              was no significant effect of <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">E</em> on the linear or quadratic growth
              rate of the wing imaginal discs (<a href="#supp1" itemscope=""
                itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>j). Each point
              corresponds to a wing disc, N<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">PGX – fed</sub> = 459 (73–86 discs were
              sampled per treatment across all time points).</p>
          </figcaption>
        </figure>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To test whether wing disc
          growth rates show either a graded or threshold response to 20E concentration in starved
          PGX larvae, we extracted the linear growth rate coefficients from our models. We then
          modelled the relationship between growth rate and 20E concentration with three nonlinear
          functions: a graded Michaelis–Menten function, and threshold three- and four-parameter
          log-logistic functions. Finally, we tested which model best fit the data using Akaike
          information criteria (AIC) and Bayesian information criteria (BIC) for model selection.
          The model with the lowest AIC and BIC values best fits the data.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">When wing disc growth rate was
          modelled with the graded Michaelis–Menten function, both the AIC and BIC values were lower
          than when it was modelled with either threshold function (<a href="#supp1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>k). This supports the
          hypothesis that growth rate increases continuously with increasing 20E concentration, with
          growth rate plateauing after 20E concentrations reach 25 ng/ml (<a href="#fig7"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 7B</a>). Thus, disc growth
          rate appears to show a graded response to 20E level in the absence of nutrition. This is
          in line with recent findings from <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a
              href="#bib77"><span>77</span><span>Strassburger et
                al.</span><span>2021</span></a></cite>, which show that proliferation and growth in
          the wing discs increase with increasing 20E concentration in the diet <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a
              href="#bib77"><span>77</span><span>Strassburger et
                al.</span><span>2021</span></a></cite>.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">The effect of 20E concentration
          on Achaete patterning was qualitatively different to its effect on growth. As before,
          Achaete patterning did not progress in either starved or fed PGX larvae (<a href="#fig8s1"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 8—figure supplement 1</a>).
          In contrast, Achaete patterning did progress in PGX larvae supplemented with 20E.
          Patterning rates for Achaete did not differ significantly between 0–6.25 ng/ml (fed) and
          0–12.5 ng/ml (starved) of 20E (<a href="#fig8" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 8A and C</a>, <a href="#supp1"
            itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>). Above 25
          ng/ml of 20E, Achaete patterning occurred at the same rapid rate in both fed and starved
          PGX larvae (<a href="#fig8" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 8A
            and C</a>).</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig8" title="Figure 8.">
          <label data-itemprop="label">Figure 8.</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 28
#&#39; @height 20
## Achaete Patterning with Ecdysone
#### Fed

dt&lt;-subset(PGX_E, food==&quot;fed&quot; &amp; genotype==&quot;PGX&quot;)

ac.fedLM &lt;- lm(ac.stage ~ poly(timepoint, 2, raw = FALSE) * d20Ecat, data = dt)
#Anova(ac.fedLM, type = &quot;III&quot;)
ac.fed.trends &lt;- emtrends(ac.fedLM, ~ d20Ecat, var = &quot;timepoint&quot;, max.degree = 1)
#multcomp::cld(ac.fed.trends)

coefs.acfed &lt;- tidy(ac.fed.trends)
coefs.acfed$d20Ecat&lt;-as.numeric(as.character(coefs.acfed$d20Ecat))
names(coefs.acfed)[1]&lt;-&quot;d20E&quot;

Figure_8A&lt;-ggplot(data=subset(PGX_E, genotype==&quot;PGX&quot; &amp; food==&quot;fed&quot;), aes(x=timepoint,y=ac.stage, color=d20Ecat))+
  scale_y_continuous(limits = c(0.5, 7.5), breaks = c(1, 2, 3, 4, 5, 6, 7))+
  xlab(&quot;Time (hours after L3 moult)&quot;)+
ylab(&quot;Achaete Stage&quot;)+
ggtitle(&quot;Fed - PGX&quot;)+
  scale_size(breaks = c(1, 5, 10, 20))+
  geom_smooth(method=&quot;lm&quot;,formula=y~poly(x, degree=2),se=F)+
  geom_count(position = position_jitter(width = 0.3, height = 0.3),shape=16, alpha=0.7)+
  theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
  scale_colour_brewer(type=&#39;seq&#39;, palette=&#39;RdGy&#39;, labels = c(&quot;0 - A&quot;,&quot;6.25 - A&quot;,&quot;12.5 - B&quot;,&quot;25 - BC&quot;,&quot;50 - BC&quot;,&quot;100 - C&quot;))

# extract coefficients from emtrends

#which model fits best?

#from emtrends
model.drm1 &lt;- drm (timepoint.trend ~ d20E, data = coefs.acfed, fct = MM.3())
model.drm2 &lt;- drm (timepoint.trend ~ d20E, data = coefs.acfed, fct = LL.3())
model.drm3 &lt;- drm (timepoint.trend ~ d20E, data = coefs.acfed, fct = LL.4())

#AIC(model.drm1, model.drm2, model.drm3)
#BIC(model.drm1, model.drm2, model.drm3)


mml &lt;- data.frame(d20E = seq(0, max(coefs.acfed$d20E), length.out = 100))
mml$timepoint.trend &lt;- predict(model.drm3, newdata = mml)

Figure_8B&lt;-ggplot(data=coefs.acfed, aes(x=d20E,y=timepoint.trend))+
   xlab(&quot;20E Concentration in Food (ng/ml)&quot;)+
ylab(&quot;Achate patterning rate&quot;)+
  ggtitle(&quot;Fed - PGX&quot;)+
 scale_y_continuous(limits = c(0, 0.25), breaks = c(0, 0.05, 0.1, 0.15, 0.2, 0.25))+
  geom_line(data = mml, aes(x = d20E, y = timepoint.trend), colour = &quot;black&quot;, size = 2)+
  geom_point(size = 5, shape = 16)+
  theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))

#Starved

dt&lt;-subset(PGX_E, food==&quot;starved&quot; &amp; genotype==&quot;PGX&quot;)

ac.starvedLM &lt;- lm(ac.stage ~ poly(timepoint, 2, raw = FALSE) * d20Ecat, data = dt)
#Anova(ac.starvedLM, type = &quot;III&quot;)
ac.starved.trends &lt;- emtrends(ac.starvedLM, ~ d20Ecat, var = &quot;timepoint&quot;, max.degree = 1)
#multcomp::cld(ac.starved.trends)


coefs.acstarved &lt;- tidy(ac.starved.trends)
coefs.acstarved$d20Ecat&lt;-as.numeric(as.character(coefs.acstarved$d20Ecat))
names(coefs.acstarved)[1]&lt;-&quot;d20E&quot;

Figure_8C&lt;-ggplot(data=subset(PGX_E, genotype==&quot;PGX&quot; &amp; food==&quot;starved&quot;), aes(x=timepoint,y=ac.stage, color=d20Ecat))+
  scale_y_continuous(limits = c(0.5, 7.5), breaks = c(1, 2, 3, 4, 5, 6, 7))+
  xlab(&quot;Time (hours after L3 moult)&quot;)+
ylab(&quot;Achaete Stage&quot;)+
  ggtitle(&quot;Starved - PGX&quot;)+
  scale_size(breaks = c(1, 5, 10, 20))+
  geom_smooth(method=&quot;lm&quot;,formula=y~poly(x, degree=2),se=F)+
  geom_count(position = position_jitter(width = 0.3, height = 0.3),shape=16, alpha=0.7)+
  theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
  scale_colour_brewer(type=&#39;seq&#39;, palette=&#39;RdGy&#39;, labels = c(&quot;0 - A&quot;,&quot;6.25 - A&quot;,&quot;12.5 - A&quot;,&quot;25 - B&quot;,&quot;50 - B&quot;,&quot;100 - B&quot;))

# extract coefficients from emtrends

model.drm1 &lt;- drm (timepoint.trend ~ d20E, data = coefs.acstarved, fct = MM.3())
model.drm2 &lt;- drm (timepoint.trend ~ d20E, data = coefs.acstarved, fct = LL.3())
model.drm3 &lt;- drm (timepoint.trend ~ d20E, data = coefs.acstarved, fct = LL.4())

#AIC(model.drm1, model.drm2, model.drm3)
#BIC(model.drm1, model.drm2, model.drm3)


mml &lt;- data.frame(d20E = seq(0, max(coefs.acstarved$d20E), length.out = 100))
mml$timepoint.trend &lt;- predict(model.drm3, newdata = mml)


Figure_8D&lt;-ggplot(data=coefs.acstarved, aes(x=d20E,y=timepoint.trend))+
   xlab(&quot;20E Concentration in Food (ng/ml)&quot;)+
ylab(&quot;Achate patterning rate&quot;)+
  ggtitle(&quot;Starved - PGX&quot;)+
  scale_y_continuous(limits = c(0, 0.25), breaks = c(0, 0.05, 0.1, 0.15, 0.2, 0.25))+
  geom_line(data = mml, aes(x = d20E, y = timepoint.trend), colour = &quot;black&quot;, size = 2)+
  geom_point(size = 5, shape = 16)+
  theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))

ggdraw() +
  draw_plot(Figure_8A, 0, 0.5, 0.66, .5) +
  draw_plot(Figure_8B, 0.66, 0.5, 0.33, .5) +
  draw_plot(Figure_8C, 0, 0, 0.66, .5) +
  draw_plot(Figure_8D, 0.66, 0, 0.33, .5) +
  draw_plot_label(c(&quot;A&quot;, &quot;B&quot;, &quot;C&quot;, &quot;D&quot;), c(0, 0.65, 0, 0.65), c(1, 1, 0.5, 0.5), size = 20)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h4 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="effect-of-supplemental-20-hydroxyecdysone-20e-supplementary-file-1eon-achaete-patterning-of-the-wing-imaginal-disc-in-a-b-fed-and-c-d-starved-genetically-ablated-prothoracic-gland-pgx-larvae">
              Effect of supplemental 20-hydroxyecdysone (20E) <a href="#supp1" itemscope=""
                itemtype="http://schema.stenci.la/Link">Supplementary file 1E</a>on Achaete
              patterning of the wing imaginal disc in (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A, B</strong>) fed and (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">C, D</strong>) starved
              genetically ablated prothoracic gland (PGX) larvae.</h4>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">In (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) and (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">C</strong>), patterning stage was modelled
              as <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">A</em> = <em
                itemscope="" itemtype="http://schema.stenci.la/Emphasis">E + T + T</em><sup
                itemscope="" itemtype="http://schema.stenci.la/Superscript"><span
                  data-itemtype="http://schema.org/Number">2</span></sup><em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">+ E * T + E * T</em><sup itemscope=""
                itemtype="http://schema.stenci.la/Superscript"><span
                  data-itemtype="http://schema.org/Number">2</span></sup>, where <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">A</em> = Achaete stage, <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">E</em> = 20E concentration, and <em
                itemscope="" itemtype="http://schema.stenci.la/Emphasis">T</em> = disc age. The size
              of each point corresponds to the number of wing disc in each stage. 20E treatments
              that do not share a letter (see legend) are significantly different in patterning
              rates as determined by post-hoc test on the slopes (for ANOVA, see <a href="#supp1"
                itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>l). In
              (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>) and
              (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">D</strong>), we
              extracted the linear patterning rate from fed (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">B</strong>) or starved (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">D</strong>) PGX larvae. We
              then modelled the relationship between patterning rate and 20E concentration using a
              four-parameter log-logistic equation: <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">y = c + (d)(–c)/(1 + e<sup itemscope=""
                  itemtype="http://schema.stenci.la/Superscript">(b(log(x))-log(a))</sup></em>),
              where <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">c</em> is the lower
              asymptote<em itemscope="" itemtype="http://schema.stenci.la/Emphasis">, d</em> is the
              upper asymptote, <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">b</em>
              is the rate of increase, and <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">a</em> is the inflection point. N<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">PGX – fed</sub> = 459,
              N<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">PGX – starved</sub> =
              409, 63–86 discs were sampled per treatment across all time points.</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig8s1"
          title="Figure 8—figure supplement 1."><label data-itemprop="label">Figure 8—figure
            supplement 1.</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 28
#&#39; @height 13
## Achaete Patterning w/o Ecdysone or Food
### Stats
#The quadratic fit is probably the best overall. Using this model, we can test the effect of starvation on pattern development, and test whether it is affected by genotype.

dt&lt;-PGX_E[PGX_E$d20E==0,]
#Anova(lm(ac.stage~food*Group*poly(timepoint, degree=2), data=dt), type=&quot;III&quot;)

# Test within PGX and Control
dt&lt;-subset(PGX_E, Group==&quot;Exp&quot; &amp; d20E==0)
#Anova(lm(ac.stage~food*poly(timepoint, degree=2), data=dt), type=&quot;III&quot;)

dt&lt;-subset(PGX_E, Group==&quot;Control&quot; &amp; d20E==0)
#Anova(lm(ac.stage~food*poly(timepoint, degree=2), data=dt), type=&quot;III&quot;)

Sup_Figure_4A&lt;- ggplot(aes(y = ac.stage, x = timepoint, colour = food, fill = food, linetype = food), data = subset(PGX_E, Group==&quot;Exp&quot; &amp; d20E==&quot;0&quot; ))+
  scale_y_continuous(limits = c(1, 7.5), breaks = c(1, 2, 3, 4, 5, 6, 7))+
  xlab(&quot;Time (hours after L3 moult)&quot;)+
ylab(&quot;Achaete Stage&quot;)+
   ggtitle(&quot;PGX&quot;)+
  geom_smooth(method = &quot;lm&quot;, formula = y ~ poly(x, degree=2), se=F, aes(color=food))+
  geom_point(aes(shape=food),position = position_jitter(width = 0.3, height = 0.3),size = 3, alpha = 0.7)+ 
  theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
  scale_shape_manual(values=c(16, 1), labels = c(&quot;fed&quot;, &quot;starved&quot;))+
  scale_linetype_manual(values = c(1,2), labels = c(&quot;fed&quot;, &quot;starved&quot;))+
 scale_colour_manual(values=c(&quot;#b2182b&quot;, &quot;#ef8a62&quot;))+
scale_fill_manual(values=c(&quot;#b2182b&quot;, &quot;#ef8a62&quot;))
  


Sup_Figure_4B&lt;- ggplot(aes(y = ac.stage, x = timepoint, color=food, fill = food, linetype = food), data = subset(PGX_E, Group==&quot;Control&quot; &amp; d20E==&quot;0&quot; ))+
  ylim(1,6)+
  scale_y_continuous(limits = c(1, 7.5), breaks = c(1, 2, 3, 4, 5, 6, 7))+
  xlab(&quot;Time (hours after L3 moult)&quot;)+
ylab(&quot;Achaete Stage&quot;)+
  ggtitle(&quot;Control&quot;)+
  geom_smooth(method = &quot;lm&quot;, formula = y ~ poly(x, degree=2), se=F, aes(color=food))+
  #geom_count(aes(color=food),position = position_jitter(width = 0.3, height = 0.3),shape=19)+
  geom_point(aes(shape = food),position = position_jitter(width = 0.3, height = 0.3),size = 3, alpha = 0.7)+ 
theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
  scale_shape_manual(values=c(16, 1), labels = c(&quot;fed&quot;, &quot;starved&quot;))+
  scale_linetype_manual(values = c(1,2), labels = c(&quot;fed&quot;, &quot;starved&quot;))+
scale_colour_manual(values=c(&quot;#4a4534&quot;, &quot;#a19670&quot;))+
scale_fill_manual(values=c(&quot;#4a4534&quot;, &quot;#a19670&quot;))

ggdraw(plot_grid(plot_grid(Sup_Figure_4A, Sup_Figure_4B,ncol=2, align=&#39;v&#39;))) +
  draw_plot_label(c(&quot;A&quot;, &quot;B&quot;), c(0, 0.5), c(1, 1), size = 20)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h4 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="achaete-patterning-in-wing-discs-from-fed-and-starved-genetically-ablated-prothoracic-gland-pgx-and-control-larvae">
              Achaete patterning in wing discs from fed and starved genetically ablated prothoracic
              gland (PGX) and control larvae.</h4>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) Patterning does not progress
              in either fed or starved PGX larvae. (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">B</strong>) Patterning does not progress
              in starved control larvae but does in fed control larvae. There is a significant
              interaction between the effects of disc age and food on Achaete patterning in control
              larvae (orthogonal polynomial regression: <span itemscope=""
                itemtype="http://schema.stenci.la/MathFragment"><span class="mjx-chtml"><span
                    class="mjx-math"
                    aria-label="{\mathrm{F}}_{{\mathrm{f}\mathrm{o}\mathrm{o}\mathrm{d}\mathrm{*}\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{}\mathrm{a}\mathrm{g}\mathrm{e}}^{2}}"><span
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                                      style="padding-top: 0.372em; padding-bottom: 0.372em;">F</span></span></span></span></span></span></span><span
                          class="mjx-sub"
                          style="font-size: 70.7%; vertical-align: -0.484em; padding-right: 0.071em;"><span
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                                              style="padding-top: 0.372em; padding-bottom: 0.372em;">d</span></span></span></span><span
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                                              style="padding-top: 0.372em; padding-bottom: 0.372em;">d</span></span></span></span><span
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                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                              style="padding-top: 0.372em; padding-bottom: 0.372em;">i</span></span></span></span><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                              style="padding-top: 0.151em; padding-bottom: 0.372em;">s</span></span></span></span><span
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                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                              style="padding-top: 0.151em; padding-bottom: 0.372em;">c</span></span></span></span><span
                                        class="mjx-texatom"><span
                                          class="mjx-mrow"></span></span><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                              style="padding-top: 0.151em; padding-bottom: 0.372em;">a</span></span></span></span><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                              style="padding-top: 0.151em; padding-bottom: 0.519em;">g</span></span></span></span><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                              style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span></span></span></span></span></span><span
                                  class="mjx-sup"
                                  style="font-size: 83.3%; vertical-align: 0.49em; padding-left: 0px; padding-right: 0.06em;"><span
                                    class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                        class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R"
                                          style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span></span></span></span></span></span></span></span>
              = 67.98, p&lt;0.001), but not in PGX larvae (orthogonal polynomial regression: <span
                itemscope="" itemtype="http://schema.stenci.la/MathFragment"><span
                  class="mjx-chtml"><span class="mjx-math"
                    aria-label="{\mathrm{F}}_{{\mathrm{f}\mathrm{o}\mathrm{o}\mathrm{d}\mathrm{*}\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{c}\mathrm{}\mathrm{a}\mathrm{g}\mathrm{e}}^{2}}"><span
                      class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span
                          class="mjx-base"><span class="mjx-texatom"><span class="mjx-mrow"><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.372em; padding-bottom: 0.372em;">F</span></span></span></span></span></span></span><span
                          class="mjx-sub"
                          style="font-size: 70.7%; vertical-align: -0.484em; padding-right: 0.071em;"><span
                            class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                class="mjx-msubsup"><span class="mjx-base"><span
                                    class="mjx-texatom"><span class="mjx-mrow"><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
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                                              style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.066em;">f</span></span></span></span><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
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                                              style="padding-top: 0.151em; padding-bottom: 0.372em;">o</span></span></span></span><span
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                                              style="padding-top: 0.151em; padding-bottom: 0.372em;">o</span></span></span></span><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                              style="padding-top: 0.372em; padding-bottom: 0.372em;">d</span></span></span></span><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                                              style="padding-top: 0.151em; padding-bottom: 0.298em;"></span></span></span></span><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                              style="padding-top: 0.372em; padding-bottom: 0.372em;">d</span></span></span></span><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                              style="padding-top: 0.372em; padding-bottom: 0.372em;">i</span></span></span></span><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                              style="padding-top: 0.151em; padding-bottom: 0.372em;">s</span></span></span></span><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                              style="padding-top: 0.151em; padding-bottom: 0.372em;">c</span></span></span></span><span
                                        class="mjx-texatom"><span
                                          class="mjx-mrow"></span></span><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                              style="padding-top: 0.151em; padding-bottom: 0.372em;">a</span></span></span></span><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                              style="padding-top: 0.151em; padding-bottom: 0.519em;">g</span></span></span></span><span
                                        class="mjx-texatom"><span class="mjx-mrow"><span
                                            class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                              style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span></span></span></span></span></span><span
                                  class="mjx-sup"
                                  style="font-size: 83.3%; vertical-align: 0.49em; padding-left: 0px; padding-right: 0.06em;"><span
                                    class="mjx-texatom" style=""><span class="mjx-mrow"><span
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                                          style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span></span></span></span></span></span></span></span></span></span></span></span></span>
              = 1.81, p=0.163). Each point corresponds to a wing disc, N<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">PGX - starved</sub> = 67, N<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">PGX - fed</sub> = 74,
              N<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">control -
                starved</sub> = 118, N<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">control - fed</sub> = 151 across all
              time points.</p>
          </figcaption>
        </figure>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To compare the progression of
          Achaete at different levels of 20E with the progression of disc growth, we modelled the
          relationship between Achaete pattern, time after third-instar ecdysis, and 20E
          concentration as second-order polynomial regression for fed and starved PGX larvae. As for
          disc growth, we then extracted the linear coefficients from this model at each level of
          20E and modelled the relationship between patterning rate and 20E using a Michaelis–Menten
          function and a three- and four-parameter log-logistic function. Both the AIC and BIC
          indicated that that a threshold four-parameter log-logistic function fit the data better
          than a graded Michaelis–Menten function (<a href="#supp1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>k). Thus, unlike growth,
          Achaete patterning showed a threshold response to 20E concentration. Specifically, Achaete
          patterning was not initiated unless 20E is above a certain concentration (12.5–25 ng/ml),
          but it progressed at the same rate regardless of how high 20E is above this concentration.
        </p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Comparing the timing of Achaete
          patterning in 20E-supplemented PGX larvae versus fed controls provides some indication of
          when in normal development the threshold level of 20E necessary to initiate Achaete
          patterning is reached. Discs from fed control larvae began to reach Achaete stage 4 by 15
          hr AEL3 (<a href="#fig8s1" itemscope="" itemtype="http://schema.stenci.la/Link">Figure
            8—figure supplement 1B</a>), while discs from both fed and starved PGX larvae
          supplemented with &gt;25 ng/ml of 20E began to reach stage 4 by 10 hr AEL3 (<a
            href="#fig8" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 8A and C</a>).
          This suggests that in control larvae ecdysone levels sufficient to initiate Achaete
          patterning are only reached 15 hr after the moult to the third larval instar.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Senseless patterning did not
          progress as far as Achaete patterning, only achieving an average of stage 3 in fed and
          stage 4 in starved larvae at 20 hr AL3E when supplemented with 20E. In both fed and
          starved larvae, supplemental 20E <a href="#supp1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Supplementary file 1E</a>at or below 12.5 ng/ml
          was insufficient to rescue Senseless patterning, while supplemental 20E at or above 25
          ng/ml rescued patterning to approximately the same extent (<a href="#fig9" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 9A and C</a>, <a href="#supp1"
            itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>m). As for
          Achaete patterning, supplemental 20E also initiated Senseless patterning in PGX larvae
          early when compared to fed controls. Discs from fed control larvae began to reach
          Senseless stage 3 at 20 hr AEL3 (<a href="#fig9s1" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 9—figure supplement 1</a>), while discs
          from both fed and starved PGX larvae supplemented with ≥25 ng/ml of 20E were at stage 3 by
          15 hr AEL3 (<a href="#fig9" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 9A
            and C</a>).</p>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig9" title="Figure 9.">
          <label data-itemprop="label">Figure 9.</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 28
#&#39; @height 20
## Senseless Patterning with Ecdysone
### Stats &amp; Plot
#### Fed

dt&lt;-subset(PGX_E, food==&quot;fed&quot; &amp; genotype==&quot;PGX&quot;)

sens.fedLM &lt;- lm(sens.stage ~ poly(timepoint, 2) * d20Ecat, data = dt)
#Anova(sens.fedLM, type = &quot;III&quot;)
sens.fed.trends &lt;- emtrends(sens.fedLM, ~ d20Ecat, var = &quot;timepoint&quot;, max.degree = 1)
#multcomp::cld(sens.fed.trends)

coefs.sensfed &lt;- tidy(sens.fed.trends)
coefs.sensfed$d20Ecat&lt;-as.numeric(as.character(coefs.sensfed$d20Ecat))
names(coefs.sensfed)[1]&lt;-&quot;d20E&quot;

dt&lt;-subset(PGX_E, food==&quot;fed&quot; &amp; genotype==&quot;PGX&quot;)

Figure_9A&lt;-ggplot(data=dt,aes(x=timepoint,y=sens.stage, color=d20Ecat))+
   scale_y_continuous(limits = c(0.5, 7.5), breaks = c(1, 2, 3, 4, 5, 6, 7))+
  xlab(&quot;Time (hours after L3 moult)&quot;)+
ylab(&quot;Senseless Stage&quot;)+
  ggtitle(&quot;Fed - PGX&quot;)+
  scale_size(breaks = c(1, 5, 10, 20))+
  geom_count(position = position_jitter(width = 0.3, height = 0.3),shape=16, alpha=0.5)+
  geom_smooth(method=&quot;lm&quot;,formula=y~poly(x, degree=2),se=F)+
theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
  scale_colour_brewer(type=&#39;seq&#39;, palette=&#39;RdGy&#39;, labels = c(&quot;0 - A&quot;,&quot;6.25 - AB&quot;,&quot;12.5 - B&quot;,&quot;25 - C&quot;,&quot;50 - C&quot;,&quot;100 - C&quot;))

# extract coefficients from emtrends
model.drm1 &lt;- drm (timepoint.trend ~ d20E, data = coefs.sensfed, fct = MM.3())
model.drm2 &lt;- drm (timepoint.trend ~ d20E, data = coefs.sensfed, fct = LL.3())
model.drm3 &lt;- drm (timepoint.trend ~ d20E, data = coefs.sensfed, fct = LL.4())

#AIC(model.drm1, model.drm2, model.drm3)
#BIC(model.drm1, model.drm2, model.drm3)


mml &lt;- data.frame(d20E = seq(0, max(coefs.sensfed$d20E), length.out = 100))
mml$timepoint.trend &lt;- predict(model.drm3, newdata = mml)

Figure_9B&lt;-ggplot(data=coefs.sensfed, aes(x=d20E,y=timepoint.trend))+
   xlab(&quot;20E Concentration in Food (ng/ml)&quot;)+
ylab(&quot;Senseless patterning rate&quot;)+
  ggtitle(&quot;Fed - PGX&quot;)+
 scale_y_continuous(limits = c(-0.01, 0.15), breaks = c(0, 0.025, 0.05, 0.075, 0.1, 0.125, 0.15))+
  geom_line(data = mml, aes(x = d20E, y = timepoint.trend), colour = &quot;black&quot;, size = 2)+
  geom_point(size = 5, shape = 16)+
  theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
  scale_colour_brewer(type=&#39;seq&#39;, palette=&#39;RdGy&#39;)

#### Starved

dt&lt;-subset(PGX_E, food==&quot;starved&quot; &amp; genotype==&quot;PGX&quot;)

sens.starvedLM &lt;- lm(sens.stage ~ poly(timepoint, 2) * d20Ecat, data = dt)
#Anova(sens.starvedLM, type = &quot;III&quot;)
sens.starved.trends &lt;- emtrends(sens.starvedLM, ~ d20Ecat, var = &quot;timepoint&quot;, max.degree = 1)
#multcomp::cld(sens.starved.trends)

coefs.sensstarved &lt;- tidy(sens.starved.trends)
coefs.sensstarved$d20Ecat&lt;-as.numeric(as.character(coefs.sensstarved$d20Ecat))
names(coefs.sensstarved)[1]&lt;-&quot;d20E&quot;

dt&lt;-subset(PGX_E, food==&quot;starved&quot; &amp; genotype==&quot;PGX&quot;)

Figure_9C&lt;-ggplot()+
   scale_y_continuous(limits = c(0.5, 7.5), breaks = c(1, 2, 3, 4, 5, 6, 7))+
  xlab(&quot;Time (hours after L3 moult)&quot;)+
ylab(&quot;Senseless Stage&quot;)+
  ggtitle(&quot;Starved - PGX&quot;)+
  scale_size(breaks = c(1, 5, 10, 20))+
  geom_smooth(data=dt,aes(x=timepoint,y=sens.stage, color=d20Ecat),method = &quot;lm&quot;, formula = y ~x, se = FALSE, size = 1)+
  geom_count(data=dt,aes(x=timepoint,y=sens.stage, color=d20Ecat),position = position_jitter(width = 0.3, height = 0.3),shape=16, alpha=0.5)+
theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
  scale_colour_brewer(type=&#39;seq&#39;, palette=&#39;RdGy&#39;, labels = c(&quot;0 - A&quot;,&quot;6.25 - A&quot;,&quot;12.5 - A&quot;,&quot;25 - B&quot;,&quot;50 - BC&quot;,&quot;100 - C&quot;))

#model coefficients from emtrends
model.drm1 &lt;- drm (timepoint.trend ~ d20E, data = coefs.sensstarved, fct = MM.3())
model.drm2 &lt;- drm (timepoint.trend ~ d20E, data = coefs.sensstarved, fct = LL.3())
model.drm3 &lt;- drm (timepoint.trend ~ d20E, data = coefs.sensstarved, fct = LL.4())

#AIC(model.drm1, model.drm2, model.drm3)
#BIC(model.drm1, model.drm2, model.drm3)

mml &lt;- data.frame(d20E = seq(0, max(coefs.sensstarved$d20E), length.out = 100))
mml$timepoint.trend &lt;- predict(model.drm2, newdata = mml)

Figure_9D&lt;-ggplot(data=coefs.sensstarved, aes(x=d20E,y=timepoint.trend))+
   xlab(&quot;20E Concentration in Food (ng/ml)&quot;)+
ylab(&quot;Senseless patterning rate&quot;)+
  ggtitle(&quot;Starved - PGX&quot;)+
 scale_y_continuous(limits = c(-0.01, 0.15), breaks = c(0, 0.025, 0.05, 0.075, 0.1, 0.125, 0.15))+
  geom_line(data = mml, aes(x = d20E, y = timepoint.trend), colour = &quot;black&quot;, size = 2)+
  geom_point(size = 5, shape = 16)+
  theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
  scale_colour_brewer(type=&#39;seq&#39;, palette=&#39;RdGy&#39;)

ggdraw() +
  draw_plot(Figure_9A, 0, 0.5, 0.66, .5) +
  draw_plot(Figure_9B, 0.66, 0.5, 0.33, .5) +
  draw_plot(Figure_9C, 0, 0, 0.66, .5) +
  draw_plot(Figure_9D, 0.66, 0, 0.33, .5) +
  draw_plot_label(c(&quot;A&quot;, &quot;B&quot;, &quot;C&quot;, &quot;D&quot;), c(0, 0.64, 0, 0.64), c(1, 1, 0.5, 0.5), size = 20)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h4 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="effect-of-supplemental-20-hydroxyecdysone-20e-supplementary-file-1eon-senseless-patterning-of-the-wing-imaginal-disc-in-a-b-fed-and-c-d-starved-genetically-ablated-prothoracic-gland-pgx-larvae">
              Effect of supplemental 20-hydroxyecdysone (20E) <a href="#supp1" itemscope=""
                itemtype="http://schema.stenci.la/Link">Supplementary file 1E</a>on Senseless
              patterning of the wing imaginal disc in (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A, B</strong>) fed and (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">C, D</strong>) starved
              genetically ablated prothoracic gland (PGX) larvae.</h4>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">In (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) and (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">C</strong>), patterning stage was modelled
              as <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">S</em> = <em
                itemscope="" itemtype="http://schema.stenci.la/Emphasis">E + T + T</em><sup
                itemscope="" itemtype="http://schema.stenci.la/Superscript"><span
                  data-itemtype="http://schema.org/Number">2</span></sup><em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">+ E * T + E * T</em><sup itemscope=""
                itemtype="http://schema.stenci.la/Superscript"><span
                  data-itemtype="http://schema.org/Number">2</span></sup>, where <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">S</em> = Senseless stage, <em
                itemscope="" itemtype="http://schema.stenci.la/Emphasis">E</em> = 20E concentration,
              and <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">T</em> = disc age.
              The size of each point corresponds to the number of wing discs in each stage. 20E
              treatments that do not share a letter (see legend) are significantly different in
              patterning rates as determined by post-hoc test on the slopes (for ANOVA, see <a
                href="#supp1" itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary
                file 1</a>m). In (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">B</strong>) and (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">D</strong>), we extracted the linear
              patterning rate in fed (<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">B</strong>) or starved (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">D</strong>) larvae. We then
              modelled the relationship between patterning rate and 20E concentration in (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>) using a
              four-parameter log-logistic equation: <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">y = c + (d)(–c)/(1 + e<sup itemscope=""
                  itemtype="http://schema.stenci.la/Superscript">(b(log(x))-log(a))</sup></em>),
              where <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">c</em> is the lower
              asymptote<em itemscope="" itemtype="http://schema.stenci.la/Emphasis">, d</em> is the
              upper asymptote, <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">b</em>
              is the rate of increase, and <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">a</em> is the inflection point. In
              (<strong itemscope="" itemtype="http://schema.stenci.la/Strong">D</strong>), we used a
              three-parameter log-logistic equation: <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">y = d/(1 + e<sup itemscope=""
                  itemtype="http://schema.stenci.la/Superscript">(b(log(x))-log(a))</sup></em>),
              where <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">d</em> is the upper
              asymptote, <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">b</em> is the
              rate of increase, and <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">a</em> is the inflection point. N<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">PGX – fed</sub> = 459,
              N<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">PGX – starved</sub> =
              409, 63–86 discs were sampled per treatment across all time points.</p>
          </figcaption>
        </figure>
        <figure itemscope="" itemtype="http://schema.stenci.la/Figure" id="fig9s1"
          title="Figure 9—figure supplement 1."><label data-itemprop="label">Figure 9—figure
            supplement 1.</label>
          <stencila-code-chunk itemscope="" itemtype="http://schema.stenci.la/CodeChunk"
            data-programminglanguage="r">
            <pre class="language-r" itemscope="" itemtype="http://schema.stenci.la/CodeBlock"
              slot="text"><code>#&#39; @width 28
#&#39; @height 13
## Senseless Patterning w/o Ecdysone or Food
### Stats

dt&lt;-PGX_E[PGX_E$d20E==0,]
#Anova(lm(sens.stage~food*Group*timepoint, data=dt), type=&quot;III&quot;)

# Test within PGX and Control
dt&lt;-subset(PGX_E, Group==&quot;Exp&quot; &amp; d20E==0)
#Anova(lm(sens.stage~food*timepoint, data=dt), type=&quot;III&quot;)

dt&lt;-subset(PGX_E, Group==&quot;Exp&quot; &amp; d20E==0)
#Anova(lm(sens.stage~food*timepoint, data=dt), type=&quot;III&quot;)
#anova(lm(sens.stage~timepoint, data=subset(dt, food==&quot;fed&quot;)))
#anova(lm(sens.stage~timepoint, data=subset(dt, food==&quot;starved&quot;)))


dt&lt;-subset(PGX_E, Group==&quot;Control&quot; &amp; d20E==0)
#Anova(lm(sens.stage~food*timepoint, data=dt), type=&quot;III&quot;)

Sup_Figure_5A&lt;- ggplot(aes(y = sens.stage, x = timepoint, colour = food, fill = food, linetype = food), data = subset(PGX_E, Group==&quot;Exp&quot; &amp; d20E==&quot;0&quot; ))+
  scale_y_continuous(limits =c(0.5,7.5), breaks = c(1, 2, 3, 4, 5, 6, 7))+
  xlab(&quot;Time (hours after L3 moult)&quot;)+
ylab(&quot;Senseless Stage&quot;)+
   ggtitle(&quot;PGX&quot;)+
  geom_smooth(method = &quot;lm&quot;, formula = y ~ poly(x, degree=2), se=F)+
  #geom_count(aes(color=food),position = position_jitter(width = 0.3, height = 0.3),shape=19)+
  geom_point(aes(shape=food),position = position_jitter(width = 0.3, height = 0.3),size = 3, alpha = 0.7)+
  theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
  scale_shape_manual(values=c(16, 1), labels = c(&quot;fed&quot;, &quot;starved&quot;))+
  scale_linetype_manual(values = c(1,2), labels = c(&quot;fed&quot;, &quot;starved&quot;))+
scale_colour_manual(values=c(&quot;#b2182b&quot;, &quot;#ef8a62&quot;))+
scale_fill_manual(values=c(&quot;#b2182b&quot;, &quot;#ef8a62&quot;))



Sup_Figure_5B&lt;- ggplot(aes(y = sens.stage, x = timepoint, colour = food, fill = food, linetype = food), data = subset(PGX_E, Group==&quot;Control&quot; &amp; d20E==&quot;0&quot; ))+
  scale_y_continuous(limits =c(0.5,7.5), breaks = c(1, 2, 3, 4, 5, 6, 7))+
  xlab(&quot;Time (hours after L3 moult)&quot;)+
ylab(&quot;Senseless Stage&quot;)+
  ggtitle(&quot;Control&quot;)+
  geom_smooth(method = &quot;lm&quot;, formula = y ~ poly(x, degree=2), se=F)+
  #geom_count(aes(color=food),position = position_jitter(width = 0.3, height = 0.3),shape=19)+
  geom_point(aes(shape = food),position = position_jitter(width = 0.3, height = 0.3),size = 3, alpha = 0.7)+
  theme_bw()+
theme(panel.grid=element_blank(),axis.title.x=element_text(size=15), axis.title.y=element_text(size=15), 
        axis.text.y=element_text(size=16), axis.text.x=element_text(size=16), panel.background = element_rect(colour = &quot;black&quot;), legend.background = element_rect(), legend.key = element_rect(colour = &quot;white&quot;), legend.text=element_text(face=&quot;italic&quot;, size=16))+
theme(legend.title=element_blank())+
 theme(axis.title.x = element_text(vjust=-0.5), axis.title.y = element_text(vjust=1.5))+
  scale_shape_manual(values=c(16, 1), labels = c(&quot;fed&quot;, &quot;starved&quot;))+
  scale_linetype_manual(values = c(1,2), labels = c(&quot;fed&quot;, &quot;starved&quot;))+
scale_colour_manual(values=c(&quot;#4a4534&quot;, &quot;#a19670&quot;))+
scale_fill_manual(values=c(&quot;#4a4534&quot;, &quot;#a19670&quot;))

ggdraw(plot_grid(plot_grid(Sup_Figure_5A, Sup_Figure_5B,ncol=2, align=&#39;v&#39;), rel_widths=c(1, 0.2))) +
  draw_plot_label(c(&quot;A&quot;, &quot;B&quot;), c(0, 0.4), c(1, 1), size = 20)</code></pre>
          </stencila-code-chunk>
          <figcaption>
            <h4 itemscope="" itemtype="http://schema.stenci.la/Heading"
              id="senseless-patterning-in-wing-discs-from-fed-and-starved-genetically-ablated-prothoracic-gland-pgx-and-control-larvae">
              Senseless patterning in wing discs from fed and starved genetically ablated
              prothoracic gland (PGX) and control larvae.</h4>
            <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">(<strong itemscope=""
                itemtype="http://schema.stenci.la/Strong">A</strong>) In PGX larvae, Senseless
              patterning does not progress at all in starved larvae (linear regression: = 0.057,
              p=0.82), but does in fed larvae (linear regression: = 9.76, p&lt;0.01). (<strong
                itemscope="" itemtype="http://schema.stenci.la/Strong">B</strong>) Patterning does
              not progress in starved control larvae but does in fed control larvae, resulting in a
              significant interaction between the effects of time and food on Senseless patterning
              in control larvae (linear regression: <span itemscope=""
                itemtype="http://schema.stenci.la/MathFragment"><span class="mjx-chtml"><span
                    class="mjx-math"
                    aria-label="{F}_{\mathrm{f}\mathrm{o}\mathrm{o}\mathrm{d}\mathrm{*}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}}"><span
                      class="mjx-mrow" aria-hidden="true"><span class="mjx-msubsup"><span
                          class="mjx-base" style="margin-right: -0.106em;"><span
                            class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mi"><span
                                  class="mjx-char MJXc-TeX-math-I"
                                  style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.106em;">F</span></span></span></span></span><span
                          class="mjx-sub"
                          style="font-size: 70.7%; vertical-align: -0.23em; padding-right: 0.071em;"><span
                            class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.446em; padding-bottom: 0.372em; padding-right: 0.066em;">f</span></span></span></span><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.151em; padding-bottom: 0.372em;">o</span></span></span></span><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.151em; padding-bottom: 0.372em;">o</span></span></span></span><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.372em; padding-bottom: 0.372em;">d</span></span></span></span><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.151em; padding-bottom: 0.298em;"></span></span></span></span><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.298em; padding-bottom: 0.372em;">t</span></span></span></span><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.372em; padding-bottom: 0.372em;">i</span></span></span></span><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.151em; padding-bottom: 0.372em;">m</span></span></span></span><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.151em; padding-bottom: 0.372em;">e</span></span></span></span></span></span></span></span></span></span></span></span>
              = 67.98, p&lt;0.001). Control genotypes are the pooled results from both parental
              controls (either the <em itemscope=""
                itemtype="http://schema.stenci.la/Emphasis">phm-GAL4; GAL80ts,</em> or <em
                itemscope="" itemtype="http://schema.stenci.la/Emphasis">UAS-GRIM</em> parental
              strain crossed to w<sup itemscope=""
                itemtype="http://schema.stenci.la/Superscript"><span
                  data-itemtype="http://schema.org/Number">1118</span></sup>). Each point
              corresponds to a wing disc, N<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">PGX - starved</sub> = 67, N<sub
                itemscope="" itemtype="http://schema.stenci.la/Subscript">PGX - fed</sub> = 74,
              N<sub itemscope="" itemtype="http://schema.stenci.la/Subscript">control -
                starved</sub> = 118, N<sub itemscope=""
                itemtype="http://schema.stenci.la/Subscript">control - fed</sub> = 151 across all
              time points.</p>
          </figcaption>
        </figure>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">We again used a second-order
          polynomial regression to model the relationship between Senseless pattern, time after
          third-instar ecdysis, and 20E concentration. The relationship between the linear
          coefficient from our model for Senseless patterning and 20E was best fit with a
          log-logistic rather than a Michaelis–Menten function. For fed PGX larvae, the
          four-parameter logistic function provided the best fit to the data (<a href="#fig9"
            itemscope="" itemtype="http://schema.stenci.la/Link">Figure 9B</a>, <a href="#supp1"
            itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file 1</a>k), whereas
          for starved PGX larvae, the three-parameter logistic function was the best fit (<a
            href="#fig9" itemscope="" itemtype="http://schema.stenci.la/Link">Figure 9D</a>, <a
            href="#supp1" itemscope="" itemtype="http://schema.stenci.la/Link">Supplementary file
            1</a>k). Thus, like Achaete patterning rate, Senseless patterning rate showed a
          threshold responses to 20E concentration.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Collectively, these data
          support a model of disc growth and patterning where ecdysone regulates disc growth as a
          graded response to basal levels of ecdysone, while ecdysone regulates disc patterning as a
          single threshold response.</p>
        <h2 itemscope="" itemtype="http://schema.stenci.la/Heading" id="discussion">Discussion</h2>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Organs are remarkably good at
          achieving correct pattern across a broad range of environmental conditions that generate
          variation in size. While this might seem a simple feat when growth and patterning occur at
          separate times or are regulated by different hormones, it is considerably less simple if
          both growth and patterning occur at the same time and are regulated by the same endocrine
          signal. In this work, we explored how the wing discs of developing <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">D. melanogaster</em> use the same hormonal
          signal to coordinate both their growth and progression of pattern. We found that ecdysone
          simultaneously regulates the plastic growth and robust patterning of the wing disc through
          independent mechanisms: plastic growth responds to ecdysone with a graded response, while
          robust patterning responds with a single threshold response. We propose that these
          differences in response represent a potentially general mechanism through which high
          levels of variation in one organ characteristic, for example, size, could be coordinated
          with low levels of variation in another characteristic of the same organ, for example,
          pattern.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">These data make an important
          contribution to our understanding of how environmental factors, specifically nutrition,
          affect growth and patterning in developing organs in <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Drosophila</em>. During normal development,
          circulating ecdysone levels are low during the first 8 hr of the third larval instar until
          attainment of a critical size initiates a hormonal cascade that causes ecdysone to
          fluctuate through a series of characteristic peaks. Each of these peaks is associated with
          key developmental transitions and prepares the larva for metamorphosis. Low nutrition
          delays attainment of critical size and the initiation of these peaks, but also appears to
          raise basal levels of circulating ecdysone between these peaks <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib42"><span>42</span><span>Lee et
                al.</span><span>2018</span></a></cite>, which slows the growth of the body <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib42"><span>42</span><span>Lee et al.</span><span>2018</span></a></cite>. At
          the same time, low nutrition also lowers the levels of circulating insulin-like peptides,
          further slowing the growth of the body. While low levels of insulin signalling will
          suppress imaginal disc growth, the increase in ecdysone concentrations resulting from
          starvation opposes some of these effects <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib36"><span>36</span><span>Herboso
                  et al.</span><span>2015</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib25"><span>25</span><span>Dye et
                  al.</span><span>2017</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib66"><span>66</span><span>Parker
                  and Shingleton</span><span>2011</span></a></cite></span> by promoting imaginal
          disc growth.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Our data suggest that these
          opposing effects are critical to robust patterning of the wing under different nutritional
          conditions. At low nutritional conditions, low insulin signalling at the beginning of the
          third larval instar slows the growth of the body and the imaginal discs. At this stage,
          growth of the wing imaginal discs is less dependent on ecdysone <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib74"><span>74</span><span>Shingleton
                et al.</span><span>2008</span></a></cite>, evident from the more moderate effects on
          growth of the wing discs during this period in fed PGX larvae. In the middle of the third
          larval instar, however, low nutritional conditions elevate basal levels of ecdysone <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib42"><span>42</span><span>Lee et al.</span><span>2018</span></a></cite>. This
          drives disc growth independent of insulin signalling to ensure the discs are of sufficient
          size to generate viable adult appendages, even as elevated ecdysone suppresses the growth
          of the body as a whole (<cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib7"><span>7</span><span>Caldwell et al.</span><span>2005</span></a></cite>;
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib15"><span>15</span><span>Colombani et
                al.</span><span>2005</span></a></cite>; <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib49"><span>49</span><span>Mirth et
                al.</span><span>2005</span></a></cite>;). At the same time, changes in the tempo of
          the ecdysone fluctuations may ensure that patterning is initiated at the appropriate
          developmental time, when discs are sufficient size to generate a viable adult appendage.
          Three factors therefore appear necessary to achieve variable size but robust patterning
          under a range of nutritional conditions: (1) a graded growth response to ecdysone, (2)
          nutritionally sensitive growth that is independent of ecdysone, and (3) a threshold
          patterning response to ecdysone.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">There is some evidence that our
          findings apply to patterning and growth of the wings in other insect species. In the
          tobacco hornworm <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">Manduca
            sexta</em> and the buckeye butterfly <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Junonia coenia</em>, wing disc growth is
          regulated by both ecdysone and insulin <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib77"><span>77</span><span>Strassburger et
                  al.</span><span>2021</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib67"><span>67</span><span>Parker
                  and Struhl</span><span>2015</span></a></cite></span>. In the butterfly <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">J. coenia,</em> the patterning
          stage of wing discs can be quantified by the extent of tracheal invasion, resulting in
          wing vein patterning <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib48"><span>48</span><span>Miner et al.</span><span>2000</span></a></cite>. In
          this species<em itemscope="" itemtype="http://schema.stenci.la/Emphasis">,</em> wing vein
          patterning progresses independently of wing size in starved versus fed caterpillars <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib48"><span>48</span><span>Miner et al.</span><span>2000</span></a></cite>.
          Thus, the independent regulation of growth and patterning, with growth regulated by both
          insulin and ecdysone signalling, may be a general mechanism to achieve robust patterning
          across a range of wing sizes.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">While ecdysone and insulin
          signalling provide systemic cues that tune organ growth to the environmental conditions,
          morphogens like Wingless and Decapentaplegic (Dpp) act to regulate growth in an
          organ-autonomous manner. The extent to which morphogen gradients respond to these systemic
          cues is unclear, although the activity of morphogens is known to interact with those of
          systemic signals at the level of the target genes. For example, insulin/TOR signalling
          regulates the activity of Yorkie, a downstream effector of patterning morphogens,
          including Wingless and Dpp, which controls the rate of cell division <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib67"><span>67</span><span>Parker and
                Struhl</span><span>2015</span></a></cite>. Similarly, reducing ecdysone signalling
          in the wing reduces the expression of Wingless and reduces Dpp signalling, measured by the
          levels of phosphorylated Mothers against Dpp expression <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib36"><span>36</span><span>Herboso
                  et al.</span><span>2015</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib25"><span>25</span><span>Dye et
                  al.</span><span>2017</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib50"><span>50</span><span>Mirth et
                  al.</span><span>2009</span></a></cite></span>. Taken together, the signalling
          pathways that regulate organ growth in response to environmental conditions interact in
          complex ways with those that regulate organ-autonomous growth, suggesting that these two
          growth-regulating mechanisms are not as independent as previously thought <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib53"><span>53</span><span>Mirth and
                Shingleton</span><span>2019</span></a></cite>.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Although the growth of the disc
          relies on insulin and ecdysone signalling, the progression of patterning for Achaete and
          Senseless in the wing disc appears to be driven by threshold responses to ecdysone. This
          is not to say that the progression of patterning does not depend on environmental
          conditions. Indeed, starvation early in the third instar impedes patterning in both the
          wing and ovary of <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">D.
            melanogaster</em> <span itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib50"><span>50</span><span>Mirth et
                  al.</span><span>2009</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib47"><span>47</span><span>Mendes
                  and Mirth</span><span>2016</span></a></cite></span>. However, rather than
          resulting from a direct effect of insulin signalling on patterning, the block in the
          progression of pattern occurs because insulin signalling controls the timing of the first
          ecdysone pulse in the third larval instar <span itemscope=""
            itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib41"><span>41</span><span>Koyama
                  et al.</span><span>2014</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib63"><span>63</span><span>Ohhara
                  et al.</span><span>2017</span></a></cite></span>. Our results here confirm that
          patterning requires suprathreshold concentrations of ecdysone to be initiated. Further,
          the manner in which ecdysone regulates the progression of patterning ensures that it
          remains robust against further environmental perturbation. By switching on pattern above
          threshold ecdysone concentrations, the disc can continue to pattern across a range of
          environmental conditions, even while growth retains sensitivity to those conditions.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">A similar threshold mechanism
          appears to regulate patterning in the wing discs of other insects. As for <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Drosophila,</em> the earliest stages of wing
          patterning depend on nutrition in <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">J. coenia</em>. If caterpillars are starved
          before the wing discs begin to pattern, then their discs remain small and their veins
          unpatterned <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib48"><span>48</span><span>Miner et al.</span><span>2000</span></a></cite>. In
          caterpillars starved at later stages after disc patterning has been initiated, the wing
          discs are small but reach the same vein patterning stage as those of fed control animals.
          Whether or not the initiation of patterning in <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">J. coenia</em> also depends on ecdysone has
          yet to be determined.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">At first glance, the
          observation that patterning shows a threshold response to ecdysone may not be surprising.
          In any given cell, patterning is inherently regulated by threshold responses because the
          expression of the patterning gene product is either on or off in that cell. However, our
          patterning scheme considers the progression of patterning across the entire field of cells
          that make up the wing disc. Cells across the wing disc turn on Achaete and Senseless
          expression at different times, resulting in a continuous progression of pattern with time
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib64"><span>64</span><span>Oliveira et al.</span><span>2014</span></a></cite>.
          Furthermore, like growth, the progression of pattern can vary in rate depending on
          environmental and hormonal conditions <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib64"><span>64</span><span>Oliveira
                et al.</span><span>2014</span></a></cite>. Consequently, the progression of
          patterning could, in principle, also show a graded response to ecdysone levels. The
          observation that once ecdysone concentrations are above threshold, the rate of patterning
          for Achaete and Senseless is independent of ecdysone provides evidence that the rate of
          patterning across an entire organ can also show a threshold response: an assumption that,
          hitherto, has not been tested.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">What determines how progression
          of pattering unfolds through time is unclear. We did not observe discs progressing from
          stage 1 immediately to stage 7 within a single 5 hr time interval even at the highest 20E
          concentrations. This suggests that there are additional temporal factors that regulate the
          order of patterning progression. Almost certainly, interactions between the gene
          regulatory networks that regulate patterning control how patterning progresses across
          regions of the wing disc. We have very little understanding if/how the different regions
          of the wing communicate with each other to achieve this. In principle, differences between
          when cells turn on Achaete and Senseless across the disc could arise in response to other
          developmental signals, such as from the Dpp, Wingless, or Hedgehog morphogen gradients
          responsible for correctly scaling and patterning the wing.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Part of this temporal signature
          might arise from ecdysone itself. In this study, we exposed animals to tonic
          concentrations of ecdysone. Developing larvae, however, secrete four pulses of
          ecdysteroids between the moult to the third instar and pupariation <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib83"><span>83</span><span>Warren et
                al.</span><span>2006</span></a></cite>. We have little understanding of how
          developmental information is encoded within these pulses. In principle, individual pulses
          could either prime tissues to become responsive to hormones or could alter their
          sensitivity – as the early ecdysone pulse does for wing disc growth and patterning <span
            itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib50"><span>50</span><span>Mirth et
                  al.</span><span>2009</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib47"><span>47</span><span>Mendes
                  and Mirth</span><span>2016</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib74"><span>74</span><span>Shingleton et
                  al.</span><span>2008</span></a></cite></span>. Future studies comparing the
          difference between tonic and phasic exposure to hormone would help clarify the roles of
          the ecdysone pulses.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">While our study has focussed on
          contrasting the robustness of patterning with plasticity of growth, depending on what is
          being measured there are instances where we expect patterning to also show plasticity
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib54"><span>54</span><span>Mirth et al.</span><span>2021</span></a></cite>.
          For example, although the specification of cell types in the correct location within an
          organ may show little variation across environmental conditions, the number of structures
          specified can vary. The total number of abdominal and sternopleural bristles varies with
          temperature <span itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib56"><span>56</span><span>Moreteau and
                  David</span><span>2005</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib55"><span>55</span><span>Moreteau
                  et al.</span><span>2003</span></a></cite></span>, as does the number of terminal
          filament stacks that are specified in the ovary, which is also affected by nutrition <span
            itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a
                href="#bib19"><span>19</span><span>David</span><span>1970</span></a></cite><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib23"><span>23</span><span>Delpuech et
                  al.</span><span>1995</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib33"><span>33</span><span>Green
                  and Extavour</span><span>2014</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib37"><span>37</span><span>Hodin
                  and Riddiford</span><span>2000</span></a></cite></span>. Plasticity in the number
          of bristle cells or terminal filament stacks presumably occurs because the mechanisms that
          specify the number of each structure do not scale with organ size. In other cases, the
          location of specific cell types may also be plastic. For example, there is extensive
          literature exploring how the relative positions of veins in the wings of <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">D. melanogaster</em> and other insects are
          affected by environmental factors such as nutrition and temperature (e.g., <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib21"><span>21</span><span>Debat et al.</span><span>2003</span></a></cite>;
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib22"><span>22</span><span>Debat et al.</span><span>2009</span></a></cite>;
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib65"><span>65</span><span>Outomuro et al.</span><span>2013</span></a></cite>;
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib5"><span>5</span><span>Bitner-Mathé and
                Klaczko</span><span>1999</span></a></cite>). Plasticity in wing shape is likely to
          be more complex and may involve a process that acts at many different points during wing
          development <span itemscope="" itemtype="http://schema.stenci.la/CiteGroup"><cite
              itemscope="" itemtype="http://schema.stenci.la/Cite"><a
                href="#bib44"><span>44</span><span>Matamoro-Vidal et
                  al.</span><span>2015</span></a></cite><cite itemscope=""
              itemtype="http://schema.stenci.la/Cite"><a href="#bib14"><span>14</span><span>Cobham
                  and Mirth</span><span>2020</span></a></cite></span>. Future studies targeting how
          the mechanisms that establish the position of cell types differ from those that determine
          the number of cells of a given type would allow us to further define what makes traits
          either sensitive or robust towards changes in environmental conditions, and at what level.
        </p>
        <h2 itemscope="" itemtype="http://schema.stenci.la/Heading" id="materials-and-methods">
          Materials and methods</h2>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="fly-stocks-and-rearing-conditions">Fly stocks and rearing conditions</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">We manipulated growth rates and
          developmental timing by altering the rates of ecdysone synthesis in developing <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">D. melanogaster</em> larvae. To
          accelerate the rates of ecdysone synthesis, we used the progeny from <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">w<sup itemscope=""
              itemtype="http://schema.stenci.la/Superscript"><span
                data-itemtype="http://schema.org/Number">1118</span></sup>;phantom-_GAL4, which is
            expressed in the PGs, crossed with yw _flp; UAS InR29.4</em> (<em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">phm&gt;InR</em>). We decreased rates of
          ecdysone synthesis by crossing <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">P0206-GAL4</em>, which drives expression
          throughout the ring gland, with <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">yw; UAS PTEN</em> (<em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">P0206&gt;PTEN</em>). Even though <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">P0206</em>-GAL4 is a weaker
          GAL4 driver for the PG and also drives expression in the corpora allata, we chose to use
          it to drive <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">UAS PTEN</em>
          because <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">phm&gt;PTEN</em>
          larvae die as first-instar larvae <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib49"><span>49</span><span>Mirth et
                al.</span><span>2005</span></a></cite>. The parental lines <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">yw flp; UAS InR29.4</em> (+<em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">&gt;InR</em>) and <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">yw; UAS PTEN</em> (+<em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">&gt;PTEN</em>) were used as a reference for
          the <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">phm&gt;InR</em> and <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">P0206&gt;PTEN</em> genotypes,
          respectively.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Flies of the above genotypes
          were raised from timed egg collections (2–6 hr) on cornmeal/molasses medium containing 45
          g of molasses, 75 g of sucrose, 70 g of cornmeal, 10 g of agar, 1100 ml of water, and 25
          ml of a 10% Nipagin solution per litre. Larvae were reared at low density (200 eggs per 60
          × 15 mm Petri dish) in a 12 hr light-dark cycle with 70% humidity and maintained at 25°C
          unless stated otherwise.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">We used a transgenic
          combination that allowed us to genetically ablate the PG and eliminate native ecdysone
          synthesis specifically in the third larval instar. We crossed a <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">tub-GAL80<sup itemscope=""
              itemtype="http://schema.stenci.la/Superscript">ts</sup>, phantom GAL4</em> strain with
          <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">UAS Grim</em> to generate <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">PGX</em> progeny <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib36"><span>36</span><span>Herboso et al.</span><span>2015</span></a></cite>.
          GAL80<sup itemscope="" itemtype="http://schema.stenci.la/Superscript">ts</sup> is a
          repressor of GAL4 active at temperatures lower than 22°C <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib45"><span>45</span><span>McGuire et
                al.</span><span>2003</span></a></cite>. Rearing PGX larvae at 17°C allows GAL80<sup
            itemscope="" itemtype="http://schema.stenci.la/Superscript">ts</sup> to remain active,
          thus the <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">phantom GAL4</em>
          cannot drive the expression of <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">UAS grim</em> to promote cell death. Under
          these conditions, larvae can moult, pupariate, and complete metamorphosis <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib36"><span>36</span><span>Herboso et al.</span><span>2015</span></a></cite>.
          Changing the larval rearing temperature to 29°C disables GAL80<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript">ts</sup> activity, thus ablating the PG
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib36"><span>36</span><span>Herboso et al.</span><span>2015</span></a></cite>.
          The progeny of the inbred control strain, <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">w1118</em>, crossed with one of two parental
          lines, either <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">phantom</em>-GAL4 (<em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">PG</em>&gt;+) or <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">UAS Grim</em> (+&gt;<em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">Grim</em>), were used as controls for
          genetic background effects. The parental controls were reared under the same thermal
          conditions as PGX larvae.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Crosses, egg collections, and
          larval rearing were done on the cornmeal/molasses medium (above) for the experiments in <a
            href="#fig2" itemscope="" itemtype="http://schema.stenci.la/Link">Figures 2</a><a
            href="#fig6" itemscope="" itemtype="http://schema.stenci.la/Link"><span
              data-itemtype="http://schema.org/Number">6</span></a> or, for the experiments in <a
            href="#fig7" itemscope="" itemtype="http://schema.stenci.la/Link">Figures 7</a><a
            href="#fig9" itemscope="" itemtype="http://schema.stenci.la/Link"><span
              data-itemtype="http://schema.org/Number">9</span></a>, on Sugar-Yeast-Agar (SYA)
          medium: 50 g of autolysed Brewer’s yeast powder (MP Biomedicals), 100 g of sugar, 10 g of
          agar, and 1200 ml of water. In addition, we added 3 ml of proprionic acid and 3 g of
          nipagen to the SYA medium to prevent bacterial and fungal growth. Egg collections were
          performed on SYA medium for 4 hr at 25°C or overnight at 17°C and larvae were reared at
          controlled densities of 200 eggs per food plate (60 × 15 mm Petri dish filled with SYA
          medium) at 17°C, as described previously <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib36"><span>36</span><span>Herboso et
                al.</span><span>2015</span></a></cite>.</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="animal-staging-and-developmental-time">Animal staging and developmental time</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To measure the effects of
          changes in the rates in ecdysone synthesis on wing disc growth and wing disc patterning,
          larvae were staged into 1 hr cohorts at ecdysis to the third larval instar as in <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib49"><span>49</span><span>Mirth et al.</span><span>2005</span></a></cite> and
          <cite itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib50"><span>50</span><span>Mirth et al.</span><span>2009</span></a></cite>. To
          do this, food plates were flooded with 20% sucrose and all second-instar larvae were
          transferred to a new food plate. After 1 hr, the food plate was flooded once again with
          20% sucrose and the newly moulted third-instar larvae were collected and transferred to
          new food plates and left to grow until the desired time interval. Animals were staged and
          their wing discs dissected at defined intervals after the larval moult as in <cite
            itemscope="" itemtype="http://schema.stenci.la/Cite"><a
              href="#bib64"><span>64</span><span>Oliveira et al.</span><span>2014</span></a></cite>.
        </p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">For the experiments in <a
            href="#fig7" itemscope="" itemtype="http://schema.stenci.la/Link">Figures 7</a><a
            href="#fig9" itemscope="" itemtype="http://schema.stenci.la/Link"><span
              data-itemtype="http://schema.org/Number">9</span></a>, PGX, <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">phm&gt;,</em> and <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">&gt;Grim</em> genotypes, larvae were raised
          from egg to second instar at 17°C. Larvae were staged into 2 hr cohorts at ecdysis to the
          third larval instar using the methods described above. We separated female and male larvae
          by examining them for the presence of testes, which are significantly larger than the
          ovaries and visible even in newly moulted males.</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="exogenous-ecdysone-feeding-treatments">Exogenous ecdysone feeding treatments</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To show that ecdysone could
          rescue patterning and growth in PGX larvae (<a href="#fig4" itemscope=""
            itemtype="http://schema.stenci.la/Link">Figure 4C and D</a>), we added either 0.15 mg of
          20E (Cayman Chemical, item no. 16145) dissolved in ethanol, or an equivalent volume of
          ethanol, to 1 ml of standard food. Both the ethanol- and ecdysone-supplemented food were
          allowed to sit at room temperature for at least 4 hr to evaporate excess ethanol before
          use. Twelve larvae were transferred to one of the two supplemented foods either at 0 hr
          AL3E and left to feed for 42 hr or at 42 hr AL3E and left to feed for 24 hr.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To determine the relative
          contributions of nutrition-dependent signalling or ecdysone to growth and patterning, we
          fed newly moulted PGX and control larvae 1 ml of starvation medium (1% sucrose with 1%
          agar) supplemented with either 0.15 mg of 20E dissolved in ethanol or an equivalent volume
          of ethanol (Figure S4). Supplemented food was left at room temperature for at least 4 hr
          to evaporate excess off ethanol before use. Larvae were collected at 24 hr AL3E for tissue
          dissection.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">For the 20E dose–response
          experiments, we conducted an initial pilot that showed that supplementing the food with
          100 ng of ecdysone/mg food could rescue most of the Achaete and Senseless patterning in
          PGX wing discs. We collected newly moulted third instar larvae, separated the sexes, and
          then transferred 10–20 larvae to either sucrose food (20% sucrose, 1% agar; starved) or
          SYA food (fed) at 29°C. We fed these larvae on one of six 20E concentrations: 0, 6.25,
          12.5, 25, 50, or 100 ng of 20E/mg food. We added the same volume of ethanol to all
          treatments.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">To quantify the relationship
          between the concentration of 20E administered and the concentration of ecdysteroids in the
          hemolymph, we allowed newly ecdysed larvae to feed on either sucrose or SYA food that had
          been supplemented with one of the six concentrations of 20E for 20 hr at 29°C. We then
          transferred them onto either sucrose food or SYA food that did not contain ecdysone but
          was dyed blue. They were left to feed for 2 hr until their guts were filled with blue
          food. This extra step was taken so that we could be sure that our hemolymph ecdysone
          titres were not contaminated with ecdysone from the food. 30–40 larvae were then weighed
          as a group and transferred to five times their weight in volume of ice-cold methanol.
          Larvae were homogenized and ecdysone titres were determined using a 20-Hydroxyecdysone
          Enzyme ImmunoAssay Kit (Cayman Chemical, item no. 501390) as per the manufacturer’s
          instructions.</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="dissections-and-immunocytochemistry">Dissections and immunocytochemistry</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">For each sample, 10–20 larvae
          were dissected on ice-cold phosphate-buffered saline (PBS) and fixed in 4% formaldehyde in
          PBS overnight at 4°C. After fixation, the tissue was washed four times (15 min per wash)
          with 0.3% Triton X-100 in PBS (PBT), then blocked for 30 min at room temperature in 2%
          heat-inactivated normal donkey serum in PBT. After blocking, the tissue was incubated in a
          primary antibody solution diluted with 2% heat-inactivated normal donkey serum in PBT
          overnight at 4°C. We used the guinea pig anti-Senseless (<cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib61"><span>61</span><span>Nolo et
                al.</span><span>2000</span></a></cite>, 1:1000) and mouse anti-Achaete
          (Developmental Studies Hybridoma Bank, contributor J. Skeath, supernatant, 1:10) primary
          antibodies. To compare signal across tissues, we stained for both antigens simultaneously.
          The washing and blocking procedure was repeated after primary antibody incubation, and
          then the tissue was incubated in a secondary antibody (1:200 each of anti-guinea pig
          [Alexa Fluor 546] and anti-mouse [Alexa Fluor 488]) overnight at 4°C. The tissues were
          washed with PBT and rinsed with PBS, and then the wing imaginal discs were mounted on
          poly-l-lysine-coated coverslips using Fluoromount-G (SouthernBiotech). Tissues were imaged
          using either a Leica LSM 510 or a Nikon C1 upright confocal microscope and processed using
          ImageJ (version 2.0) and Adobe Photoshop CC 2017.</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading"
          id="quantifications-of-wing-imaginal-disc-size-and-achaete-and-senseless-pattern">
          Quantifications of wing imaginal disc size and Achaete and Senseless pattern</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">We quantified wing disc size
          using disc area as a proxy. All quantifications were done using ImageJ. Wing discs show
          exponential growth in the third instar. Thus, we studied the growth trajectories of the
          discs by ln-transforming disc area.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Achaete and Senseless stage was
          quantified using the staging scheme developed by <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a href="#bib64"><span>64</span><span>Oliveira
                et al.</span><span>2014</span></a></cite>, associating each of the wing imaginal
          discs to an Achaete or Senseless stage varying from 1 to 7.</p>
        <h3 itemscope="" itemtype="http://schema.stenci.la/Heading" id="statistical-analysis">
          Statistical analysis</h3>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">All the analyses were conducted
          in R and the annotated R markdown scripts, and data for the analyses are deposited on
          Figshare (doi: <a href="https://doi.org/10.26180/13393676" itemscope=""
            itemtype="http://schema.stenci.la/Link">10.26180/13393676</a>).</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">For the relationship between
          time after third-instar ecdysis and disc size (log µm<sup itemscope=""
            itemtype="http://schema.stenci.la/Superscript"><span
              data-itemtype="http://schema.org/Number">2</span></sup>) or disc pattern (Achaete or
          Senseless), we fit either linear or Gompertz models and selected the model that best fit
          the data using ANOVA and AIC. The Gompertz model was parameterized as <span itemscope=""
            itemtype="http://schema.stenci.la/MathFragment"><span class="mjx-chtml"><span
                class="mjx-math" aria-label="y=a{e}^{{-b*c}^{x}}"><span class="mjx-mrow"
                  aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                      style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span
                    class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"
                      style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span
                    class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I"
                      style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span
                    class="mjx-msubsup"><span class="mjx-base"><span class="mjx-texatom"><span
                          class="mjx-mrow"><span class="mjx-mi"><span
                              class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span></span></span><span
                      class="mjx-sup"
                      style="font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;"><span
                        class="mjx-texatom" style=""><span class="mjx-mrow"><span
                            class="mjx-msubsup"><span class="mjx-base"><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.298em; padding-bottom: 0.446em;"></span></span><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span
                                    class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                                      style="padding-top: 0.151em; padding-bottom: 0.298em;"></span></span><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span></span></span></span><span
                              class="mjx-sup"
                              style="font-size: 83.3%; vertical-align: 0.477em; padding-left: 0px; padding-right: 0.06em;"><span
                                class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span></span></span></span></span></span></span></span>
          , where <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">y</em> is disc
          size/pattern, <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">x</em> is time,
          <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">a</em> is the asymptote of
          <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">y</em>, <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">b</em> controls where along the x-axis the
          curve is positioned, and <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">c</em> is the scaling constant, such that
          <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">c</em> = <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">eg,</em> where <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">g</em> is the growth/patterning rate (thus,
          the higher <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">g</em> the lower
          <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">c</em>). To compare the
          parameters of linear models between treatments and genotypes, we used ANOVA. To compare
          the parameters of Gompertz models between treatments and genotypes, we used ANOVA to
          compare the fit of models that assign the same constants across groups versus models that
          assigned group-specific constants.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">For the relationship between
          disc size (log µm<sup itemscope="" itemtype="http://schema.stenci.la/Superscript"><span
              data-itemtype="http://schema.org/Number">2</span></sup>) and Senseless pattern, we fit
          a four-parameter logistic model parametrized as <span itemscope=""
            itemtype="http://schema.stenci.la/MathFragment"><span class="mjx-chtml"><span
                class="mjx-math" aria-label="y=c+\frac{(d-c)}{1+{e}^{\left(b-x\right)/a}}"><span
                  class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span
                      class="mjx-char MJXc-TeX-math-I"
                      style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span
                    class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"
                      style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span
                    class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I"
                      style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span
                    class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R"
                      style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span
                    class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked"
                      style="width: 3.517em; padding: 0px 0.12em;"><span class="mjx-numerator"
                        style="font-size: 70.7%; width: 4.974em; top: -1.706em;"><span
                          class="mjx-mrow" style=""><span class="mjx-mo"><span
                              class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.298em; padding-bottom: 0.446em;"></span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span><span
                        class="mjx-denominator"
                        style="font-size: 70.7%; width: 4.974em; bottom: -1.042em;"><span
                          class="mjx-mrow" style=""><span class="mjx-mn"><span
                              class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span
                            class="mjx-msubsup"><span class="mjx-base"><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span></span></span><span
                              class="mjx-sup"
                              style="font-size: 83.3%; vertical-align: 0.408em; padding-left: 0px; padding-right: 0.06em;"><span
                                class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                    class="mjx-mrow"><span class="mjx-mo"><span
                                        class="mjx-char MJXc-TeX-main-R"
                                        style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span
                                      class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                        style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span
                                      class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                                        style="padding-top: 0.298em; padding-bottom: 0.446em;"></span></span><span
                                      class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                        style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span
                                      class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                                        style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span><span
                                    class="mjx-texatom"><span class="mjx-mrow"><span
                                        class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                                          style="padding-top: 0.446em; padding-bottom: 0.593em;">/</span></span></span></span><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span></span></span></span></span></span></span><span
                        style="border-bottom: 1.3px solid; top: -0.296em; width: 3.517em;"
                        class="mjx-line"></span></span><span
                      style="height: 1.943em; vertical-align: -0.737em;"
                      class="mjx-vsize"></span></span></span></span></span></span> where <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">y</em> is disc pattern, <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">x</em> is disc size, <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">c</em> is the minimum
          asymptote, <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">d</em> is the
          maximum asymptote, <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">b</em> is
          the inflection point, and <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">a</em> is the scaling constant, such that
          <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">a</em> = 1 <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">/k</em>, where <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">k</em> is the logistic growth rate. We again
          used ANOVA to compare the fit of models that assign the same parameters across groups
          versus models that assigned group-specific parameters. The relationship between disc size
          and Achaete pattern was fit using a linear model and compared across treatments using
          ANOVA.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">We used ANOVA to compare disc
          size/pattern at specific time points between treatments and genotypes using a Tukey’s HSD
          test to allow comparison among groups.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">Finally, to compare the effects
          of 20E supplementation in the diet on the progression of wing disc growth, Achaete
          patterning, and Senseless patterning, we fit a second-order orthogonal polynomial
          regression using disc size/patterning stage as our dependent variable, and 20E
          concentration and linear and quadratic terms for time as fixed effects. Fitting a single
          model to the data allowed us to compare the same model parameters for growth and
          patterning. We then extracted the linear rate of change at each 20E concentration using
          the <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">emtrends</em> function of
          the <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">emmeans</em> package in
          <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">R</em> <cite itemscope=""
            itemtype="http://schema.stenci.la/Cite"><a
              href="#bib43"><span>43</span><span>Lenth</span><span>2020</span></a></cite>. The
          changes in growth/patterning rate with 20E concentration were modelled using three
          nonlinear functions: (1) a continuous Michaelis–Menten function: <span itemscope=""
            itemtype="http://schema.stenci.la/MathFragment"><span class="mjx-chtml"><span
                class="mjx-math" aria-label="y=c+\frac{(d-c)}{1+b / x}"><span class="mjx-mrow"
                  aria-hidden="true"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                      style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span
                    class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"
                      style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span
                    class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I"
                      style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span
                    class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R"
                      style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span
                    class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked"
                      style="width: 2.106em; padding: 0px 0.12em;"><span class="mjx-numerator"
                        style="font-size: 70.7%; width: 2.979em; top: -1.706em;"><span
                          class="mjx-mrow" style=""><span class="mjx-mo"><span
                              class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.298em; padding-bottom: 0.446em;"></span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span><span
                        class="mjx-denominator"
                        style="font-size: 70.7%; width: 2.979em; bottom: -0.999em;"><span
                          class="mjx-mrow" style=""><span class="mjx-mn"><span
                              class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span
                            class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span
                                  class="mjx-char MJXc-TeX-main-R"
                                  style="padding-top: 0.446em; padding-bottom: 0.593em;">/</span></span></span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span><span
                        style="border-bottom: 1.3px solid; top: -0.296em; width: 2.106em;"
                        class="mjx-line"></span></span><span
                      style="height: 1.913em; vertical-align: -0.707em;"
                      class="mjx-vsize"></span></span></span></span></span></span>, where <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">c</em> is <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">y</em> at <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">x</em> = 0<em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">, d</em> is the maximum asymptote, and <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">b</em> is <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">x</em> where <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">y</em> is halfway between <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">c</em> and <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">d</em>; (2) a threshold three-parameter
          log-logistic function: <span itemscope=""
            itemtype="http://schema.stenci.la/MathFragment"><span class="mjx-chtml"><span
                class="mjx-math"
                aria-label="y=\frac{d}{1+{e}^{b\left(\mathrm{log}x-\mathrm{log}a\right)}}"><span
                  class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span
                      class="mjx-char MJXc-TeX-math-I"
                      style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span
                    class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"
                      style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span
                    class="mjx-mfrac MJXc-space3"><span class="mjx-box MJXc-stacked"
                      style="width: 4.729em; padding: 0px 0.12em;"><span class="mjx-numerator"
                        style="font-size: 70.7%; width: 6.688em; top: -1.41em;"><span class="mjx-mi"
                          style=""><span class="mjx-char MJXc-TeX-math-I"
                            style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span></span><span
                        class="mjx-denominator"
                        style="font-size: 70.7%; width: 6.688em; bottom: -1.042em;"><span
                          class="mjx-mrow" style=""><span class="mjx-mn"><span
                              class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span
                            class="mjx-msubsup"><span class="mjx-base"><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span></span></span><span
                              class="mjx-sup"
                              style="font-size: 83.3%; vertical-align: 0.408em; padding-left: 0px; padding-right: 0.06em;"><span
                                class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span
                                    class="mjx-mrow"><span class="mjx-mo"><span
                                        class="mjx-char MJXc-TeX-main-R"
                                        style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span
                                      class="mjx-texatom"><span class="mjx-mrow"><span
                                          class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                            style="padding-top: 0.372em; padding-bottom: 0.372em;">l</span></span><span
                                          class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                            style="padding-top: 0.151em; padding-bottom: 0.372em;">o</span></span><span
                                          class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                            style="padding-top: 0.151em; padding-bottom: 0.519em;">g</span></span></span></span><span
                                      class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                        style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span
                                      class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                                        style="padding-top: 0.298em; padding-bottom: 0.446em;"></span></span><span
                                      class="mjx-texatom"><span class="mjx-mrow"><span
                                          class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                            style="padding-top: 0.372em; padding-bottom: 0.372em;">l</span></span><span
                                          class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                            style="padding-top: 0.151em; padding-bottom: 0.372em;">o</span></span><span
                                          class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                            style="padding-top: 0.151em; padding-bottom: 0.519em;">g</span></span></span></span><span
                                      class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                        style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span
                                      class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                                        style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></span></span></span><span
                        style="border-bottom: 1.3px solid; top: -0.296em; width: 4.729em;"
                        class="mjx-line"></span></span><span
                      style="height: 1.734em; vertical-align: -0.737em;"
                      class="mjx-vsize"></span></span></span></span></span></span>, where <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">d</em> is the maximum
          asymptote, <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">b</em> is the rate
          of increase, and <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">a</em> is
          the inflection point; and (3) a threshold four-parameter log-logistic function: <span
            itemscope="" itemtype="http://schema.stenci.la/MathFragment"><span
              class="mjx-chtml"><span class="mjx-math"
                aria-label="y=c+\frac{(d-c)}{1+{e}^{b\left(\mathrm{log}x-\mathrm{log}a\right)}}"><span
                  class="mjx-mrow" aria-hidden="true"><span class="mjx-mi"><span
                      class="mjx-char MJXc-TeX-math-I"
                      style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span
                    class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R"
                      style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span
                    class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I"
                      style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span
                    class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R"
                      style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span
                    class="mjx-mfrac MJXc-space2"><span class="mjx-box MJXc-stacked"
                      style="width: 4.729em; padding: 0px 0.12em;"><span class="mjx-numerator"
                        style="font-size: 70.7%; width: 6.688em; top: -1.706em;"><span
                          class="mjx-mrow" style=""><span class="mjx-mo"><span
                              class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.446em; padding-bottom: 0.298em; padding-right: 0.003em;">d</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.298em; padding-bottom: 0.446em;"></span></span><span
                            class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                              style="padding-top: 0.225em; padding-bottom: 0.298em;">c</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span><span
                        class="mjx-denominator"
                        style="font-size: 70.7%; width: 6.688em; bottom: -1.042em;"><span
                          class="mjx-mrow" style=""><span class="mjx-mn"><span
                              class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.372em; padding-bottom: 0.372em;">1</span></span><span
                            class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                              style="padding-top: 0.298em; padding-bottom: 0.446em;">+</span></span><span
                            class="mjx-msubsup"><span class="mjx-base"><span
                                class="mjx-texatom"><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.225em; padding-bottom: 0.298em;">e</span></span></span></span></span><span
                              class="mjx-sup"
                              style="font-size: 83.3%; vertical-align: 0.408em; padding-left: 0px; padding-right: 0.06em;"><span
                                class="mjx-texatom" style=""><span class="mjx-mrow"><span
                                    class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                      style="padding-top: 0.446em; padding-bottom: 0.298em;">b</span></span><span
                                    class="mjx-mrow"><span class="mjx-mo"><span
                                        class="mjx-char MJXc-TeX-main-R"
                                        style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span
                                      class="mjx-texatom"><span class="mjx-mrow"><span
                                          class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                            style="padding-top: 0.372em; padding-bottom: 0.372em;">l</span></span><span
                                          class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                            style="padding-top: 0.151em; padding-bottom: 0.372em;">o</span></span><span
                                          class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                            style="padding-top: 0.151em; padding-bottom: 0.519em;">g</span></span></span></span><span
                                      class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                        style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span
                                      class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                                        style="padding-top: 0.298em; padding-bottom: 0.446em;"></span></span><span
                                      class="mjx-texatom"><span class="mjx-mrow"><span
                                          class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                            style="padding-top: 0.372em; padding-bottom: 0.372em;">l</span></span><span
                                          class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                            style="padding-top: 0.151em; padding-bottom: 0.372em;">o</span></span><span
                                          class="mjx-mi"><span class="mjx-char MJXc-TeX-main-R"
                                            style="padding-top: 0.151em; padding-bottom: 0.519em;">g</span></span></span></span><span
                                      class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I"
                                        style="padding-top: 0.225em; padding-bottom: 0.298em;">a</span></span><span
                                      class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"
                                        style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span></span></span></span></span><span
                        style="border-bottom: 1.3px solid; top: -0.296em; width: 4.729em;"
                        class="mjx-line"></span></span><span
                      style="height: 1.943em; vertical-align: -0.737em;"
                      class="mjx-vsize"></span></span></span></span></span></span>, where <em
            itemscope="" itemtype="http://schema.stenci.la/Emphasis">c</em> is the minimum
          asymptote, <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">d</em> is the
          maximum asymptote, <em itemscope="" itemtype="http://schema.stenci.la/Emphasis">b</em> is
          the rate of increase, and <em itemscope=""
            itemtype="http://schema.stenci.la/Emphasis">a</em> is the inflection point. For each
          model, we calculated the AIC and BIC to allow model selection. The model that produces the
          lowest AIC and BIC value best fits the data.</p>
        <p itemscope="" itemtype="http://schema.stenci.la/Paragraph">For all parametric tests, we
          checked for homoscedasticity and normality of errors.</p>
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