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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Anim. Sci.</journal-id>
<journal-title-group>
<journal-title>Frontiers in Animal Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Anim. Sci.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">2673-6225</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fanim.2025.1624560</article-id>
<article-version article-version-type="Version of Record" vocab="NISO-RP-8-2008"/>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Original Research</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Trace minerals for maintenance and weight gain in male and female hair sheep</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name><surname>Justino</surname><given-names>Evandra da Silva</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
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<contrib contrib-type="author">
<name><surname>Santos</surname><given-names>Edson Mauro</given-names></name>
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<contrib contrib-type="author">
<name><surname>Abreu</surname><given-names>Matheus Lima Corr&#xea;a</given-names></name>
<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
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<contrib contrib-type="author">
<name><surname>Herbster</surname><given-names>Caio Julio Lima</given-names></name>
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<contrib contrib-type="author">
<name><surname>Brito Neto</surname><given-names>Antonio de Sousa</given-names></name>
<xref ref-type="aff" rid="aff4"><sup>4</sup></xref>
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<contrib contrib-type="author">
<name><surname>Marcondes</surname><given-names>Marcos In&#xe1;cio</given-names></name>
<xref ref-type="aff" rid="aff5"><sup>5</sup></xref>
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<contrib contrib-type="author">
<name><surname>Silva</surname><given-names>Luciano Pinheiro da</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
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<contrib contrib-type="author">
<name><surname>Bezerra</surname><given-names>Leilson Rocha</given-names></name>
<xref ref-type="aff" rid="aff6"><sup>6</sup></xref>
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<contrib contrib-type="author">
<name><surname>Santos</surname><given-names>Stefanie Alvarenga</given-names></name>
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<contrib contrib-type="author">
<name><surname>Oliveira</surname><given-names>Ronaldo Lopes</given-names></name>
<xref ref-type="aff" rid="aff7"><sup>7</sup></xref>
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<contrib contrib-type="author" corresp="yes">
<name><surname>Pereira</surname><given-names>Elzania Sales</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>*</sup></xref>
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<aff id="aff1"><label>1</label><institution>Department of Animal Science, Federal University of Ceara</institution>, <city>Fortaleza</city>,&#xa0;<country country="br">Brazil</country></aff>
<aff id="aff2"><label>2</label><institution>Department of Animal Science, Federal University of Paraiba</institution>, <city>Areia</city>,&#xa0;<country country="br">Brazil</country></aff>
<aff id="aff3"><label>3</label><institution>Department of Animal Science, Federal University of Mato Grosso</institution>, <city>Cuiaba</city>,&#xa0;<country country="br">Brazil</country></aff>
<aff id="aff4"><label>4</label><institution>Department of Animal Science, Federal University of Vi&#xe7;osa</institution>, <city>Minas Gerais</city>,&#xa0;<country country="br">Brazil</country></aff>
<aff id="aff5"><label>5</label><institution>William H. Miner Agricultural Research Institute</institution>, <city>Chazy</city>, <state>NY</state>,&#xa0;<country country="us">United States</country></aff>
<aff id="aff6"><label>6</label><institution>Center of Health and Agricultural Technology, Federal University of Campina Grande</institution>, <city>Patos</city>,&#xa0;<country country="br">Brazil</country></aff>
<aff id="aff7"><label>7</label><institution>Department of Veterinary Medicine and Animal Science, Federal University of Bahia</institution>, <city>Salvador</city>,&#xa0;<country country="br">Brazil</country></aff>
<author-notes>
<corresp id="c001"><label>*</label>Correspondence: Elzania Sales Pereira, <email xlink:href="mailto:elzania@hotmail.com">elzania@hotmail.com</email></corresp>
</author-notes>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2025-09-17">
<day>17</day>
<month>09</month>
<year>2025</year>
</pub-date>
<pub-date publication-format="electronic" date-type="collection">
<year>2025</year>
</pub-date>
<volume>6</volume>
<elocation-id>1624560</elocation-id>
<history>
<date date-type="received">
<day>07</day>
<month>05</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>18</day>
<month>08</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2025 Justino, Santos, Abreu, Herbster, Brito Neto, Marcondes, Silva, Bezerra, Santos, Oliveira and Pereira.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Justino, Santos, Abreu, Herbster, Brito Neto, Marcondes, Silva, Bezerra, Santos, Oliveira and Pereira</copyright-holder>
<license>
<ali:license_ref start_date="2025-09-17">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</license-p>
</license>
</permissions>
<abstract>
<p>The objective of this study was to estimate the net requirements for gain (NCu<sub>g</sub>, NFe<sub>g</sub>; NMn<sub>g</sub>; NZn<sub>g</sub>, NCo<sub>g</sub>, and NCr<sub>g</sub>) and maintenance (NCu<sub>m</sub>, NFe<sub>m</sub>; NMn<sub>m</sub>, NZn<sub>m</sub>, NCo<sub>m</sub>; and NCr<sub>m</sub>) in males and female hair sheep. Data from six studies, comprising 248 individual records (139 non-castrated males, 75 castrated males, and 34 females), were used to estimate net trace mineral requirements for weight gain. For maintenance requirements, 52 observations (26 intact and 26 castrated males) were analyzed. A meta-analytical approach was employed, incorporating non-linear mixed-effects models with the study treated as a random effect. Model selection was guided by the corrected Akaike information criterion (AICc) and some AICc-derived functions (Akaike difference, model probability, evidence ratio, and number of parameters of the fitted combination), which indicated that heterogeneous variance functions provided a better fit, with minimal model selection uncertainty. The final models selected effectively accounted for variability associated with sex and exhibited high confidence levels (model weights w &#x2265; 0.9), supporting their adequacy in describing trace mineral requirements. Sex did not affect the intercept and slope of the linear equations, and the net mineral requirements for maintenance were 34.85, 39.63, 6.11, 194, 6.06, and 11.67&#x3bc;g/kg of BW for Cu, Fe, Mn, Zn, Co, and Cr, respectively. The Fe requirements for gain decreased with increasing BW from 10 to 30 kg and average daily gain (ADG) of 150 g/day, ranging from 11.54 &#x2013; 8.93; 10.58- 6.81; 7.16-2.91 mg for non-castrated males, castrated males, and females, respectively. The estimated dietary requirements for males with a BW of 30 kg and an average daily gain of 150 g were 69.6 mg/day for Fe;76.06 mg/day for Mn, and 2.62 mg/day for Co. Nutritional requirements for growth differ among castrated male, non-castrated male and female sheep for Fe, Mn, Zn and Cr. Thus, this study represents a significant advancement in the recommendation of nutritional requirements for trace elements in sheep breeds raised in tropical conditions.</p>
</abstract>
<kwd-group>
<kwd>micromineral</kwd>
<kwd>models</kwd>
<kwd>sex classes</kwd>
<kwd>sheep</kwd>
<kwd>tropical areas</kwd>
</kwd-group>
<funding-group>
<funding-statement>The author(s) declare financial support was received for the research and/or publication of this article. The authors thank the grants provided by Conselho Nacional de Desenvolvimento Cient&#xed;fico e Tecnol&#xf3;gico &#x2013; CNPq, Coordena&#xe7;&#xe3;o de Aperfei&#xe7;oamento de Pessoal de N&#xed;vel Superior&#x2013; CAPES and Institutos Nacionais de Ci&#xea;ncia e Tecnologia INCT&#x2013; Ci&#xea;ncia Animal and Cadeia Produtiva da Carne -INCT- Carne.</funding-statement>
</funding-group>
<counts>
<fig-count count="2"/>
<table-count count="7"/>
<equation-count count="6"/>
<ref-count count="56"/>
<page-count count="13"/>
<word-count count="8381"/>
</counts>
<custom-meta-group>
<custom-meta>
<meta-name>section-in-acceptance</meta-name>
<meta-value>Animal Nutrition</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<body>
<sec id="s1" sec-type="intro">
<label>1</label>
<title>Introduction</title>
<p>Mineral requirements have been studied, given that their precise estimation is essential for optimizing animal nutrition, reducing mineral excretion, and mitigating environmental contamination. The bioavailability of minerals can be modulated by complex interactions within the organism (<xref ref-type="bibr" rid="B20">Lee et&#xa0;al., 2002</xref>), which may either enhance or inhibit their absorption and utilization (<xref ref-type="bibr" rid="B49">Underwood and Suttle, 1999</xref>). Such interactions can compromise the fulfillment of dietary requirements and contribute to the onset of metabolic disturbances (<xref ref-type="bibr" rid="B33">NRC, 1985</xref>).</p>
<p>Microminerals or trace elements are distributed throughout the animal body in small quantities, corresponding to less than 0.3% of the total minerals deposited in the body, but are of great importance for maintaining normal cellular metabolism (<xref ref-type="bibr" rid="B45">Suttle, 2022</xref>). Among trace minerals Copper, Mn and Zn are components of enzymes and contribute to increased resistance to infection, play essential physiological roles in ruminants. Zinc is involved in numerous biological processes, including DNA synthesis, gene expression, and cell proliferation. It also plays a pivotal role in bone formation through its structural integration into the enzyme alkaline phosphatase, which is crucial for bone mineralization (<xref ref-type="bibr" rid="B17">Hosnedlov&#xe1; et&#xa0;al., 2007</xref>). Iron, in turn, is a fundamental component of the heme group within the protoporphyrin ring of hemoglobin, facilitating the transport of oxygen from the lungs to peripheral tissues as oxyhemoglobin, and the return of carbon dioxide as carboxyhemoglobin via the venous circulation. Furthermore, Fe acts as a cofactor for various enzymes associated with the tricarboxylic acid (Krebs) cycle and participates in oxidative metabolism through its role in catalases and peroxidases (<xref ref-type="bibr" rid="B45">Suttle, 2022</xref>). Mn is a required component of manganese superoxide dismutase (MnSOD) for reducing mitochondrial oxidative stress (<xref ref-type="bibr" rid="B21">Li and Yang, 2018</xref>). The Iron and manganese minerals prevent the deleterious action of free radicals, being classified as preventive antioxidants.</p>
<p>Deficiencies in these trace minerals may adversely affect growth performance and maintenance of normal cellular metabolism (<xref ref-type="bibr" rid="B56">Zhang et&#xa0;al., 2018</xref>), attenuate immune function, and heighten the animal&#x2019;s vulnerability to infectious and metabolic diseases. In this context, the functional significance of trace minerals in maintaining and promoting animal health has received growing scientific attention (<xref ref-type="bibr" rid="B29">Mortazavi et&#xa0;al., 2025</xref>).</p>
<p>Historically, equations to estimate mineral requirements for sheep do not consider the effect of sex (<xref ref-type="bibr" rid="B34">NRC, 2007</xref>). However, studies have shown differences between males and females (<xref ref-type="bibr" rid="B51">Vargas et&#xa0;al., 2017</xref>; <xref ref-type="bibr" rid="B15">Herbster et&#xa0;al., 2023</xref>). These differences may lead to variations in mineral concentrations in tissues and blood between the sexes (<xref ref-type="bibr" rid="B1">AFRC, 1998</xref>; <xref ref-type="bibr" rid="B26">Meschy, 2000</xref>; <xref ref-type="bibr" rid="B34">NRC, 2007</xref>). Knowing the amount of minerals consumed by the animal as well as the amount retained in its body is necessary to determine the need for trace elements for the maintenance and growth of the animals. Adequate mineral nutrition is essential to optimize animal performance because trace minerals play roles in animals such as structural function, constituents of body fluids, acid-base balance, control of osmotic pressure, enzyme cofactors, and the formation of metalloenzymes (<xref ref-type="bibr" rid="B25">McDowell, 2003</xref>; <xref ref-type="bibr" rid="B53">Wilson et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B45">Suttle, 2022</xref>). Additionally, most studies have not considered the effect of sex classes on trace element requirements, which is an imminent need.</p>
<p>Furthermore, when estimating dietary mineral requirements based on each mineral&#x2019;s absorption coefficient, it assumes minimal urinary mineral excretion. However, not every mineral is absorbed and retained, and has important functions in the body (<xref ref-type="bibr" rid="B5">BR-Corte, 2016</xref>). Therefore, determining mineral maintenance requirements by assessing the balance between mineral intake and retention in the animal&#x2019;s body is more accurate than using the absorption coefficient, as the retention coefficient accurately reflects the proportion of ingested minerals that are effectively retained, providing a more accurate assessment of mineral utilization in sheep.</p>
<p>We hypothesized that the traces elements requirements of hair sheep differ between sex classes. Thus, this study aimed to estimate the net requirements for gain (NCug, NFeg; NMng; NZng, NCog, and NCrg) and maintenance (NCum, NFem; NMnm, NZnm, NCom; and NCrm) in males and female hair sheep.</p>
</sec>
<sec id="s2" sec-type="materials|methods">
<label>2</label>
<title>Materials and methods</title>
<sec id="s2_1">
<label>2.1</label>
<title>Study and data set inclusion criteria</title>
<p>A comprehensive dataset was compiled from six comparative slaughter studies (<xref ref-type="bibr" rid="B7">Cabral et&#xa0;al., 2008</xref>; <xref ref-type="bibr" rid="B41">Silva et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B35">Pereira et&#xa0;al., 2016</xref>, <xref ref-type="bibr" rid="B37">2017</xref>, <xref ref-type="bibr" rid="B36">2018a</xref>, <xref ref-type="bibr" rid="B38">b</xref>), incorporating reference data, qualifying variables (e.g., sex, intake level), and essential quantitative measurements. The dataset included detailed information on days on feed, initial and final body weight (BW), empty body weight (EBW), empty body weight gain (EBWG), daily mineral intake, and mineral body composition of Cu, Fe, Mn, Zn, and Co for each animal. Mineral body composition was determined based on the chemical analysis of all body tissues. Additionally, data on daily mineral intake and individual animal records were available, allowing for precise evaluation of mineral retention and metabolism. Description of the studies of database used to estimate net traces element requirements for maintenance and weight gain of hair sheep is shown in <xref ref-type="table" rid="T1"><bold>Table&#xa0;1</bold></xref>. The dataset was composed of 248 individual observations of hair sheep with three sexes (139 non-castrated, 75 castrated males, and 34 females non-pregnant and non-lactating).</p>
<table-wrap id="T1" position="float">
<label>Table&#xa0;1</label>
<caption>
<p>Description of the studies of database used to estimate net traces element requirements for maintenance and weight gain of hair sheep.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="center">Study</th>
<th valign="middle" align="center">n</th>
<th valign="middle" align="center">Genotype</th>
<th valign="middle" align="center">Sex Class</th>
<th valign="middle" align="center">Age (days)</th>
<th valign="middle" align="center">Trial (days)</th>
<th valign="middle" align="center">BW (kg)</th>
<th valign="middle" align="center">EBW (kg)</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" align="center"><xref ref-type="bibr" rid="B7">Cabral et&#xa0;al. (2008)</xref></td>
<td valign="middle" align="center">24</td>
<td valign="middle" align="center">Santa Ines</td>
<td valign="middle" align="center">C</td>
<td valign="middle" align="center">105</td>
<td valign="middle" align="center">75</td>
<td valign="middle" align="center">17.90 &#x2013; 24.40</td>
<td valign="middle" align="center">13.13 &#x2013; 22.65</td>
</tr>
<tr>
<td valign="middle" align="center"><xref ref-type="bibr" rid="B35">Pereira et&#xa0;al. (2016)</xref></td>
<td valign="middle" align="center">40</td>
<td valign="middle" align="center">Morada Nova</td>
<td valign="middle" align="center">NC</td>
<td valign="middle" align="center">60</td>
<td valign="middle" align="center">175</td>
<td valign="middle" align="center">10.12 &#x2013; 31.62</td>
<td valign="middle" align="center">6.58 &#x2013; 27.10</td>
</tr>
<tr>
<td valign="middle" rowspan="3" align="center"><xref ref-type="bibr" rid="B41">Silva et&#xa0;al. (2016)</xref></td>
<td valign="middle" align="center">19</td>
<td valign="middle" rowspan="3" align="center">Crossbred</td>
<td valign="middle" align="center">NC</td>
<td valign="middle" rowspan="3" align="center">150</td>
<td valign="middle" rowspan="3" align="center">58</td>
<td valign="middle" align="center">10.64 &#x2013; 33.60</td>
<td valign="middle" align="center">9.77 &#x2013; 30.10</td>
</tr>
<tr>
<td valign="middle" align="center">17</td>
<td valign="middle" align="center">C</td>
<td valign="middle" align="center">7.97 &#x2013; 31.70</td>
<td valign="middle" align="center">7.68 &#x2013; 29.44</td>
</tr>
<tr>
<td valign="middle" align="center">18</td>
<td valign="middle" align="center">F</td>
<td valign="middle" align="center">7.98 &#x2013; 29.40</td>
<td valign="middle" align="center">7.68 &#x2013; 26.28</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center"><xref ref-type="bibr" rid="B37">Pereira et&#xa0;al. (2017)</xref><sup>1</sup></td>
<td valign="middle" align="center">19</td>
<td valign="middle" rowspan="2" align="center">Santa Ines</td>
<td valign="middle" align="center">NC</td>
<td valign="middle" rowspan="2" align="center">60</td>
<td valign="middle" rowspan="2" align="center">120</td>
<td valign="middle" align="center">11.20 &#x2013; 33.20</td>
<td valign="middle" align="center">8.30 &#x2013; 24.57</td>
</tr>
<tr>
<td valign="middle" align="center">18</td>
<td valign="middle" align="center">C</td>
<td valign="middle" align="center">12.60 &#x2013; 31.56</td>
<td valign="middle" align="center">8.50 &#x2013; 29.30</td>
</tr>
<tr>
<td valign="middle" align="center"><xref ref-type="bibr" rid="B36">Pereira et&#xa0;al. (2018a)</xref></td>
<td valign="middle" align="center">47</td>
<td valign="middle" align="center">Brazilian Somali</td>
<td valign="middle" align="center">NC</td>
<td valign="middle" align="center">60</td>
<td valign="middle" align="center">105</td>
<td valign="middle" align="center">10.90 &#x2013; 35.74</td>
<td valign="middle" align="center">7.95 &#x2013; 31.18</td>
</tr>
<tr>
<td valign="middle" rowspan="3" align="center"><xref ref-type="bibr" rid="B38">Pereira et&#xa0;al. (2018b)</xref><sup>1</sup></td>
<td valign="middle" align="center">14</td>
<td valign="middle" rowspan="3" align="center">Morada Nova</td>
<td valign="middle" align="center">NC</td>
<td valign="middle" rowspan="3" align="center">120</td>
<td valign="middle" rowspan="3" align="center">120</td>
<td valign="middle" align="center">13.66 &#x2013; 38.28</td>
<td valign="middle" align="center">9.62 &#x2013; 29.38</td>
</tr>
<tr>
<td valign="middle" align="center">16</td>
<td valign="middle" align="center">C</td>
<td valign="middle" align="center">12.54 &#x2013; 31.25</td>
<td valign="middle" align="center">8.66 &#x2013; 23.08</td>
</tr>
<tr>
<td valign="middle" align="center">16</td>
<td valign="middle" align="center">F</td>
<td valign="middle" align="center">12.74 &#x2013; 26.95</td>
<td valign="middle" align="center">8.89 &#x2013; 21.71</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>BW, body weight; EBW, empty body weight; n, number of information. </p></fn>
<fn>
<p><sup>1</sup>Studies used to estimate net maintenance requirements.</p></fn>
</table-wrap-foot>
</table-wrap>
<p>The trace elements collected in the data set used to estimate growth requirements varied within each study. For Zn and Fe, data were collected from 224 animals (139 non-castrated males, 51 castrated males, and 34 females) from four studies (<xref ref-type="bibr" rid="B41">Silva et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B35">Pereira et&#xa0;al., 2016</xref>, <xref ref-type="bibr" rid="B36">2018a</xref>, <xref ref-type="bibr" rid="B38">b</xref>). The data for Cu were obtained from 224 animals (139 non-castrated males, 51 castrated males, and 34 females), also from four studies. For Mn, data were gathered from 177 animals (112 non-castrated males, 41 castrated males, and 24 females). Finally, the data for Co and chromium Cr were obtained from 83 animals (33 non-castrated males, 34 castrated males, and 16 females from two studies (<xref ref-type="bibr" rid="B37">Pereira et&#xa0;al., 2017</xref>, <xref ref-type="bibr" rid="B38">2018b</xref>).</p>
<p>After confirming that the selected studies met the aforementioned inclusion criteria, a graphical analysis was conducted following the methodology described by <xref ref-type="bibr" rid="B43">St-Pierre (2007)</xref>. This analysis confirmed the consistency among studies and indicated the absence of outliers.</p>
<p>For maintenance requirements, the data set was formed by two individual studies <xref ref-type="bibr" rid="B37">Pereira et&#xa0;al., 2017</xref>, <xref ref-type="bibr" rid="B38">2018b</xref>) containing 52 individual observations of hair sheep with two sex classes (26 non-castrated males and 26 castrated males). The maintenance requirements were estimated based on the mass of trace elements (mg) daily retained in EBW and the intake (mg/day) of each trace element.</p>
<p>The descriptive analyses of the variables used to generate models for growth and maintenance are provided in <xref ref-type="table" rid="T2"><bold>Tables&#xa0;2</bold></xref> and <xref ref-type="table" rid="T3"><bold>3</bold></xref>, respectively. The variables contained in the maintenance and growth data set were body weight (BW), empty body weight (EBW), and mass of each mineral in the EBW. More detailed information about BW and EBW can be seen in <xref ref-type="bibr" rid="B15">Herbster et&#xa0;al. (2023)</xref>.</p>
<table-wrap id="T2" position="float">
<label>Table&#xa0;2</label>
<caption>
<p>Descriptive statistics of the data used to estimate net requirements of microminerals for growing in hair sheep.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="center">Variables</th>
<th valign="middle" align="center">n</th>
<th valign="middle" align="center">Mean</th>
<th valign="middle" align="center">SD</th>
<th valign="middle" align="center">Maximum</th>
<th valign="middle" align="center">Minimum</th>
</tr>
</thead>
<tbody>
<tr>
<th valign="middle" colspan="6" align="center">Non-castrated male</th>
</tr>
<tr>
<td valign="middle" align="center">BW (kg)</td>
<td valign="middle" align="center">139</td>
<td valign="middle" align="center">21.56</td>
<td valign="middle" align="center">6.54</td>
<td valign="middle" align="center">38.28</td>
<td valign="middle" align="center">10.12</td>
</tr>
<tr>
<td valign="middle" align="center">EBW (kg)</td>
<td valign="middle" align="center">139</td>
<td valign="middle" align="center">17.23</td>
<td valign="middle" align="center">5.93</td>
<td valign="middle" align="center">31.18</td>
<td valign="middle" align="center">6.58</td>
</tr>
<tr>
<th valign="middle" colspan="6" align="center">Retention (mg)</th>
</tr>
<tr>
<td valign="middle" align="center">Cu</td>
<td valign="middle" align="center">139</td>
<td valign="middle" align="center">58.57</td>
<td valign="middle" align="center">66.29</td>
<td valign="middle" align="center">309.82</td>
<td valign="middle" align="center">1.52</td>
</tr>
<tr>
<td valign="middle" align="center">Fe</td>
<td valign="middle" align="center">139</td>
<td valign="middle" align="center">1278.85</td>
<td valign="middle" align="center">921.33</td>
<td valign="middle" align="center">6829.34</td>
<td valign="middle" align="center">143.60</td>
</tr>
<tr>
<td valign="middle" align="center">Mn</td>
<td valign="middle" align="center">139</td>
<td valign="middle" align="center">24.84</td>
<td valign="middle" align="center">24.18</td>
<td valign="middle" align="center">153.25</td>
<td valign="middle" align="center">0.00</td>
</tr>
<tr>
<td valign="middle" align="center">Zn</td>
<td valign="middle" align="center">139</td>
<td valign="middle" align="center">617.05</td>
<td valign="middle" align="center">921.33</td>
<td valign="middle" align="center">5612.29</td>
<td valign="middle" align="center">169.30</td>
</tr>
<tr>
<td valign="middle" align="center">Co</td>
<td valign="middle" align="center">33</td>
<td valign="middle" align="center">23.84</td>
<td valign="middle" align="center">13.65</td>
<td valign="middle" align="center">60.53</td>
<td valign="middle" align="center">6.75</td>
</tr>
<tr>
<td valign="middle" align="center">Cr</td>
<td valign="middle" align="center">33</td>
<td valign="middle" align="center">31.83</td>
<td valign="middle" align="center">18.54</td>
<td valign="middle" align="center">82.18</td>
<td valign="middle" align="center">18.54</td>
</tr>
<tr>
<th valign="middle" colspan="6" align="center">Castrated male</th>
</tr>
<tr>
<td valign="middle" align="center">BW (kg)</td>
<td valign="middle" align="center">75</td>
<td valign="middle" align="center">21.50</td>
<td valign="middle" align="center">5.76</td>
<td valign="middle" align="center">31.70</td>
<td valign="middle" align="center">7.97</td>
</tr>
<tr>
<td valign="middle" align="center">EBW (kg)</td>
<td valign="middle" align="center">75</td>
<td valign="middle" align="center">16.81</td>
<td valign="middle" align="center">4.87</td>
<td valign="middle" align="center">29.44</td>
<td valign="middle" align="center">7.68</td>
</tr>
<tr>
<th valign="middle" colspan="6" align="center">Retention (mg)</th>
</tr>
<tr>
<td valign="middle" align="center">Cu</td>
<td valign="middle" align="center">51</td>
<td valign="middle" align="center">103.56</td>
<td valign="middle" align="center">90.31</td>
<td valign="middle" align="center">407.57</td>
<td valign="middle" align="center">0.90</td>
</tr>
<tr>
<td valign="middle" align="center">Fe</td>
<td valign="middle" align="center">51</td>
<td valign="middle" align="center">1738.81</td>
<td valign="middle" align="center">904.56</td>
<td valign="middle" align="center">3918.77</td>
<td valign="middle" align="center">215.07</td>
</tr>
<tr>
<td valign="middle" align="center">Mn</td>
<td valign="middle" align="center">41</td>
<td valign="middle" align="center">22.36</td>
<td valign="middle" align="center">15.88</td>
<td valign="middle" align="center">93.52</td>
<td valign="middle" align="center">1.98</td>
</tr>
<tr>
<td valign="middle" align="center">Zn</td>
<td valign="middle" align="center">51</td>
<td valign="middle" align="center">993.18</td>
<td valign="middle" align="center">904.56</td>
<td valign="middle" align="center">3918.77</td>
<td valign="middle" align="center">215.07</td>
</tr>
<tr>
<td valign="middle" align="center">Co</td>
<td valign="middle" align="center">34</td>
<td valign="middle" align="center">24.65</td>
<td valign="middle" align="center">15.41</td>
<td valign="middle" align="center">71.14</td>
<td valign="middle" align="center">5.88</td>
</tr>
<tr>
<td valign="middle" align="center">Cr</td>
<td valign="middle" align="center">34</td>
<td valign="middle" align="center">30.42</td>
<td valign="middle" align="center">23.51</td>
<td valign="middle" align="center">106.66</td>
<td valign="middle" align="center">5.05</td>
</tr>
<tr>
<th valign="middle" colspan="6" align="center">Female</th>
</tr>
<tr>
<td valign="middle" align="center">BW (kg)</td>
<td valign="middle" align="center">34</td>
<td valign="middle" align="center">18.91</td>
<td valign="middle" align="center">5.36</td>
<td valign="middle" align="center">29.40</td>
<td valign="middle" align="center">7.98</td>
</tr>
<tr>
<td valign="middle" align="center">EBW (kg)</td>
<td valign="middle" align="center">34</td>
<td valign="middle" align="center">16.03</td>
<td valign="middle" align="center">4.99</td>
<td valign="middle" align="center">26.28</td>
<td valign="middle" align="center">7.68</td>
</tr>
<tr>
<th valign="middle" colspan="6" align="center">Retention (mg)</th>
</tr>
<tr>
<td valign="middle" align="center">Cu</td>
<td valign="middle" align="center">34</td>
<td valign="middle" align="center">128.39</td>
<td valign="middle" align="center">83.32</td>
<td valign="middle" align="center">328.77</td>
<td valign="middle" align="center">30.25</td>
</tr>
<tr>
<td valign="middle" align="center">Fe</td>
<td valign="middle" align="center">34</td>
<td valign="middle" align="center">1530.35</td>
<td valign="middle" align="center">854.65</td>
<td valign="middle" align="center">3216.52</td>
<td valign="middle" align="center">96.83</td>
</tr>
<tr>
<td valign="middle" align="center">Mn</td>
<td valign="middle" align="center">34</td>
<td valign="middle" align="center">15.74</td>
<td valign="middle" align="center">84.08</td>
<td valign="middle" align="center">328.77</td>
<td valign="middle" align="center">0.00</td>
</tr>
<tr>
<td valign="middle" align="center">Zn</td>
<td valign="middle" align="center">34</td>
<td valign="middle" align="center">1087.53</td>
<td valign="middle" align="center">854.65</td>
<td valign="middle" align="center">3216.52</td>
<td valign="middle" align="center">96.83</td>
</tr>
<tr>
<td valign="middle" align="center">Co</td>
<td valign="middle" align="center">34</td>
<td valign="middle" align="center">19.83</td>
<td valign="middle" align="center">13.46</td>
<td valign="middle" align="center">49.66</td>
<td valign="middle" align="center">5.67</td>
</tr>
<tr>
<td valign="middle" align="center">Cr</td>
<td valign="middle" align="center">34</td>
<td valign="middle" align="center">18.64</td>
<td valign="middle" align="center">4.86</td>
<td valign="middle" align="center">26.51</td>
<td valign="middle" align="center">9.58</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>BW, body weight; EBW, empty body weight; n, number of information; SD, standard deviation.</p></fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T3" position="float">
<label>Table&#xa0;3</label>
<caption>
<p>Descriptive statistics of the data used to estimate net requirements of microminerals (Cu, Fe, Mn, Zn, Co, and Cr) for maintenance of hair sheep.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="center">Variables</th>
<th valign="middle" align="center">n</th>
<th valign="middle" align="center">Mean</th>
<th valign="middle" align="center">SD</th>
<th valign="middle" align="center">Maximum</th>
<th valign="middle" align="center">Minimum</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" align="center">BW (kg)</td>
<td valign="middle" align="center">52</td>
<td valign="middle" align="center">19.33</td>
<td valign="middle" align="center">2.90</td>
<td valign="middle" align="center">38.28</td>
<td valign="middle" align="center">11.20</td>
</tr>
<tr>
<td valign="middle" align="center">EBW (kg)</td>
<td valign="middle" align="center">52</td>
<td valign="middle" align="center">14.24</td>
<td valign="middle" align="center">2.42</td>
<td valign="middle" align="center">29.38</td>
<td valign="middle" align="center">8.30</td>
</tr>
<tr>
<th valign="middle" colspan="6" align="center">Intake (&#xb5;g/day)</th>
</tr>
<tr>
<td valign="middle" align="center">Cu</td>
<td valign="middle" align="center">52</td>
<td valign="middle" align="center">312.25</td>
<td valign="middle" align="center">68.16</td>
<td valign="middle" align="center">437.33</td>
<td valign="middle" align="center">205.61</td>
</tr>
<tr>
<td valign="middle" align="center">Fe</td>
<td valign="middle" align="center">52</td>
<td valign="middle" align="center">3519.4</td>
<td valign="middle" align="center">1298.40</td>
<td valign="middle" align="center">6489.90</td>
<td valign="middle" align="center">1821.80</td>
</tr>
<tr>
<td valign="middle" align="center">Mn</td>
<td valign="middle" align="center">52</td>
<td valign="middle" align="center">1755.3</td>
<td valign="middle" align="center">538.20</td>
<td valign="middle" align="center">2750.90</td>
<td valign="middle" align="center">913.70</td>
</tr>
<tr>
<td valign="middle" align="center">Zn</td>
<td valign="middle" align="center">52</td>
<td valign="middle" align="center">1303</td>
<td valign="middle" align="center">311.70</td>
<td valign="middle" align="center">1926.90</td>
<td valign="middle" align="center">797.20</td>
</tr>
<tr>
<td valign="middle" align="center">Co</td>
<td valign="middle" align="center">52</td>
<td valign="middle" align="center">79.40</td>
<td valign="middle" align="center">24.70</td>
<td valign="middle" align="center">139.50</td>
<td valign="middle" align="center">33.10</td>
</tr>
<tr>
<td valign="middle" align="center">Cr</td>
<td valign="middle" align="center">52</td>
<td valign="middle" align="center">28.46</td>
<td valign="middle" align="center">17.03</td>
<td valign="middle" align="center">59.80</td>
<td valign="middle" align="center">3.66</td>
</tr>
<tr>
<th valign="middle" colspan="6" align="center">Retention (&#xb5;g/day)</th>
</tr>
<tr>
<td valign="middle" align="center">Cu</td>
<td valign="middle" align="center">52</td>
<td valign="middle" align="center">35.76</td>
<td valign="middle" align="center">28.90</td>
<td valign="middle" align="center">94.26</td>
<td valign="middle" align="center">-29.34</td>
</tr>
<tr>
<td valign="middle" align="center">Fe</td>
<td valign="middle" align="center">52</td>
<td valign="middle" align="center">418.60</td>
<td valign="middle" align="center">385.3</td>
<td valign="middle" align="center">1734.30</td>
<td valign="middle" align="center">-262.20</td>
</tr>
<tr>
<td valign="middle" align="center">Mn</td>
<td valign="middle" align="center">52</td>
<td valign="middle" align="center">6.70</td>
<td valign="middle" align="center">6.90</td>
<td valign="middle" align="center">32.70</td>
<td valign="middle" align="center">-2.23</td>
</tr>
<tr>
<td valign="middle" align="center">Zn</td>
<td valign="middle" align="center">52</td>
<td valign="middle" align="center">178.40</td>
<td valign="middle" align="center">105.2</td>
<td valign="middle" align="center">416.20</td>
<td valign="middle" align="center">1.41</td>
</tr>
<tr>
<td valign="middle" align="center">Co</td>
<td valign="middle" align="center">52</td>
<td valign="middle" align="center">4.80</td>
<td valign="middle" align="center">6.10</td>
<td valign="middle" align="center">19.50</td>
<td valign="middle" align="center">-5.10</td>
</tr>
<tr>
<td valign="middle" align="center">Cr</td>
<td valign="middle" align="center">52</td>
<td valign="middle" align="center">10.28</td>
<td valign="middle" align="center">8.67</td>
<td valign="middle" align="center">36.58</td>
<td valign="middle" align="center">-1.23</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>BW, body weight; EBW, empty body weight; n, number of information; SD, standard deviation.</p></fn>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="s2_2">
<label>2.2</label>
<title>Slaughter procedures</title>
<p>In all studies, similar slaughter procedures were adopted. Before slaughter, the animals were fasted from solids and liquids (water) for 18 hours and then weighed to obtain fasting body weight (FBW). Subsequently, the slaughter was carried out by brain concussion followed by a jugular vein incision until the animals were completely bled out. After that, the animals were skinned and eviscerated. The blood was weighed and sampled.</p>
<p>The gastrointestinal tract (rumen, reticulum, omasum, abomasum, and the small and large intestines) was separated and weighed full. Subsequently, it was emptied, washed, and after draining, weighed empty. The internal organs (liver, kidneys, heart, lungs with trachea, tongue with esophagus, reproductive tract, and spleen), other body parts (carcass, head, skin, blood, and feet), and fats (omental, perirenal, mesenteric, and heart fats) were also weighed. The empty body weight (EBW) was considered as the FBW minus the contents of the gastrointestinal tract, bladder, and gallbladder.</p>
<p>The carcasses were refrigerated at 4 &#xb0;C for 24 hours and then divided into right and left half-carcasses. Subsequently, the right half-carcasses, non-carcass components (blood, head, paws, internal organs, and the cleaned gastrointestinal tract), and skins were frozen at -20 &#xb0;C. Then, they are cut separately with the help of a band saw, ground in an industrial cutter, and homogenized. After homogenization, a portion of approximately 500g of each sample was collected and stored in a freezer at - 20 &#xb0;C for later analysis.</p>
</sec>
<sec id="s2_3">
<label>2.3</label>
<title>Chemical analyses</title>
<p>To determine body mineral composition, 500 grams of samples were taken from ground samples of right half-carcasses, non-carcass parts, and hides. The samples were initially pre-dried at 55 &#xb0;C until reaching a constant weight, and then the dry matter (DM) content was determined (<xref ref-type="bibr" rid="B2">AOAC, 1990</xref>; method 967.03). For the studies by <xref ref-type="bibr" rid="B7">Cabral et&#xa0;al. (2008)</xref> and <xref ref-type="bibr" rid="B41">Silva et&#xa0;al. (2016)</xref>, the samples were defatted by successive washings with petroleum ether according to the methodology recommended by <xref ref-type="bibr" rid="B19">Kock and Preston (1979)</xref>. For other studies (<xref ref-type="bibr" rid="B35">Pereira et&#xa0;al., 2016</xref>, <xref ref-type="bibr" rid="B37">2017</xref>, <xref ref-type="bibr" rid="B36">2018a</xref>, <xref ref-type="bibr" rid="B38">b</xref>) the samples were defatted through extraction in a Soxhlet apparatus (<xref ref-type="bibr" rid="B2">AOAC, 1990</xref>; method 920.39). Subsequently, the fat-free body component samples were ground using a ball mill and analyzed for dry matter (<xref ref-type="bibr" rid="B2">AOAC, 1990</xref>; method 967.03).</p>
<p>For the studies by <xref ref-type="bibr" rid="B7">Cabral et&#xa0;al. (2008)</xref>; <xref ref-type="bibr" rid="B41">Silva et&#xa0;al. (2016)</xref>, and <xref ref-type="bibr" rid="B35">Pereira et&#xa0;al. (2016)</xref> samples of roughage, concentrate, orts, and body components of each study were analyzed for mineral composition through digestion in nitric acid and perchloric acid according to the methodology described by <xref ref-type="bibr" rid="B40">Silva and Queiroz (2002)</xref>. In the studies by <xref ref-type="bibr" rid="B35">Pereira et&#xa0;al. (2016)</xref>; <xref ref-type="bibr" rid="B37">Pereira et&#xa0;al. (2017)</xref>; <xref ref-type="bibr" rid="B36">Pereira et&#xa0;al. (2018a)</xref>, and <xref ref-type="bibr" rid="B38">Pereira et&#xa0;al. (2018b)</xref>, the samples of roughage, concentrate, orts, and body components were analyzed for mineral composition through digestion in nitroperchloric acid (<xref ref-type="bibr" rid="B11">Detmann et&#xa0;al., 2012</xref>; method INCT-CA M-004/3). Mineral concentrations of Cu, Fe, Mn, Zn, Co, and Cr were determined using inductively coupled plasma-atomic emission spectroscopy with ultrasonic nebulization (<xref ref-type="bibr" rid="B4">Braselton et&#xa0;al., 1997</xref>).</p>
</sec>
<sec id="s2_4">
<label>2.4</label>
<title>Models for predicting growth and maintenance requirements</title>
<p>The models for predicting the maintenance and retention of trace minerals used, as well as the procedures for fitting and selection of models, are the same as those described in the article by <xref ref-type="bibr" rid="B15">Herbster et&#xa0;al. (2023)</xref>, a complementary paper on macromineral requirements. Therefore, the models used for maintenance were the linear model (<xref ref-type="disp-formula" rid="eq1">Equation 1</xref>) and for trace mineral gain, the allometric models (<xref ref-type="disp-formula" rid="eq2">Equations 2</xref>, <xref ref-type="disp-formula" rid="eq3">3</xref>).</p>
<disp-formula id="eq1"><label>(1)</label>
<mml:math display="block" id="M1"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mi>I</mml:mi></mml:mrow></mml:math>
</disp-formula>
<p>The term <inline-formula>
<mml:math display="inline" id="im1"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> denotes the retention of the Y-th trace element. The parameters <italic>&#x3b2;</italic><sub>0</sub> and <italic>&#x3b2;</italic><sub>1</sub> in represent, respectively, the intercept and the slope of the linear model used for predicting the maintenance requirement of the Y-th trace mineral. The maintenance requirement of the Y-th trace element was estimated when <inline-formula>
<mml:math display="inline" id="im2"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula><inline-formula>
<mml:math display="inline" id="im3"><mml:mrow><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></inline-formula>. The retention coefficient at maintenance is given by <italic>&#x3b2;</italic><sub>1</sub>. The intake rate of the Y-th trace mineral (<inline-formula>
<mml:math display="inline" id="im4"><mml:mi>I</mml:mi></mml:math></inline-formula>; mg/day) at the maintenance level was estimated as follows: <inline-formula>
<mml:math display="inline" id="im5"><mml:mrow><mml:msub><mml:mi mathvariant="normal">I</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">/</mml:mo><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
<disp-formula id="eq2"><label>(2)</label>
<mml:math display="block" id="M2"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>Y</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>&#x3b1;</mml:mi><mml:msup><mml:mi>X</mml:mi><mml:mi>&#x3b2;</mml:mi></mml:msup></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eq3"><label>(3)</label>
<mml:math display="block" id="M3"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:msub><mml:mi>Y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x3b1;</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msubsup><mml:mi>X</mml:mi><mml:mi>i</mml:mi><mml:mrow><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msubsup></mml:mrow></mml:math>
</disp-formula>
<p>The term <inline-formula>
<mml:math display="inline" id="im6"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mi>Y</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> represents the expected mean retention of the Y-th trace element (<inline-formula>
<mml:math display="inline" id="im7"><mml:mrow><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mo>&#xa0;</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:mo>,</mml:mo><mml:mo>&#xa0;</mml:mo><mml:mn>6</mml:mn></mml:mrow></mml:math></inline-formula>, in milligrams (mg), as a function of empty body weight (EBW, kg), denoted by the letter X. The subscript &#x201c; <inline-formula>
<mml:math display="inline" id="im8"><mml:mi>i</mml:mi></mml:math></inline-formula> &#x201c; in <xref ref-type="disp-formula" rid="eq3">Equation 3</xref> denotes the i-th category (i = 1, 2, and 3), which corresponds to the prediction of the requirement of the Y-th trace element for non-castrated, castrated males, and females, respectively. The parameters <inline-formula>
<mml:math display="inline" id="im9"><mml:mi>&#x3b1;</mml:mi></mml:math></inline-formula> (<xref ref-type="disp-formula" rid="eq2">Equation 2</xref>) and <italic>&#x3b1;<sub>i</sub></italic> (<xref ref-type="disp-formula" rid="eq3">Equation 3</xref>) are proportionality parameters that fit the magnitude of the requirement for the Y-th trace mineral for a given value of EBW. The parameters <inline-formula>
<mml:math display="inline" id="im10"><mml:mi>&#x3b2;</mml:mi></mml:math></inline-formula> and <italic>&#x3b2;<sub>i</sub></italic> are allometric exponents that describe the requirement for the growth of the Y-th trace mineral scales to EBW.</p>
<p>Combined with these models (<xref ref-type="disp-formula" rid="eq1">Equations 1</xref>-<xref ref-type="disp-formula" rid="eq3">3</xref>), different variance functions were tested, including homogeneous variance (<inline-formula>
<mml:math display="inline" id="im11"><mml:mrow><mml:msubsup><mml:mo>&#x3c3;</mml:mo><mml:mtext>Y</mml:mtext><mml:mn>2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:msup><mml:mtext>&#x3c3;</mml:mtext><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>), assuming homoscedasticity, exponential variance (<inline-formula>
<mml:math display="inline" id="im12"><mml:mrow><mml:msubsup><mml:mo>&#x3c3;</mml:mo><mml:mtext>Y</mml:mtext><mml:mn>2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:msup><mml:mtext>&#x3c3;</mml:mtext><mml:mn>2</mml:mn></mml:msup><mml:mo>&#xd7;</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mo stretchy="false">[</mml:mo><mml:mrow><mml:mtext>&#x3c1;X</mml:mtext></mml:mrow><mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>), and power of the means variance (<inline-formula>
<mml:math display="inline" id="im13"><mml:mrow><mml:msubsup><mml:mo>&#x3c3;</mml:mo><mml:mtext>Y</mml:mtext><mml:mn>2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:msup><mml:mtext>&#x3c3;</mml:mtext><mml:mn>2</mml:mn></mml:msup><mml:mo>&#xd7;</mml:mo><mml:mrow><mml:mo stretchy="false">|</mml:mo><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>Y</mml:mi></mml:msub></mml:mrow><mml:msup><mml:mo stretchy="false">|</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mi>&#x3d5;</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula>. Details on how these variance functions were tested can be found in the study by <xref ref-type="bibr" rid="B15">Herbster et&#xa0;al. (2023)</xref>.</p>
<p>The normality and dispersion of residuals were evaluated, and records with studentized residuals exceeding 2.5 and/or Cook&#x2019;s distance greater than 1 were identified as influential points (<xref ref-type="bibr" rid="B8">Cook, 1979</xref>; <xref ref-type="bibr" rid="B47">Tedeschi, 2006</xref>).</p>
<p>The nonlinear mixed models (<xref ref-type="disp-formula" rid="eq1">Equations 1</xref>-<xref ref-type="disp-formula" rid="eq3">3</xref>) were analyzed using the PROC NLMIXED procedure in SAS (University Edition) with the Newton-Raphson algorithm (tech=NEWRAP) to estimate the maximum likelihood function. Data normality was assumed, i.e., <italic>Y</italic>~ Normal(<inline-formula>
<mml:math display="inline" id="im38"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mi>,</mml:mi><mml:mi>&#xa0;</mml:mi><mml:msubsup><mml:mo>&#x3c3;</mml:mo><mml:mtext>Y</mml:mtext><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>), e<sub>x</sub> ~ Normal(<inline-formula>
<mml:math display="inline" id="im39"><mml:mrow><mml:mi>0</mml:mi><mml:mi>,</mml:mi><mml:mi>&#xa0;</mml:mi><mml:msubsup><mml:mo>&#x3c3;</mml:mo><mml:mtext>Y</mml:mtext><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>). The selection of the best candidate combination (model and variance function) for predicting each of the trace minerals was carried out using the corrected Akaike information criterion (AICc) (<xref ref-type="bibr" rid="B44">Sugiura, 1978</xref>) and some AICc-derived functions for candidate combination (<xref ref-type="disp-formula" rid="eq1">Equations 1</xref>-<xref ref-type="disp-formula" rid="eq3">3</xref>) and variance function combinations) among those analyzed (<xref ref-type="bibr" rid="B6">Burnham and Anderson, 2002</xref>).</p>
<p>The retention of trace minerals per unit of daily weight gain was obtained through the first derivative of <xref ref-type="disp-formula" rid="eq2">Equation 2</xref> or <xref ref-type="disp-formula" rid="eq3">Equation 3</xref> (<xref ref-type="bibr" rid="B52">Vieira et&#xa0;al., 2018</xref>), according to the model selected for each trace mineral, as presented in <xref ref-type="disp-formula" rid="eq4">Equation 4</xref> and <xref ref-type="disp-formula" rid="eq5">Equation 5</xref>, respectively.</p>
<disp-formula id="eq4"><label>(4)</label>
<mml:math display="block" id="M4"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mi>Y</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>X</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mi>&#x3b1;</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>&#x3b2;</mml:mi><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:mi>&#x3b2;</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo stretchy="true">^</mml:mo></mml:mover></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eq5"><label>(5)</label>
<mml:math display="block" id="M5"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:msub><mml:mi>Y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>X</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x3b1;</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo stretchy="true">^</mml:mo></mml:mover></mml:mrow></mml:math>
</disp-formula>
<p>The terms <inline-formula>
<mml:math display="inline" id="im16"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mi>Y</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>X</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:math></inline-formula> (<xref ref-type="disp-formula" rid="eq4">Equation 4</xref>) and <inline-formula>
<mml:math display="inline" id="im17"><mml:mrow><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:msub><mml:mi>Y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>X</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:math></inline-formula> (<xref ref-type="disp-formula" rid="eq5">Equation 5</xref>) represent the retention in mg of the Y-th (<inline-formula>
<mml:math display="inline" id="im18"><mml:mtext>Y</mml:mtext></mml:math></inline-formula><inline-formula>
<mml:math display="inline" id="im19"><mml:mo>=</mml:mo></mml:math></inline-formula><inline-formula>
<mml:math display="inline" id="im20"><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#xa0;</mml:mtext><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mtext>&#xa0;and&#xa0;</mml:mtext><mml:mn>6</mml:mn></mml:mrow></mml:math></inline-formula>) trace mineral per g of EBW. The subscript &#x2018; <inline-formula>
<mml:math display="inline" id="im21"><mml:mi>i</mml:mi></mml:math></inline-formula> &#x2018; denotes the i-th (<inline-formula>
<mml:math display="inline" id="im22"><mml:mrow><mml:mtext>i&#xa0;</mml:mtext><mml:mo>=</mml:mo><mml:mtext>&#xa0;</mml:mtext><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#xa0;</mml:mtext><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mtext>&#xa0;and&#xa0;</mml:mtext><mml:mn>3</mml:mn></mml:mrow></mml:math></inline-formula>) category (<xref ref-type="disp-formula" rid="eq5">Equation 5</xref>). The predictor variable EBW is represented by the letter <inline-formula>
<mml:math display="inline" id="im23"><mml:mi>X</mml:mi></mml:math></inline-formula>, and the parameters <inline-formula>
<mml:math display="inline" id="im24"><mml:mtext>&#x3b1;</mml:mtext></mml:math></inline-formula>, <inline-formula>
<mml:math display="inline" id="im25"><mml:mi>&#x3b2;</mml:mi></mml:math></inline-formula>, and <inline-formula>
<mml:math display="inline" id="im26"><mml:mrow><mml:msub><mml:mi>&#x3b1;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula>
<mml:math display="inline" id="im27"><mml:mrow><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, are the coefficients of the allometric model presented in <xref ref-type="disp-formula" rid="eq2">Equation 2</xref> and <xref ref-type="disp-formula" rid="eq3">Equation 3</xref>, respectively.</p>
<p>The linear equations suggested by <xref ref-type="bibr" rid="B16">Herbster et&#xa0;al. (2020)</xref> were used to estimate the empty body weight (EBW) and the gain in empty body weight (EBWG), corresponding to body weight (BW) and average daily gain (ADG), respectively. Accordingly, trace element retention predictions were carried out for ADGs of 100, 150, and 200g for each BW of 10, 20, and 30kg. The mean predictions were accompanied by &#xbd; amplitude of the 95% confidence intervals (95% CI; <xref ref-type="disp-formula" rid="eq6">Equation 6</xref>). The predicted mean values with their 95% CI were obtained using EBW and EBWG values equivalent to the respective BW and ADG values previously estimated.</p>
<disp-formula id="eq6"><label>(6)</label>
<mml:math display="block" id="M6"><mml:mrow><mml:mn>95</mml:mn><mml:mo>%</mml:mo><mml:mi mathvariant="italic">C</mml:mi><mml:mi mathvariant="italic">I</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="italic">M</mml:mi><mml:mi mathvariant="italic">E</mml:mi><mml:mi mathvariant="italic">A</mml:mi><mml:mi mathvariant="italic">N</mml:mi><mml:mo>&#xb1;</mml:mo><mml:msub><mml:mi mathvariant="italic">t</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn mathvariant="italic">1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi mathvariant="italic">&#x3b1;</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">d</mml:mi><mml:mi mathvariant="italic">f</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msub><mml:mi mathvariant="italic">S</mml:mi><mml:mi mathvariant="italic">E</mml:mi></mml:mrow></mml:math>
</disp-formula>
<p>95% CI denotes the 95% confidence interval. The term MEAN represents the predicted average value of trace mineral retention (mg) according to Equations 4 and 5 for a given ADG (g) and BW. The confidence interval was estimated using the <italic>t</italic>-test, with a significance level (<inline-formula>
<mml:math display="inline" id="im28"><mml:mi>&#x3b1;</mml:mi></mml:math></inline-formula>) of 0.05 and the degrees of freedom (<inline-formula>
<mml:math display="inline" id="im29"><mml:mrow><mml:mi>d</mml:mi><mml:mi>f</mml:mi></mml:mrow></mml:math></inline-formula>) multiplied by the standard error (SE). The degrees of freedom were calculated by subtracting the number of parameters (<inline-formula>
<mml:math display="inline" id="im30"><mml:mi>&#x3b8;</mml:mi></mml:math></inline-formula>) in the allometric model (<xref ref-type="disp-formula" rid="eq2">Equation 2</xref> or <xref ref-type="disp-formula" rid="eq3">Equation 3</xref>), the variance function, and the random parameters from the total number of observations (<inline-formula>
<mml:math display="inline" id="im31"><mml:mi>n</mml:mi></mml:math></inline-formula>) (<inline-formula>
<mml:math display="inline" id="im32"><mml:mrow><mml:mi>d</mml:mi><mml:mi>f</mml:mi><mml:mo>=</mml:mo><mml:mi>n</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>&#x3b8;</mml:mi></mml:mrow></mml:math></inline-formula>).</p>
<p>The dietary requirements for trace elements were calculated as a sum of the net requirements for maintenance and gain divided by the retention coefficient.</p>
</sec>
</sec>
<sec id="s3" sec-type="results">
<label>3</label>
<title>Results</title>
<p>Following the selection of the optimal combinations between the allometric models and variance functions for each trace element, the corresponding model parameters and variance structures were used to estimate growth mineral requirements, as presented in <xref ref-type="table" rid="T4"><bold>Table&#xa0;4</bold></xref>. As no significant effect of sex was observed, generalized prediction equations for net concentrations of mineral use for gain (NCug and NCog) were developed.</p>
<table-wrap id="T4" position="float">
<label>Table&#xa0;4</label>
<caption>
<p>Goodness-of-fit measures used in selecting the best fit among all combinations of allometric model, variance function, and random effects fitted to micromineral growth requirement for hair sheep.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="left">Micromineral</th>
<th valign="middle" align="left">Models</th>
<th valign="middle" align="left">Variance functions <sup>6</sup></th>
<th valign="middle" align="left">Random</th>
<th valign="middle" align="left">AICc</th>
<th valign="middle" align="left">&#x394;</th>
<th valign="middle" align="left">W</th>
<th valign="middle" align="left">ER</th>
<th valign="middle" align="left">&#x398;</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" rowspan="3" align="left">Cu</td>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq2">Equation 2</xref></td>
<td valign="middle" align="left">Power of the mean<sup>1</sup></td>
<td valign="middle" align="left">a; b</td>
<td valign="middle" align="left">2309.7</td>
<td valign="middle" align="left">0.0</td>
<td valign="middle" align="left">0.60</td>
<td valign="middle" align="left">1.00</td>
<td valign="middle" align="left">6</td>
</tr>
<tr>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq3">Equation 3</xref></td>
<td valign="middle" align="left">Power of the mean<sup>1</sup></td>
<td valign="middle" align="left">a<sub>i</sub>; b<sub>i</sub></td>
<td valign="middle" align="left">2311.6</td>
<td valign="middle" align="left">1.9</td>
<td valign="middle" align="left">0.23</td>
<td valign="middle" align="left">2.59</td>
<td valign="middle" align="left">14</td>
</tr>
<tr>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq3">Equation 3</xref></td>
<td valign="middle" align="left">Power of the mean<sup>2</sup></td>
<td valign="middle" align="left">a<sub>i</sub>; b<sub>i</sub></td>
<td valign="middle" align="left">2313.3</td>
<td valign="middle" align="left">3.6</td>
<td valign="middle" align="left">0.10</td>
<td valign="middle" align="left">6.05</td>
<td valign="middle" align="left">16</td>
</tr>
<tr>
<td valign="middle" rowspan="3" align="left">Fe</td>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq3">Equation 3</xref></td>
<td valign="middle" align="left">Power of the mean<sup>1</sup></td>
<td valign="middle" align="left">a<sub>i</sub>; b<sub>i</sub></td>
<td valign="middle" align="left">3469.0</td>
<td valign="middle" align="left">0.0</td>
<td valign="middle" align="left">0.68</td>
<td valign="middle" align="left">1.00</td>
<td valign="middle" align="left">14</td>
</tr>
<tr>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq3">Equation 3</xref></td>
<td valign="middle" align="left">Power of the mean<sup>4</sup></td>
<td valign="middle" align="left">a<sub>i</sub>; b<sub>i</sub></td>
<td valign="middle" align="left">3471.4</td>
<td valign="middle" align="left">2.4</td>
<td valign="middle" align="left">0.21</td>
<td valign="middle" align="left">3.32</td>
<td valign="middle" align="left">18</td>
</tr>
<tr>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq3">Equation 3</xref></td>
<td valign="middle" align="left">Power of the mean<sup>3</sup></td>
<td valign="middle" align="left">a<sub>i</sub>; b<sub>i</sub></td>
<td valign="middle" align="left">3473.1</td>
<td valign="middle" align="left">4.1</td>
<td valign="middle" align="left">0.09</td>
<td valign="middle" align="left">7.77</td>
<td valign="middle" align="left">16</td>
</tr>
<tr>
<td valign="middle" align="left">Mn</td>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq3">Equation 3</xref></td>
<td valign="middle" align="left">Power of the mean<sup>2</sup></td>
<td valign="middle" align="left">a<sub>i</sub>; b<sub>i</sub></td>
<td valign="middle" align="left">1395.4</td>
<td valign="middle" align="left">0.0</td>
<td valign="middle" align="left">0.93</td>
<td valign="middle" align="left">1.00</td>
<td valign="middle" align="left">18</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="left">Zn</td>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq3">Equation 3</xref></td>
<td valign="middle" align="left">Power of the mean<sup>2</sup></td>
<td valign="middle" align="left">a<sub>i</sub>; b<sub>i</sub></td>
<td valign="middle" align="left">3027.4</td>
<td valign="middle" align="left">0.0</td>
<td valign="middle" align="left">0.59</td>
<td valign="middle" align="left">1.00</td>
<td valign="middle" align="left">16</td>
</tr>
<tr>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq3">Equation 3</xref></td>
<td valign="middle" align="left">Power of the mean<sup>3</sup></td>
<td valign="middle" align="left">a<sub>i</sub>; b<sub>i</sub></td>
<td valign="middle" align="left">3028.4</td>
<td valign="middle" align="left">1.0</td>
<td valign="middle" align="left">0.36</td>
<td valign="middle" align="left">1.65</td>
<td valign="middle" align="left">16</td>
</tr>
<tr>
<td valign="middle" rowspan="5" align="left">Co</td>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq2">Equation 2</xref></td>
<td valign="middle" align="left">Power of the mean<sup>1</sup></td>
<td valign="middle" align="left">a; b</td>
<td valign="middle" align="left">577.7</td>
<td valign="middle" align="left">0.0</td>
<td valign="middle" align="left">0.52</td>
<td valign="middle" align="left">1.00</td>
<td valign="middle" align="left">4</td>
</tr>
<tr>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq2">Equation 2</xref></td>
<td valign="middle" align="left">Exponential<sup>5</sup></td>
<td valign="middle" align="left">&#x2013;</td>
<td valign="middle" align="left">579.6</td>
<td valign="middle" align="left">1.9</td>
<td valign="middle" align="left">0.20</td>
<td valign="middle" align="left">2.59</td>
<td valign="middle" align="left">6</td>
</tr>
<tr>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq2">Equation 2</xref></td>
<td valign="middle" align="left">Exponential<sup>5</sup></td>
<td valign="middle" align="left">&#x2013;</td>
<td valign="middle" align="left">580.6</td>
<td valign="middle" align="left">2.9</td>
<td valign="middle" align="left">0.12</td>
<td valign="middle" align="left">4.26</td>
<td valign="middle" align="left">4</td>
</tr>
<tr>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq3">Equation 3</xref></td>
<td valign="middle" align="left">Power of the mean<sup>3</sup></td>
<td valign="middle" align="left">ai; bi</td>
<td valign="middle" align="left">582.9</td>
<td valign="middle" align="left">5.2</td>
<td valign="middle" align="left">0.04</td>
<td valign="middle" align="left">13.5</td>
<td valign="middle" align="left">16</td>
</tr>
<tr>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq3">Equation 3</xref></td>
<td valign="middle" align="left">Power of the mean<sup>3</sup></td>
<td valign="middle" align="left">ai; bi</td>
<td valign="middle" align="left">583.1</td>
<td valign="middle" align="left">5.4</td>
<td valign="middle" align="left">0.03</td>
<td valign="middle" align="left">14.9</td>
<td valign="middle" align="left">16</td>
</tr>
<tr>
<td valign="middle" rowspan="4" align="left">Cr</td>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq3">Equation 3</xref></td>
<td valign="middle" align="left">Power of the mean<sup>1</sup></td>
<td valign="middle" align="left">a<sub>i</sub>; b<sub>i</sub></td>
<td valign="middle" align="left">615.2</td>
<td valign="middle" align="left">0.0</td>
<td valign="middle" align="left">0.69</td>
<td valign="middle" align="left">1.00</td>
<td valign="middle" align="left">14</td>
</tr>
<tr>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq3">Equation 3</xref></td>
<td valign="middle" align="left">Power of the mean<sup>3</sup></td>
<td valign="middle" align="left">a<sub>i</sub>; b<sub>i</sub></td>
<td valign="middle" align="left">619.0</td>
<td valign="middle" align="left">3.8</td>
<td valign="middle" align="left">0.10</td>
<td valign="middle" align="left">6.69</td>
<td valign="middle" align="left">16</td>
</tr>
<tr>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq3">Equation 3</xref></td>
<td valign="middle" align="left">Power of the mean<sup>2</sup></td>
<td valign="middle" align="left">a<sub>i</sub>; b<sub>i</sub></td>
<td valign="middle" align="left">619.4</td>
<td valign="middle" align="left">4.2</td>
<td valign="middle" align="left">0.08</td>
<td valign="middle" align="left">8.17</td>
<td valign="middle" align="left">16</td>
</tr>
<tr>
<td valign="middle" align="left"><xref ref-type="disp-formula" rid="eq3">Equation 3</xref></td>
<td valign="middle" align="left">Power of the mean<sup>4</sup></td>
<td valign="middle" align="left">a<sub>i</sub>; b<sub>i</sub></td>
<td valign="middle" align="left">619.7</td>
<td valign="middle" align="left">4.5</td>
<td valign="middle" align="left">0.07</td>
<td valign="middle" align="left">9.49</td>
<td valign="middle" align="left">18</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>AICc, Akaike&#x2019;s information criterion corrected for small sample; &#x394;, Akaike difference; w, model probability; ER, evidence ratio; &#x398;, number of parameters of the fitted combination.</p></fn>
<fn>
<p><sup>1</sup><italic>power1</italic>: <inline-formula>
<mml:math display="inline" id="im33"><mml:mrow><mml:msubsup><mml:mo>&#x3c3;</mml:mo><mml:mtext>Y</mml:mtext><mml:mn>2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:msup><mml:mtext>&#x3c3;</mml:mtext><mml:mn>2</mml:mn></mml:msup><mml:mo>&#xd7;</mml:mo><mml:msup><mml:mrow><mml:mo stretchy="false">|</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi>Y</mml:mi></mml:msub><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mtext>&#x3d5;</mml:mtext></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>.</p></fn>
<fn>
<p><sup>2</sup><italic>power2</italic>: <inline-formula>
<mml:math display="inline" id="im34"><mml:mrow><mml:msubsup><mml:mtext>&#x3c3;</mml:mtext><mml:mrow><mml:msub><mml:mi>Y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mtext>&#x3c3;</mml:mtext><mml:mi>i</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:msub><mml:mo>&#xd7;</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mi>&#x3d5;</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>.</p></fn>
<fn>
<p><sup>3</sup><italic>power3</italic>: <inline-formula>
<mml:math display="inline" id="im35"><mml:mrow><mml:msubsup><mml:mtext>&#x3c3;</mml:mtext><mml:mrow><mml:msub><mml:mi>Y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:msup><mml:mtext>&#x3c3;</mml:mtext><mml:mn>2</mml:mn></mml:msup><mml:msub><mml:mo>&#xd7;</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:msub><mml:mi>&#x3d5;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>.</p></fn>
<fn>
<p><sup>4</sup><italic>power4</italic>: <inline-formula>
<mml:math display="inline" id="im36"><mml:mrow><mml:msubsup><mml:mtext>&#x3c3;</mml:mtext><mml:mrow><mml:msub><mml:mi>Y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mtext>&#x3c3;</mml:mtext><mml:mi>i</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:msub><mml:mo>&#xd7;</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:msub><mml:mi>&#x3d5;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>.</p></fn>
<fn>
<p><sup>5</sup><italic>Exp</italic>: <inline-formula>
<mml:math display="inline" id="im37"><mml:mrow><mml:mtext>c</mml:mtext><mml:mo>=</mml:mo><mml:msup><mml:mtext>&#x3c3;</mml:mtext><mml:mn>2</mml:mn></mml:msup><mml:mo>&#xd7;</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mtext>&#x3c1;X</mml:mtext></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>.</p></fn>
<fn>
<p><sup>6</sup> Details of the variance functions are in the text and in <xref ref-type="bibr" rid="B15">Herbster et&#xa0;al. (2023)</xref>.</p></fn>
</table-wrap-foot>
</table-wrap>
<p>The combination of the linear model with exponential variance was the best choice for Mn, Zn, Co, and Cu. However, this combination was unanimous (w &gt; 0.90) only for Mn and Cr. For Fe and Cu, the allometric model with homogeneous variance was the best choice among the candidate models (<xref ref-type="table" rid="T5"><bold>Table&#xa0;5</bold></xref>).</p>
<table-wrap id="T5" position="float">
<label>Table&#xa0;5</label>
<caption>
<p>Goodness-of-fit measures for selecting the best combination between the linear model and the variance functions fitted to predict the micromineral maintenance requirement of hair sheep.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="center">Microminerals</th>
<th valign="middle" align="center">Variance Function<sup>1</sup></th>
<th valign="middle" align="center">AICc</th>
<th valign="middle" align="center">&#x394;</th>
<th valign="middle" align="center">w</th>
<th valign="middle" align="center">ER</th>
<th valign="middle" align="center">&#x398;</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" rowspan="3" align="center">Cu</td>
<td valign="middle" align="center">Homogeneous</td>
<td valign="middle" align="center">485.5</td>
<td valign="middle" align="center">0.00</td>
<td valign="middle" align="center">0.58</td>
<td valign="middle" align="center">1.00</td>
<td valign="middle" align="center">3</td>
</tr>
<tr>
<td valign="middle" align="center">Exponential</td>
<td valign="middle" align="center">487.6</td>
<td valign="middle" align="center">2.10</td>
<td valign="middle" align="center">0.20</td>
<td valign="middle" align="center">2.86</td>
<td valign="middle" align="center">4</td>
</tr>
<tr>
<td valign="middle" align="center">Power of the mean</td>
<td valign="middle" align="center">487.4</td>
<td valign="middle" align="center">1.90</td>
<td valign="middle" align="center">0.22</td>
<td valign="middle" align="center">2.59</td>
<td valign="middle" align="center">4</td>
</tr>
<tr>
<td valign="middle" rowspan="3" align="center">Fe</td>
<td valign="middle" align="center">Homogeneous</td>
<td valign="middle" align="center">761.2</td>
<td valign="middle" align="center">0.00</td>
<td valign="middle" align="center">0.49</td>
<td valign="middle" align="center">1.00</td>
<td valign="middle" align="center">3</td>
</tr>
<tr>
<td valign="middle" align="center">Exponential</td>
<td valign="middle" align="center">762.0</td>
<td valign="middle" align="center">0.80</td>
<td valign="middle" align="center">0.33</td>
<td valign="middle" align="center">1.49</td>
<td valign="middle" align="center">4</td>
</tr>
<tr>
<td valign="middle" align="center">Power of the mean</td>
<td valign="middle" align="center">763.1</td>
<td valign="middle" align="center">1.90</td>
<td valign="middle" align="center">0.19</td>
<td valign="middle" align="center">2.59</td>
<td valign="middle" align="center">4</td>
</tr>
<tr>
<td valign="middle" rowspan="3" align="center">Mn</td>
<td valign="middle" align="center">Homogeneous</td>
<td valign="middle" align="center">320.4</td>
<td valign="middle" align="center">28.10</td>
<td valign="middle" align="center">0.00</td>
<td valign="middle" align="center">1.26&#xd7;10<sup>6</sup></td>
<td valign="middle" align="center">3</td>
</tr>
<tr>
<td valign="middle" align="center">Exponential</td>
<td valign="middle" align="center">292.3</td>
<td valign="middle" align="center">0.00</td>
<td valign="middle" align="center">0.98</td>
<td valign="middle" align="center">1.00</td>
<td valign="middle" align="center">4</td>
</tr>
<tr>
<td valign="middle" align="center">Power of the mean</td>
<td valign="middle" align="center">300.5</td>
<td valign="middle" align="center">8.20</td>
<td valign="middle" align="center">0.02</td>
<td valign="middle" align="center">60.34</td>
<td valign="middle" align="center">4</td>
</tr>
<tr>
<td valign="middle" rowspan="3" align="center">Zn</td>
<td valign="middle" align="center">Homogeneous</td>
<td valign="middle" align="center">586.1</td>
<td valign="middle" align="center">3.60</td>
<td valign="middle" align="center">0.09</td>
<td valign="middle" align="center">6.05</td>
<td valign="middle" align="center">3</td>
</tr>
<tr>
<td valign="middle" align="center">Exponential</td>
<td valign="middle" align="center">582.5</td>
<td valign="middle" align="center">0.00</td>
<td valign="middle" align="center">0.53</td>
<td valign="middle" align="center">1.00</td>
<td valign="middle" align="center">4</td>
</tr>
<tr>
<td valign="middle" align="center">Power of the mean</td>
<td valign="middle" align="center">583.2</td>
<td valign="middle" align="center">0.70</td>
<td valign="middle" align="center">0.38</td>
<td valign="middle" align="center">1.42</td>
<td valign="middle" align="center">4</td>
</tr>
<tr>
<td valign="middle" rowspan="3" align="center">Co</td>
<td valign="middle" align="center">Homogeneous</td>
<td valign="middle" align="center">318.0</td>
<td valign="middle" align="center">1.30</td>
<td valign="middle" align="center">0.34</td>
<td valign="middle" align="center">1.92</td>
<td valign="middle" align="center">3</td>
</tr>
<tr>
<td valign="middle" align="center">Exponential</td>
<td valign="middle" align="center">316.7</td>
<td valign="middle" align="center">0.00</td>
<td valign="middle" align="center">0.66</td>
<td valign="middle" align="center">1.00</td>
<td valign="middle" align="center">4</td>
</tr>
<tr>
<td valign="middle" align="center">Power of the mean</td>
<td valign="middle" align="center">&#x2013;</td>
<td valign="middle" align="center">&#x2013;</td>
<td valign="middle" align="center">&#x2013;</td>
<td valign="middle" align="center">&#x2013;</td>
<td valign="middle" align="center">4</td>
</tr>
<tr>
<td valign="middle" rowspan="3" align="center">Cr</td>
<td valign="middle" align="center">Homogeneous</td>
<td valign="middle" align="center">373.0</td>
<td valign="middle" align="center">24.40</td>
<td valign="middle" align="center">0.00</td>
<td valign="middle" align="center">1.9&#xd7;10<sup>6</sup></td>
<td valign="middle" align="center">3</td>
</tr>
<tr>
<td valign="middle" align="center">Exponential</td>
<td valign="middle" align="center">348.6</td>
<td valign="middle" align="center">0.00</td>
<td valign="middle" align="center">1.00</td>
<td valign="middle" align="center">1.00</td>
<td valign="middle" align="center">4</td>
</tr>
<tr>
<td valign="middle" align="center">Power of the mean</td>
<td valign="middle" align="center">&#x2013;</td>
<td valign="middle" align="center">&#x2013;</td>
<td valign="middle" align="center">&#x2013;</td>
<td valign="middle" align="center">&#x2013;</td>
<td valign="middle" align="center">4</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>AICc, Akaike&#x2019;s Information Criterion corrected for small sample; &#x394;, Akaike difference; w, model probability; ER, evidence ratio; &#x398;, number of parameters of the fitted combination.</p></fn>
<fn>
<p><sup>1</sup>Description of these variance functions are in the text and in <xref ref-type="bibr" rid="B15">Herbster et&#xa0;al. (2023)</xref>.</p></fn>
</table-wrap-foot>
</table-wrap>
<p>The models for estimating the net requirement for weight gain are presented in <xref ref-type="table" rid="T6"><bold>Table&#xa0;6</bold></xref>. The net requirements for gain in hair sheep, along with their respective confidence intervals, are summarized in <xref ref-type="table" rid="T7"><bold>Table&#xa0;7</bold></xref>. Irrespective of sex, the Fe requirements for gain decreased with increasing BW from 10 to 30kg and average daily gain (ADG) of 150 g/day, ranging from 11.54&#x2013;8.93; 10.58-6.81; 7.16-2.91 mg of Fe for non-castrated males, castrated males, and females, respectively. During growth, non-castrated males showed greater requirements for Mn than castrated males, and females showed greater Mn requirements than castrated males, irrespective of gain. Castrated males had a higher chromium requirement than males and females during growth.</p>
<table-wrap id="T6" position="float">
<label>Table&#xa0;6</label>
<caption>
<p>Models for estimating body composition and net requirements for microminerals for gain of hair sheep.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="center">Microminerals</th>
<th valign="middle" align="center">Sex classes</th>
<th valign="middle" align="center">Model</th>
<th valign="middle" align="center">Variance parameters</th>
<th valign="middle" align="center">Net requirements for gain (g/day)<sup>1</sup></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" align="center">Cu</td>
<td valign="middle" align="center">General</td>
<td valign="middle" align="center">10.72 (7.28) EBW <sup>0.7124 (0.1508)</sup></td>
<td valign="middle" align="center">&#x3c3;= 0.173; &#x3d5;= 1.316</td>
<td valign="middle" align="center">EBWG &#xd7; [(7.64) &#xd7; EBW <sup>-0.2876</sup>]</td>
</tr>
<tr>
<td valign="middle" rowspan="3" align="center">Fe</td>
<td valign="middle" align="center">Non-castrated male</td>
<td valign="middle" align="center">151.7 (53.8) EBW <sup>0.8024 (0.1344)</sup></td>
<td valign="middle" rowspan="3" align="center">&#x3c3;= 0.001; &#x3d5;= 1.769</td>
<td valign="middle" align="center">EBWG &#xd7; [(121.72) &#xd7; EBW <sup>-0.1976</sup>]</td>
</tr>
<tr>
<td valign="middle" align="center">Castrated male</td>
<td valign="middle" align="center">219.5 (97.4) EBW <sup>0.6597 (0.1630)</sup></td>
<td valign="middle" align="center">EBWG &#xd7; [(144.8) &#xd7; EBW <sup>-0.3403</sup>]</td>
</tr>
<tr>
<td valign="middle" align="center">Females</td>
<td valign="middle" align="center">608.3 (313.2) EBW <sup>0.3067 (0.2044)</sup></td>
<td valign="middle" align="center">EBWG &#xd7; [(186.57) &#xd7; EBW <sup>-0.6933</sup>]</td>
</tr>
<tr>
<td valign="middle" rowspan="3" align="center">Mn</td>
<td valign="middle" align="center">Non-castrated male</td>
<td valign="middle" align="center">3.36 (1.57) EBW <sup>1.045 (0.2655)</sup></td>
<td valign="middle" align="center">&#x3c3;= 0.787; &#x3d5;= 0.8685</td>
<td valign="middle" align="center">EBWG &#xd7; [(3.51) &#xd7; EBW <sup>0.045</sup>]</td>
</tr>
<tr>
<td valign="middle" align="center">Castrated male</td>
<td valign="middle" align="center">3.73 (1.60) EBW <sup>0.7155 (0.2679)</sup></td>
<td valign="middle" align="center">&#x3c3;= 0.480; &#x3d5;= 0.8685</td>
<td valign="middle" align="center">EBWG &#xd7; [(2.67) &#xd7; EBW <sup>-0.2845</sup>]</td>
</tr>
<tr>
<td valign="middle" align="center">Female</td>
<td valign="middle" align="center">3.54 (1.59) EBW <sup>0.8722 (0.2743)</sup></td>
<td valign="middle" align="center">&#x3c3;= 0.641; &#x3d5;= 0.8685</td>
<td valign="middle" align="center">EBWG &#xd7; [(3.09) &#xd7; EBW <sup>-0.1278</sup>]</td>
</tr>
<tr>
<td valign="middle" rowspan="3" align="center">Zn</td>
<td valign="middle" align="center">Non-castrated male</td>
<td valign="middle" align="center">48.08(10.38) EBW <sup>0.9526 (0.1191)</sup></td>
<td valign="middle" align="center">&#x3c3;= 0.010; &#x3d5;= 1.525</td>
<td valign="middle" align="center">EBWG &#xd7; [(45.8) &#xd7; EBW <sup>-0.0474</sup>]</td>
</tr>
<tr>
<td valign="middle" align="center">Castrated male</td>
<td valign="middle" align="center">52.98(11.22) EBW <sup>0.9125 (0.1237)</sup></td>
<td valign="middle" align="center">&#x3c3;= 0.007; &#x3d5;= 1.525</td>
<td valign="middle" align="center">EBWG &#xd7; [(48.34) &#xd7; EBW <sup>-0.0875</sup>]</td>
</tr>
<tr>
<td valign="middle" align="center">Females</td>
<td valign="middle" align="center">242.83(134.97) EBW<sup>0.3559(0.2369)</sup></td>
<td valign="middle" align="center">&#x3c3;= 0.013; &#x3d5;= 1.525</td>
<td valign="middle" align="center">EBWG &#xd7; [(86.42) &#xd7; EBW <sup>-0.6441</sup>]</td>
</tr>
<tr>
<td valign="middle" align="center">Co</td>
<td valign="middle" align="center">General</td>
<td valign="middle" align="center">1.37 (0.51) EBW <sup>1.00 (0.147)</sup></td>
<td valign="middle" align="center">&#x3c3;= 0.011; &#x3d5;= 2.127</td>
<td valign="middle" align="center">EBWG &#xd7; [(1.37) &#xd7; EBW <sup>0.0000</sup>]</td>
</tr>
<tr>
<td valign="middle" rowspan="3" align="center">Cr</td>
<td valign="middle" align="center">Non-castrated male</td>
<td valign="middle" align="center">1.01 (0.26) EBW <sup>1.305 (0.1909)</sup></td>
<td valign="middle" rowspan="3" align="center">&#x3c3;= 0.179; &#x3d5;= 1.161</td>
<td valign="middle" align="center">EBWG &#xd7; [(1.32) &#xd7; EBW <sup>0.3050</sup>]</td>
</tr>
<tr>
<td valign="middle" align="center">Castrated male</td>
<td valign="middle" align="center">0.84 (0.20) EBW <sup>1.390 (0.1595)</sup></td>
<td valign="middle" align="center">EBWG &#xd7; [(1.17) &#xd7; EBW <sup>0.3900</sup>]</td>
</tr>
<tr>
<td valign="middle" align="center">Female</td>
<td valign="middle" align="center">9.95 (16.85) EBW <sup>0.3689 (0.6394)</sup></td>
<td valign="middle" align="center">EBWG &#xd7; [(3.67) &#xd7; EBW <sup>-0.6311</sup>]</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>EBW, empty body weight; EBWG, empty body weight gain; &#x3c3;, standard deviation; &#x3d5;, scaling parameter of the scaling function.</p></fn>
<fn>
<p><sup>1</sup> The EBWG was estimated according to equation recommended by <xref ref-type="bibr" rid="B16">Herbster et&#xa0;al. (2020)</xref>.</p></fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T7" position="float">
<label>Table&#xa0;7</label>
<caption>
<p>Prediction of net trace mineral requirements for growth of hair sheep with different body weights and average daily gains and respective confidence intervals.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="center">BW</th>
<th valign="middle" align="center">ADG (g/day)</th>
<th valign="middle" align="center">Sex classes</th>
<th valign="middle" align="center">Cu</th>
<th valign="middle" align="center">Fe</th>
<th valign="middle" align="center">Mn</th>
<th valign="middle" align="center">Zn</th>
<th valign="middle" align="center">Co</th>
<th valign="middle" align="center">Cr</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" rowspan="12" align="center">10 kg</td>
<td valign="middle" align="center">100</td>
<td valign="middle" align="center">Non-castrated male</td>
<td valign="middle" rowspan="3" align="center"/>
<td valign="middle" align="center">7.72 &#xb1; 7.52</td>
<td valign="middle" align="center">0.347 &#xb1; 0.396</td>
<td valign="middle" align="center">3.82 &#xb1; 3.51</td>
<td valign="middle" rowspan="3" align="center"/>
<td valign="middle" align="center">0.210 &#xb1; 0.572</td>
</tr>
<tr>
<td valign="middle" align="center">100</td>
<td valign="middle" align="center">Castrated male</td>
<td valign="middle" align="center">7.08 &#xb1; 7.92</td>
<td valign="middle" align="center">0.144 &#xb1; 0.233</td>
<td valign="middle" align="center">3.75 &#xb1; 3.49</td>
<td valign="middle" align="center">0.216 &#xb1; 0.643</td>
</tr>
<tr>
<td valign="middle" align="center">100</td>
<td valign="middle" align="center">Female</td>
<td valign="middle" align="center">4.79 &#xb1; 15.99</td>
<td valign="middle" align="center">0.222 &#xb1; 0.318</td>
<td valign="middle" align="center">2.43 &#xb1; 5.15</td>
<td valign="middle" align="center">0.106 &#xb1; 0.220</td>
</tr>
<tr>
<td valign="middle" align="center">100</td>
<td valign="middle" align="center">General</td>
<td valign="middle" align="center">0.411 &#xb1; 0.54</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center">0.125 &#xb1; 0.014</td>
<td valign="middle" align="center"/>
</tr>
<tr>
<td valign="middle" align="center">150</td>
<td valign="middle" align="center">Non-castrated male</td>
<td valign="middle" rowspan="3" align="center"/>
<td valign="middle" align="center">11.54 &#xb1; 11.24</td>
<td valign="middle" align="center">0.519 &#xb1; 0.591</td>
<td valign="middle" align="center">5.71 &#xb1; 5.24</td>
<td valign="middle" rowspan="3" align="center"/>
<td valign="middle" align="center">0.313 &#xb1; 0.854</td>
</tr>
<tr>
<td valign="middle" align="center">150</td>
<td valign="middle" align="center">Castrated male</td>
<td valign="middle" align="center">10.58 &#xb1; 11.84</td>
<td valign="middle" align="center">0.216 &#xb1; 0.349</td>
<td valign="middle" align="center">5.60 &#xb1; 5.22</td>
<td valign="middle" align="center">0.323 &#xb1; 0.961</td>
</tr>
<tr>
<td valign="middle" align="center">150</td>
<td valign="middle" align="center">Female</td>
<td valign="middle" align="center">7.16 &#xb1; 23.9</td>
<td valign="middle" align="center">0.332 &#xb1; 0.475</td>
<td valign="middle" align="center">3.63 &#xb1; 7.70</td>
<td valign="middle" align="center">0.158 &#xb1; 0.329</td>
</tr>
<tr>
<td valign="middle" align="center">150</td>
<td valign="middle" align="center">General</td>
<td valign="middle" align="center">0.614 &#xb1; 0.807</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center">0.187 &#xb1; 0.021</td>
<td valign="middle" align="center"/>
</tr>
<tr>
<td valign="middle" align="center">200</td>
<td valign="middle" align="center">Non-castrated male</td>
<td valign="middle" rowspan="3" align="center"/>
<td valign="middle" align="center">15.36 &#xb1; 14.96</td>
<td valign="middle" align="center">0.690 &#xb1; 0.787</td>
<td valign="middle" align="center">7.60 &#xb1; 6.97</td>
<td valign="middle" rowspan="3" align="center"/>
<td valign="middle" align="center">0.417 &#xb1; 1.137</td>
</tr>
<tr>
<td valign="middle" align="center">200</td>
<td valign="middle" align="center">Castrated male</td>
<td valign="middle" align="center">14.09 &#xb1; 15.76</td>
<td valign="middle" align="center">0.287 &#xb1; 0.464</td>
<td valign="middle" align="center">7.46 &#xb1; 6.94</td>
<td valign="middle" align="center">0.429 &#xb1; 1.278</td>
</tr>
<tr>
<td valign="middle" align="center">200</td>
<td valign="middle" align="center">Female</td>
<td valign="middle" align="center">9.53 &#xb1; 31.81</td>
<td valign="middle" align="center">0.442 &#xb1; 0.632</td>
<td valign="middle" align="center">4.83 &#xb1; 10.25</td>
<td valign="middle" align="center">0.210 &#xb1; 0.437</td>
</tr>
<tr>
<td valign="middle" align="center">200</td>
<td valign="middle" align="center">General</td>
<td valign="middle" align="center">0.818 &#xb1; 1.074</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center">0.249 &#xb1; 0.027</td>
<td valign="middle" align="center"/>
</tr>
<tr>
<td valign="middle" rowspan="12" align="center">20 kg</td>
<td valign="middle" align="center">100</td>
<td valign="middle" align="center">Non-castrated male</td>
<td valign="middle" rowspan="3" align="center"/>
<td valign="middle" align="center">6.54 &#xb1; 9.39</td>
<td valign="middle" align="center">0.360 &#xb1; 0.645</td>
<td valign="middle" align="center">3.67 &#xb1; 4.34</td>
<td valign="middle" rowspan="3" align="center"/>
<td valign="middle" align="center">0.271 &#xb1; 0.885</td>
</tr>
<tr>
<td valign="middle" align="center">100</td>
<td valign="middle" align="center">Castrated male</td>
<td valign="middle" align="center">5.32 &#xb1; 9.31</td>
<td valign="middle" align="center">0.114 &#xb1; 0.262</td>
<td valign="middle" align="center">3.48 &#xb1; 4.23</td>
<td valign="middle" align="center">0.300 &#xb1; 1.065</td>
</tr>
<tr>
<td valign="middle" align="center">100</td>
<td valign="middle" align="center">Female</td>
<td valign="middle" align="center">2.67 &#xb1; 11.52</td>
<td valign="middle" align="center">0.200 &#xb1; 0.423</td>
<td valign="middle" align="center">1.41 &#xb1; 3.83</td>
<td valign="middle" align="center">0.062 &#xb1; 0.148</td>
</tr>
<tr>
<td valign="middle" align="center">100</td>
<td valign="middle" align="center">General</td>
<td valign="middle" align="center">0.323 &#xb1; 0.426</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center">0.125 &#xb1; 0.042</td>
<td valign="middle" align="center"/>
</tr>
<tr>
<td valign="middle" align="center">150</td>
<td valign="middle" align="center">Non-castrated male</td>
<td valign="middle" rowspan="3" align="center"/>
<td valign="middle" align="center">9.77 &#xb1; 14.04</td>
<td valign="middle" align="center">0.539 &#xb1; 0.964</td>
<td valign="middle" align="center">5.49 &#xb1; 6.49</td>
<td valign="middle" rowspan="3" align="center"/>
<td valign="middle" align="center">0.405 &#xb1; 1.323</td>
</tr>
<tr>
<td valign="middle" align="center">150</td>
<td valign="middle" align="center">Castrated Male</td>
<td valign="middle" align="center">7.95 &#xb1; 13.92</td>
<td valign="middle" align="center">0.170 &#xb1; 0.391</td>
<td valign="middle" align="center">5.21 &#xb1; 6.33</td>
<td valign="middle" align="center">0.448 &#xb1; 1.592</td>
</tr>
<tr>
<td valign="middle" align="center">150</td>
<td valign="middle" align="center">Female</td>
<td valign="middle" align="center">3.99 &#xb1; 17.22</td>
<td valign="middle" align="center">0.298 &#xb1; 0.632</td>
<td valign="middle" align="center">2.11 &#xb1; 5.73</td>
<td valign="middle" align="center">0.093 &#xb1; 0.221</td>
</tr>
<tr>
<td valign="middle" align="center">150</td>
<td valign="middle" align="center">General</td>
<td valign="middle" align="center">0.482 &#xb1; 0.637</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center">0.187 &#xb1; 0.063</td>
<td valign="middle" align="center"/>
</tr>
<tr>
<td valign="middle" align="center">200</td>
<td valign="middle" align="center">Non-castrated male</td>
<td valign="middle" rowspan="3" align="center"/>
<td valign="middle" align="center">13.01 &#xb1; 18.68</td>
<td valign="middle" align="center">0.717 &#xb1; 1.283</td>
<td valign="middle" align="center">7.31 &#xb1; 8.64</td>
<td valign="middle" rowspan="3" align="center"/>
<td valign="middle" align="center">0.539 &#xb1; 1.760</td>
</tr>
<tr>
<td valign="middle" align="center">200</td>
<td valign="middle" align="center">Castrated male</td>
<td valign="middle" align="center">10.57 &#xb1; 18.52</td>
<td valign="middle" align="center">0.226 &#xb1; 0.520</td>
<td valign="middle" align="center">6.93 &#xb1; 8.42</td>
<td valign="middle" align="center">0.597 &#xb1; 2.118</td>
</tr>
<tr>
<td valign="middle" align="center">200</td>
<td valign="middle" align="center">Female</td>
<td valign="middle" align="center">5.31 &#xb1; 22.92</td>
<td valign="middle" align="center">0.397 &#xb1; 0.842</td>
<td valign="middle" align="center">2.81 &#xb1; 7.62</td>
<td valign="middle" align="center">0.123 &#xb1; 0.294</td>
</tr>
<tr>
<td valign="middle" align="center">200</td>
<td valign="middle" align="center">General</td>
<td valign="middle" align="center">0.642 &#xb1; 0.848</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center">0.249 &#xb1; 0.084</td>
<td valign="middle" align="center"/>
</tr>
<tr>
<td valign="middle" rowspan="11" align="center">30 kg</td>
<td valign="middle" align="center">100</td>
<td valign="middle" align="center">Non-castrated male</td>
<td valign="middle" rowspan="3" align="center"/>
<td valign="middle" align="center">5.98 &#xb1; 10.4</td>
<td valign="middle" align="center">0.368 &#xb1; 0.794</td>
<td valign="middle" align="center">3.59 &#xb1; 4.80</td>
<td valign="middle" rowspan="3" align="center"/>
<td valign="middle" align="center">0.311 &#xb1; 1.109</td>
</tr>
<tr>
<td valign="middle" align="center">100</td>
<td valign="middle" align="center">Castrated male</td>
<td valign="middle" align="center">4.55 &#xb1; 9.75</td>
<td valign="middle" align="center">0.100 &#xb1; 0.268</td>
<td valign="middle" align="center">3.35 &#xb1; 4.61</td>
<td valign="middle" align="center">0.358 &#xb1; 1.384</td>
</tr>
<tr>
<td valign="middle" align="center">100</td>
<td valign="middle" align="center">Female</td>
<td valign="middle" align="center">1.95 &#xb1; 9.44</td>
<td valign="middle" align="center">0.188 &#xb1; 0.472</td>
<td valign="middle" align="center">1.05 &#xb1; 3.20</td>
<td valign="middle" align="center">0.047 &#xb1; 0.119</td>
</tr>
<tr>
<td valign="middle" align="center">100</td>
<td valign="middle" align="center">General</td>
<td valign="middle" align="center">0.283 &#xb1; 0.390</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center">0.125 &#xb1; 0.059</td>
<td valign="middle" align="center"/>
</tr>
<tr>
<td valign="middle" align="center">150</td>
<td valign="middle" align="center">Non-castrated male</td>
<td valign="middle" rowspan="3" align="center"/>
<td valign="middle" align="center">8.93 &#xb1; 15.55</td>
<td valign="middle" align="center">0.550 &#xb1; 1.186</td>
<td valign="middle" align="center">5.37 &#xb1; 7.18</td>
<td valign="middle" rowspan="3" align="center"/>
<td valign="middle" align="center">0.465 &#xb1; 1.657</td>
</tr>
<tr>
<td valign="middle" align="center">150</td>
<td valign="middle" align="center">Castrated male</td>
<td valign="middle" align="center">6.81 &#xb1; 14.57</td>
<td valign="middle" align="center">0.149 &#xb1; 0.400</td>
<td valign="middle" align="center">5.00 &#xb1; 6.89</td>
<td valign="middle" align="center">0.535 &#xb1; 2.068</td>
</tr>
<tr>
<td valign="middle" align="center">150</td>
<td valign="middle" align="center">Female</td>
<td valign="middle" align="center">2.91 &#xb1; 14.11</td>
<td valign="middle" align="center">0.282 &#xb1; 0.705</td>
<td valign="middle" align="center">1.57 &#xb1; 4.79</td>
<td valign="middle" align="center">0.070 &#xb1; 0.178</td>
</tr>
<tr>
<td valign="middle" align="center">150</td>
<td valign="middle" align="center">General</td>
<td valign="middle" align="center">0.423 &#xb1; 0.582</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center">0.187 &#xb1; 0.088</td>
<td valign="middle" align="center"/>
</tr>
<tr>
<td valign="middle" align="center">200</td>
<td valign="middle" align="center">Non-castrated male</td>
<td valign="middle" rowspan="3" align="center">0.563 &#xb1; 0.775</td>
<td valign="middle" align="center">11.89 &#xb1; 20.69</td>
<td valign="middle" align="center">0.731 &#xb1; 1.578</td>
<td valign="middle" align="center">7.15 &#xb1; 9.55</td>
<td valign="middle" rowspan="3" align="center">0.249 &#xb1; 0.117</td>
<td valign="middle" align="center">0.619 &#xb1; 2.206</td>
</tr>
<tr>
<td valign="middle" align="center">200</td>
<td valign="middle" align="center">Castrated male</td>
<td valign="middle" align="center">9.06 &#xb1; 19.39</td>
<td valign="middle" align="center">0.199 &#xb1; 0.532</td>
<td valign="middle" align="center">6.66 &#xb1; 9.17</td>
<td valign="middle" align="center">0.712 &#xb1; 2.752</td>
</tr>
<tr>
<td valign="middle" align="center">200</td>
<td valign="middle" align="center">Female</td>
<td valign="middle" align="center">3.88 &#xb1; 18.78</td>
<td valign="middle" align="center">0.375 &#xb1; 0.938</td>
<td valign="middle" align="center">2.09 &#xb1; 6.37</td>
<td valign="middle" align="center">0.093 &#xb1; 0.237</td>
</tr>
<tr>
<td valign="middle" align="center"/>
<td valign="middle" align="center">200</td>
<td valign="middle" align="center">General</td>
<td valign="middle" align="center">0.563 &#xb1; 0.775</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center"/>
<td valign="middle" align="center">0.249 &#xb1; 0.117</td>
<td valign="middle" align="center"/>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>BW, body weight; ADG, average daily gain.</p></fn>
</table-wrap-foot>
</table-wrap>
<p>The trace element requirements for maintenance were estimated by relationships between minerals retained and mineral intake. No significant effect of sex was observed on the intercepts or slopes of the linear regression models used to estimate the net requirements of Cu, Fe, Mn, Zn, Co, and Cr (<xref ref-type="fig" rid="f1"><bold>Figure&#xa0;1</bold></xref>). The net requirements for maintenance (&#xb5;g/kg of body weight) and coefficient retention (%) were as follows:34.85&#xb5;g/kg of BW and 23% for Cu; 39.63 &#xb5;g/kg of BW and 13,00% for Fe; 6.11 &#xb5;g/kg of BW and 0,7% for Mn; 194,00 &#xb5;g/kg of BW and 28.7% for Zn; 6.06 &#xb5;g/kg of BW and 13.8% for Co; 11.67 &#xb5;g/kg of BW and 8.6% for Cr, respectively.</p>
<fig id="f1" position="float">
<label>Figure&#xa0;1</label>
<caption>
<p>Panels <bold>(A&#x2013;F)</bold> show the retention behaviours of the trace minerals copper (Cu), iron (Fe), manganese (Mn), zinc (Zn), cobalt (Co), and chromium (Cr) as a function of their intake. The observed retention values of the trace minerals are represented by circular markers, the solid line represents the predicted mean retention values by the linear model, and the dashed lines are the predicted values of the lower and upper bounds of the 95% confidence interval (95%CI).</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fanim-06-1624560-g001.tif">
<alt-text content-type="machine-generated">Six scatter plots labeled A to F analyze the relationship between daily intake and body retention of various elements: copper (Cu), iron (Fe), manganese (Mn), zinc (Zn), cobalt (Co), and chromium (Cr). Each plot shows a linear regression line with dotted lines indicating confidence intervals. Mathematical equations and 95% confidence intervals (IC95%) are provided for each element, showing varying degrees of positive or negative correlation between intake and retention.</alt-text>
</graphic>
</fig>
<p>The trace element requirements of non-castrated, castrated males and females from 10 to 35kg BW and an ADG of 150g for Fe were (81.94 mg/day; 68.26 and 38.89 mg/day, respectively); Mn (96.58; 43.97 and 62.24 mg/day, respectively); Zn (34.30; 33.30 and 22.82 mg/day, respectively); Cr (7.85; 8.44 and 4.17 mg/day respectively).</p>
<p>The total dietary requirements of this study, as well as those presented by the <xref ref-type="bibr" rid="B34">NRC (2007)</xref> and <xref ref-type="bibr" rid="B18">INRA (2018)</xref> Committees, are shown in <xref ref-type="fig" rid="f2"><bold>Figure&#xa0;2</bold></xref>. The estimated dietary requirements for males with a body weight (BW) of 30kg and an average daily gain (ADG) of 150g in the present study were 69.6 mg/day for Fe, 76.06 mg/day for Mn, and 2.62 mg/day for Co. These values exceed the recommendations established by the <xref ref-type="bibr" rid="B34">NRC (2007)</xref>, which suggest 47.62, 17.4, and 0.17 mg/day for Fe, Mn, and Co, respectively. When compared to the <xref ref-type="bibr" rid="B18">INRA (2018)</xref>, the current results also indicate elevated requirements for Mn and Co, which were reported as 46.87 and 0.28 mg/day, respectively. The estimated dietary requirements for Cu and Zn in hair sheep males were 6.38 and 38.34 mg/day, respectively, exceeding the values recommended by the <xref ref-type="bibr" rid="B34">NRC (2007)</xref>, which are 4.65 mg/day for Cu and 19.60 mg/day for Zn. In contrast, the Zn requirement determined in the present study was lower than that proposed by <xref ref-type="bibr" rid="B18">INRA (2018)</xref>, which recommends 46.87 mg/day for animals with similar physiological characteristics.</p>
<fig id="f2" position="float">
<label>Figure&#xa0;2</label>
<caption>
<p>Comparison between the dietary requirements of trace minerals obtained in this study and the recommendations of the <xref ref-type="bibr" rid="B34">NRC (2007)</xref> and <xref ref-type="bibr" rid="B18">INRA (2018)</xref> considering body weight ranging from 10 to 35 kg and an average daily gain of 150 g/day of non-castrated males (NC), castrated males (C) and females (F).</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fanim-06-1624560-g002.tif">
<alt-text content-type="machine-generated">Six bar graphs present mineral consumption by body weight in kilograms. (A) Copper, (B) Iron, (C) Manganese, (D) Zinc, (E) Cobalt, (F) Chromium. Each graph compares various guidelines, including NRC 2007 and INRA 2018. The x-axis represents body weight from 10 to 35 kilograms, while the y-axis shows mineral intake in milligrams per day. Bars indicate different standards or conditions, displaying variations in mineral requirements across weights and guidelines.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s4" sec-type="discussion">
<label>4</label>
<title>Discussion</title>
<p>A factorial approach has been used to describe trace elements requirements (<xref ref-type="bibr" rid="B3">ARC, 1980</xref>). The method entails estimating maintenance, growth, pregnancy, and lactation requirements separately, and subsequently summing them to estimate the total net requirement. The significant advantage of using the factorial method lies in the capability to predict requirements across a diverse range of production circumstances. By dividing the sum of maintenance and production requirements by the absorption coefficient (<xref ref-type="bibr" rid="B34">NRC, 2007</xref>) or retention (<xref ref-type="bibr" rid="B5">BR-CORTE, 2016</xref>) of the mineral, the dietary requirements can be determined.</p>
<p>In our study, regardless of sex, the sheep exhibited similar requirements for Cu and Co, and the demands increased with increasing body weight. Cu has essential functions in the organism of animals, being necessary for cellular respiration, bone formation, cardiac function, connective tissue development, spinal cord myelination, and keratinization (<xref ref-type="bibr" rid="B31">NASEM, 2016</xref>). Based on the present findings, the estimated Cu requirement for maintenance was 0.03485 mg/kg of body weight (BW), with a retention coefficient of 23%. These values are notably higher than those reported by <xref ref-type="bibr" rid="B45">Suttle (2022)</xref> and <xref ref-type="bibr" rid="B13">Grace and Clark (1991)</xref>, who estimated net Cu maintenance requirements at approximately 4 &#xb5;g/kg BW/day for animals weighing between 20 and 35kg. Cu requirements are peculiar, as they are affected by interactions with Fe, Mo, and S, making it necessary to specify the conditions under which the requirements are applied. Mo in the presence of S markedly reduces the uptake, storage, and utilization of Cu. This occurs through the synthesis of thiomolybdates in the rumen-reticle and formation of insoluble copper in digesta (<xref ref-type="bibr" rid="B46">Suttle and Field, 1983</xref>). In our study, sheep weighing 30kg with an ADG of 150g (GPVZ of 136g), the demand corresponds to 1.05 and 63.85 mg Cu/day for the net requirements of maintenance and weight gain. In <xref ref-type="bibr" rid="B34">NRC (2007)</xref>, using the factorial method, the value of 0.004 mg Cu/kg of BW (4 &#xb5;g Cu/kg of BW) is adopted, considering the Cu absorption coefficient of 6.0% in lambs, under feedlot conditions. Cu requirements for sheep were first described as 5 mg/kg DM (<xref ref-type="bibr" rid="B32">NRC, 1975</xref>) and were later adjusted to 7&#x2013;11 mg (<xref ref-type="bibr" rid="B33">NRC, 1985</xref>). In the <xref ref-type="bibr" rid="B3">ARC (1980)</xref>, it was suggested that requirements vary from 1 to 8.6 mg of Cu/kg of DM, depending on the physiological state of the animals.</p>
<p>In our study, males and females have similar dietary demands for Co. Co is the precursor of vitamin B12, and is therefore related to energy metabolism, but the amount of dietary Co converted into vitamin B12 varies from 3 to 13% of the Co consumed (<xref ref-type="bibr" rid="B42">Smith, 1987</xref>). Studies by <xref ref-type="bibr" rid="B27">Monroe et&#xa0;al. (1952)</xref>; <xref ref-type="bibr" rid="B23">Looney et&#xa0;al. (1976)</xref> with cattle found that 84 to 98% of the Co supplied in the diet was found in the feces, around 5 to 14 days after intake. In this study, the value of 13.8% was estimated as the true retention coefficient, showing that 86.2% of the intake was excreted via feces and urine. Furthermore, the net Co requirements for maintenance in sheep were estimated at 6.06 &#xb5;g/kg BW. The present study indicates that the net cobalt requirement to support a daily weight gain of 200g in sheep is 2.63 mg/day for an individual with a BW of 30kg. The dietary requirement is relatively higher than the suggestions of <xref ref-type="bibr" rid="B18">INRA (2018)</xref>, which recommendations of 0.28 mg of Co/day. The <xref ref-type="bibr" rid="B34">NRC (2007)</xref> recommends 0.10-0.20 mg Co/kg DM for sheep. <xref ref-type="bibr" rid="B9">CSIRO (2007)</xref> suggests a value of 0.11 mg Co/kg DM. According to <xref ref-type="bibr" rid="B25">McDowell (2003)</xref>, except for P, Co deficiency is one of the most severe mineral deficiencies affecting ruminants in tropical pastures. Co is essential for the synthesis of vitamin B12 by rumen microorganisms (<xref ref-type="bibr" rid="B50">Van Soest, 1994</xref>). In the metabolism of ruminants, vitamin B12 is an essential part of multiple enzymes involved in the metabolism of carbohydrates, lipids, some amino acids, and DNA (<xref ref-type="bibr" rid="B12">Gonz&#xe1;lez-Monta&#xf1;a et&#xa0;al., 2020</xref>).</p>
<p>In this study, sex influenced weight gain requirements for Fe, Mn, Zn, and Cr. Around 60% of the Fe in the animal&#x2019;s body is associated with hemoglobin. The Fe requirement for hair sheep for maintenance is 0.03963 mg of Fe/kg of BW and a retention coefficient of 13%. Sex classes influence the requirements for weight gain, for non-castrated, castrated males, and females weighing 30kg with an ADG of 150g (EBWG of 136). The amount of Fe deposited in the gain and, therefore, the net amount of the mineral required is 8.93, 6.81, and 2.91 mg Fe/day, respectively. The estimates obtained for males by this study are similar to the general recommendation for growing sheep from <xref ref-type="bibr" rid="B34">NRC (2007)</xref>, of 8.25 mg/day. Fe is one of the most abundant mineral nutrients in the organism and plays a critical role in the synthesis of nucleic acids and proteins, electron transport, cellular respiration, proliferation, and differentiation (<xref ref-type="bibr" rid="B22">Lieu et&#xa0;al., 2001</xref>), all of which are intimately related to spermatogenesis and spermatozoa metabolism (<xref ref-type="bibr" rid="B54">Wise et&#xa0;al., 2003</xref>).</p>
<p>The net Mn requirement for maintenance was 0.00611 mg/kg of BW and a retention coefficient of 0.7%. For a sheep weighing 30kg BW, the maintenance and dietary Mn requirements are 0.183 and 72.86 mg Mn/day, respectively. In both <xref ref-type="bibr" rid="B3">ARC (1980)</xref> and <xref ref-type="bibr" rid="B33">NRC (1985)</xref> Systems, values of 10 and 20 mg of Mn/kg of DM are suggested, respectively. <xref ref-type="bibr" rid="B24">Masters et&#xa0;al. (1988)</xref> recommended 13 mg Mn/kg DM. The <xref ref-type="bibr" rid="B34">NRC (2007)</xref> suggests a requirement for a weight gain of 0.47 mg of Mn/kg BW. Using the prediction equation of this study to estimate the requirement of females with 30kg of BW, with an ADG of 150g (EBWG of 136g), the demand corresponds to 0.28 mg Mn/day, a requirement lower than that of non-castrated males, which require 0.55 mg Mn/day. Males have greater Mn requirements due to testicular growth. Thus, Mn requirements for spermatogenesis and testicular development may be significant. A similar situation occurs with Cu and Mn for females in the reproductive period (<xref ref-type="bibr" rid="B48">Underwood, 1981</xref>).</p>
<p>Zinc plays a pivotal role in cellular proliferation, preservation of cellular integrity, and modulation of immune responses, being a key component in the host defense against pathogenic agents (<xref ref-type="bibr" rid="B29">Mortazavi et&#xa0;al., 2025</xref>). Since most trace elements, the key role of Zn in animal organism is related to its structural function in some proteins or as an enzyme activator (<xref ref-type="bibr" rid="B45">Suttle, 2022</xref>). In this sense, approximately a thousand proteins associated with Zn are recognized in animal organisms. Zinc, an essential component of life in the three domains, follows iron as the second most abundant transition metal ion in living organisms (<xref ref-type="bibr" rid="B10">Cuajungco et&#xa0;al., 2021</xref>). Based on the findings of the present study, a net maintenance requirement of 0.194 mg of Zn/kg of body weight (BW) and a retention coefficient of 28% are proposed for sheep, regardless of sex class.</p>
<p>Comparatively, the <xref ref-type="bibr" rid="B3">ARC (1980)</xref> established Zn requirements for growing sheep ranging from 24 to 51 mg/kg of dry matter (DM), while the <xref ref-type="bibr" rid="B33">NRC (1985)</xref> adopted a value of 20 mg/kg DM. More recently, the <xref ref-type="bibr" rid="B34">NRC (2007)</xref> recommended a net maintenance requirement of 0.076 mg Zn/kg BW, with an estimated absorption efficiency of 30% for lambs. This study suggests that non-castrated, castrated males, and females weighing 30kg with an ADG of 150g (EBWG of 136g) demand 5.37, 5.0, and 1.57 mg Zn/day, respectively. Zinc is a component of many metalloenzymes involved in almost every metabolic pathway of the body (<xref ref-type="bibr" rid="B39">Salgueiro et&#xa0;al., 2000</xref>). Zinc deficiency alters prostaglandin synthesis, which may affect luteal function (<xref ref-type="bibr" rid="B14">Graham, 1991</xref>).</p>
<p>Discussions occur about whether or not chromium is considered an essential element, however, <xref ref-type="bibr" rid="B34">NRC (2007)</xref> and <xref ref-type="bibr" rid="B31">NASEM (2016)</xref> consider this element as essential. Our study makes an interesting contribution to the requirements for chromium, as it is considered an element, suggesting that the net requirement for maintenance is 0.011 mg Cr/kg BW, and the retention coefficient is 8.6%. For a 30kg sheep, the value of 0.35 mg/day is suggested as a net requirement for maintenance. For dietary requirements, 9.47, 10.31, and 4.88 mg of Cr/day are recommended for non-castrated, castrated, and females, respectively. Although studies on chromium essentiality in sheep are scarce, <xref ref-type="bibr" rid="B34">NRC (2007)</xref> states that neither deficiency nor toxicity will likely occur under normal conditions. Therefore, there are no reports of signs of mineral deficiency in animals and humans. However, considering Cr&#x2019;s relationship with the immune system and its anti-stress effect, some studies have shown reduced morbidity, mortality and increased efficiency in animals recently transported over long distances, both calves and steers that received supplementation with Cr, especially in the organic form (<xref ref-type="bibr" rid="B28">Moonsie-Shageer and Mowat, 1993</xref>; <xref ref-type="bibr" rid="B30">Mowat et&#xa0;al., 1993</xref>). Likewise, Cr improves the resistance of cattle to diseases, due to its role in stimulating the immune response (<xref ref-type="bibr" rid="B55">Wright et&#xa0;al., 1994</xref>). According to the equations suggested in our study for non-castrated, castrated males, and females weighing 30kg with an ADG of 150g (EBWG of 136g), the net amount of the mineral required is 0.46, 0.54 and 0.07 mg of Cr/day, respectively. The net Cr requirement for growing sheep is greater for castrated sheep.</p>
<p>Based on the present study, the trace element requirements for hair sheep were different from those reported by the World Committees. Both the <xref ref-type="bibr" rid="B34">NRC (2007)</xref> and <xref ref-type="bibr" rid="B18">INRA (2018)</xref> recommendations for trace mineral requirements are based primarily on estimates established by the <xref ref-type="bibr" rid="B3">ARC (1980)</xref>. In these Committees, trace element requirements were determined using the dose-response methodology and absorption coefficients. In dose-response, the animal&#x2019;s requirement for a nutrient is given at the maximum response level in the parameters evaluated, such as maximum weight gain, for example. This method may lead to underestimation or overestimation of the estimates, since it is not possible to vary the production levels, since the estimate is based on the maximum response to the productive demand. Furthermore, most studies did not consider the trace elements contained in the feeds that made up the experimental diets.</p>
<p>Another approach that should be considered is the differences between organic and inorganic nutrients in terms of their requirements for maintenance and production result in different metabolic pathways. Organic nutrients, such as protein, for example, after being absorbed, enter the body&#x2019;s metabolic pool and can be converted to energy, used for tissue synthesis or maintenance; they can be metabolized and deposited; or they can be lost, as end products of metabolism, through normal pathways. In contrast, inorganic ions released during metabolism are not altered, nor do they become unavailable to the tissues. These ions remain available for reformulation of their functional combinations, in the same way as inorganic ions absorbed by the digestive system (<xref ref-type="bibr" rid="B48">Underwood, 1981</xref>). This reuse of minerals by the tissues could theoretically be complete, resulting in the absence of maintenance requirements for these nutrients. However, in practice, the mineral conservation processes in the body are not as efficient, resulting in loss of minerals through the kidneys, intestinal mucosa, digestive glands, and skin, thus constituting the mineral requirements for maintenance. The recommendations of various Committees take into account their calculations of endogenous losses through feces. The mineral maintenance requirements encompass not only urinary and fecal losses, but also potential losses through the skin, sweat, and other routes. Regarding the mineral retention coefficients, the values observed for manganese and chromium were relatively lower, which may be attributed to the high concentrations of these minerals in the diet, thereby resulting in increased excretion. can be attributed to endogenous losses associated with variations in voluntary intake, which directly influence maintenance needs. Therefore, the use of the true retention coefficient seems to be more accurate compared to the absorption coefficient for estimating mineral requirements. Thus, while the estimates have been refined, the retention coefficients identified in this study are not definitive and may fluctuate in response to tissue growth. Younger animals typically exhibit higher retention coefficients compared to adults. Therefore, the extent of variation in retention and absorption coefficients concerning growth stages remains to be further elucidated.</p>
<p>Minerals play an important role in animal metabolism, and study contributes to improving our knowledge about recommendations for mineral requirements in hair sheep. However, there exists a need for additional efforts to better understand the effects of genotype and degree of maturity on trace elements requirements, especially requirements for maintenance and growth. Herein, there is a great contribution in providing up-to-date recommendations on trace elements requirements for sexes. Furthermore, the importance of future studies to determine trace elements requirements is highlighted. Finally, there is a need for more in-depth knowledge of the retention coefficients of different minerals. Continuous efforts to improve models for estimating trace elements requirements, together with a better understanding of retention coefficients, will provide greater reliability in the formulation of diets for sheep raised in tropical regions.</p>
</sec>
<sec id="s5" sec-type="conclusion">
<label>5</label>
<title>Conclusion</title>
<p>In conclusion, our study makes a significant contribution by demonstrating the influence of sex on the trace mineral requirements of hair sheep. The requirements for Mn, Co, and Cr increased with increasing body weights, whereas Fe and Zn showed a stable tendency. Our study indicated that the hair sheep trace elements requirements are different from the main nutritional requirements established by <xref ref-type="bibr" rid="B34">NRC (2007)</xref> and <xref ref-type="bibr" rid="B18">INRA (2018)</xref>. Accurate estimation of the mineral requirements of growing sheep necessitates precise knowledge of mineral deposition in the body. It is important to emphasize that trace elements requirements serve as guidelines for the animal&#x2019;s needs and should be reassessed as new information becomes available. Estimating the various requirements through multiple approaches is advisable. Achieving reasonable agreement between methods means greater confidence in the estimated trace mineral requirements.</p>
</sec>
</body>
<back>
<sec id="s6" sec-type="data-availability">
<title>Data availability statement</title>
<p>The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.</p></sec>
<sec id="s7" sec-type="author-contributions">
<title>Author contributions</title>
<p>EJ: Writing &#x2013; review &amp; editing, Formal analysis. ES: Investigation, Writing &#x2013; review &amp; editing, Methodology. MA: Investigation, Writing &#x2013; review &amp; editing, Formal analysis, Methodology. CH: Formal analysis, Writing &#x2013; original draft, Methodology, Investigation. AB: Formal analysis, Methodology, Investigation, Writing &#x2013; review &amp; editing. MM: Conceptualization, Methodology, Writing &#x2013; review &amp; editing, Formal analysis. LS: Formal analysis, Methodology, Writing &#x2013; review &amp; editing. LB: Methodology, Conceptualization, Writing &#x2013; review &amp; editing, Formal analysis. SS: Writing &#x2013; review &amp; editing, Methodology, Investigation. RO: Methodology, Conceptualization, Formal analysis, Writing &#x2013; review &amp; editing. EP: Methodology, Project administration, Conceptualization, Supervision, Writing &#x2013; original draft, Writing &#x2013; review &amp; editing.</p></sec>
<sec id="s9" sec-type="COI-statement">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p></sec>
<sec id="s10" sec-type="ai-statement">
<title>Generative AI statement</title>
<p>The author(s) declare that no Generative AI was used in the creation of this manuscript.</p>
<p>Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.</p></sec>
<sec id="s11" sec-type="disclaimer">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p></sec>
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<fn id="n1" fn-type="custom" custom-type="edited-by">
<p>Edited by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1177275">Adugna Tolera</ext-link>, Hawassa University, Ethiopia</p></fn>
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