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Thus, the objective of this study was to compare the predictive ability of different genomic single-step methods using AFC information from Murrah buffaloes. From a pedigree file containing 3320 buffaloes, 2247 cows had AFC records and 553 animals were genotyped. The following models were performed: pedigree-based BLUP (PBLUP), single-step GBLUP (ssGBLUP), weighted single-step GBLUP (WssGBLUP), and single-step Bayesian regression methods (ssBR-BayesA, BayesBπ, BayesCπ, Bayes-Lasso, and BayesRR). To compare the methodologies, the accuracy and dispersion of (G)EBVs were assessed using the LR method. Accuracy estimates for the genotyped animals ranged from 0.30 (PBLUP) to 0.39 (WssGBLUP). Predictions with the traditional model (PBLUP) were very dispersed from what was expected, while BayesCπ (0.99) and WssGBLUP (1.00) obtained the lowest dispersion. The results indicate that the use of genomic information can improve the genetic gain for AFC by increasing the accuracy and reducing inflation/deflation of predictions compared to the traditional pedigree-based model. In addition, among all genomic single-step models studied, WssGBLUP and single-step BayesA were the most advantageous methods to be used in the genomic evaluation of AFC of buffaloes from this population."> <meta name="citation_doi" content="10.1017/S0021859624000364"> <link rel="alternate" href="/core/journals/journal-of-agricultural-science/article/comparison-of-singlestep-methods-for-genomic-prediction-of-age-at-first-calving-in-dairy-buffaloes/EE7AD86B2F8357591452CD46DAD1D5EA" hreflang="en" /> <link rel="icon" href="/core/cambridge-core/public/images/favicon.ico" type="image/x-icon"/> <link rel="shortcut icon" href="/core/cambridge-core/public/images/favicon.ico" type="image/x-icon"/> <link href='//fonts.googleapis.com/css?family=Noto+Sans:400,700,400italic,700italic' rel='stylesheet' type='text/css'>  <link rel="stylesheet" href="/core/cambridge-core/public/css/app.css?version=v7.337.1-hotfix"/> <link rel="dns-prefetch" href="https://usage.prod.aop.cambridge.org/v1/events"> <link 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data-v-63dfaf6e>The Journal of Agricultural Science</span> </a></li><li class="page-breadcrumbs__item" data-v-3692cf84><span aria-hidden="true" class="breadcrumbs-wrapper__arrow" data-v-3692cf84>></span><a href="/core/journals/journal-of-agricultural-science/firstview" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-3692cf84><span data-v-63dfaf6e>FirstView</span> </a></li><li class="page-breadcrumbs__item" data-v-3692cf84><span aria-hidden="true" class="breadcrumbs-wrapper__arrow" data-v-3692cf84>></span><span data-v-3692cf84>Comparison of single-step methods for genomic prediction...</span></li></ul></div></div> <div class="language" data-v-3692cf84><ul class="language-switch" data-v-6b1118dd data-v-3692cf84><li aria-label="English" data-v-6b1118dd><span class="language-option current divider" data-v-6b1118dd>English</span></li><li aria-label="Français" data-v-6b1118dd><span role="button" tabindex="0" href="#" lang="fr" class="language-option" data-v-6b1118dd> Français </span></li></ul></div></div></div></div> <div class="container container__modified" data-v-01274b1d>  <div class="row" data-v-01274b1d><div role="complementary" aria-label="table of content" class="column__left" data-v-01274b1d><div class="col journal-container row" data-v-146270e8 data-v-01274b1d><img src="https://static.cambridge.org/covers/AGS_0_0_0/the-journal-of-agricultural-science.jpg" alt="" class="journal__image" data-v-146270e8> <a href="/core/journals/journal-of-agricultural-science" class="app-link journal__title app-link__text app-link--underlined" data-v-63dfaf6e data-v-146270e8><span class="text" data-v-63dfaf6e>The Journal of Agricultural Science </span> </a> <hr aria-hidden="true" class="separator default" data-v-7036083a data-v-146270e8></div>  <div id="toc" class="table-of-content" data-v-01274b1d><h2>Article contents</h2> <div id="toc-list-wrapper" class="table-of-content__wrapper"><ul id="toc-list" class="list"><li class="list__item"><a href="#sec0" class="list__item__link"><span class="toc-title">Abstract</span></a></li> <li class="list__item"><a href="#sec1" class="list__item__link"> <span><div class="toc-title">Introduction</div></span></a></li><li class="list__item"><a href="#sec2" class="list__item__link"> <span><div class="toc-title">Materials and methods</div></span></a></li><li class="list__item"><a href="#sec3" class="list__item__link"> <span><div class="toc-title">Results</div></span></a></li><li class="list__item"><a href="#sec4" class="list__item__link"> <span><div class="toc-title">Discussion</div></span></a></li><li class="list__item"><a href="#sec-nts1" class="list__item__link"> <span><div class="toc-title">Authors’ contributions</div></span></a></li><li class="list__item"><a href="#sec-fs1" class="list__item__link"> <span><div class="toc-title">Funding statement</div></span></a></li><li class="list__item"><a href="#sec-ci1" class="list__item__link"> <span><div class="toc-title">Competing interests</div></span></a></li><li class="list__item"><a href="#sec-nts2" class="list__item__link"> <span><div class="toc-title">Ethical standards</div></span></a></li>  <li class="list__item"><a href="#references-list" class="list__item__link"><span class="toc-title">References</span></a></li></ul></div></div></div> <div class="column__main" data-v-01274b1d><div class="row" data-v-01274b1d><div class="column__main__left" data-v-01274b1d><div id="maincontent" class="col" data-v-862424e6 data-v-01274b1d> <hgroup data-v-862424e6><h1 data-v-862424e6>Comparison of single-step methods for genomic prediction of age at first calving in dairy buffaloes</h1> </hgroup>     <div class="row published-date" data-v-862424e6><p data-v-862424e6> Published online by Cambridge University Press: <strong data-v-862424e6>14 November 2024</strong></p></div>   <div class="contributors-details" data-v-99f6eb26 data-v-862424e6><div class="row contributors" data-v-99f6eb26><div class="col" data-v-99f6eb26><div class="row contributor-type" data-v-792406ce data-v-99f6eb26> <div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=Jessica%20Cristina%20Gon%C3%A7alves%20dos%20Santos&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>Jessica Cristina Gonçalves dos Santos</span> </a>  <span data-v-792406ce>,</span></div><div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=Francisco%20Ribeiro%20de%20Ara%C3%BAjo%20Neto&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>Francisco Ribeiro de Araújo Neto</span> </a> <a target="_blank" href="https://orcid.org/0000-0003-1064-5614" data-test-orcid="Francisco Ribeiro de Araújo Neto" class="app-link contributor-type__contributor__orcid app-link__icon app-link--" data-v-63dfaf6e data-v-792406ce><img src="data:image/svg+xml;base64,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" alt="Open the ORCID record for Francisco Ribeiro de Araújo Neto" class="app-icon icon orcid" data-v-d2c09870 data-v-63dfaf6e> <span class="sr-only" data-v-63dfaf6e>[Opens in a new window]</span></a> <span data-v-792406ce>,</span></div><div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=Gabriela%20Stefani%20Fernandez&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>Gabriela Stefani Fernandez</span> </a>  <span data-v-792406ce>,</span></div><div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=Daniel%20Jordan%20de%20Abreu%20Santos&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>Daniel Jordan de Abreu Santos</span> </a>  <span data-v-792406ce>,</span></div><div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=Felipe%20Pereira%20Cunha&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>Felipe Pereira Cunha</span> </a>  <span data-v-792406ce>,</span></div><div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=Rusbel%20Raul%20Aspilcueta-Borquis&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>Rusbel Raul Aspilcueta-Borquis</span> </a>  <span data-v-792406ce> and</span></div><div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=Humberto%20Tonhati&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>Humberto Tonhati</span> </a>  <span data-v-792406ce></span></div> </div> </div> <div class="col-2 collapse-link" data-v-99f6eb26><a href="#authors-details" data-toggle="collapse" aria-expanded="false" aria-controls="authors-details" class="app-link collapsed app-link__text-icon app-link--secondary reverse" data-v-63dfaf6e data-v-99f6eb26><img src="data:image/svg+xml;base64,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" alt="" class="app-icon icon arrow-down" data-v-d2c09870 data-v-63dfaf6e><span class="text" data-v-63dfaf6e>Show author details </span> </a></div></div> <hr aria-hidden="true" class="separator default" data-v-7036083a data-v-99f6eb26> <dl id="authors-details" class="authors-details collapse" data-v-2edb8da6 data-v-99f6eb26><div data-test-author="Jessica Cristina Gonçalves dos Santos" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>Jessica Cristina Gonçalves dos Santos</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>Faculdade de Ciências Agrárias e Veterinárias de Jaboticabal – UNESP, Jaboticabal, São Paulo, Brazil</span> </span></div></dd></div><div data-test-author="Francisco Ribeiro de Araújo Neto" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>Francisco Ribeiro de Araújo Neto*</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>Instituto Federal de Ciência e Tecnologia Goiano – IFGoiano, Rio Verde, Goiás</span> </span></div></dd></div><div data-test-author="Gabriela Stefani Fernandez" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>Gabriela Stefani Fernandez</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>Faculdade de Ciências Agrárias e Veterinárias de Jaboticabal – UNESP, Jaboticabal, São Paulo, Brazil</span> </span></div></dd></div><div data-test-author="Daniel Jordan de Abreu Santos" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>Daniel Jordan de Abreu Santos</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>Faculdade de Ciências Agrárias e Veterinárias de Jaboticabal – UNESP, Jaboticabal, São Paulo, Brazil</span> </span></div></dd></div><div data-test-author="Felipe Pereira Cunha" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>Felipe Pereira Cunha</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>Instituto Federal de Ciência e Tecnologia Goiano – IFGoiano, Rio Verde, Goiás</span> </span></div></dd></div><div data-test-author="Rusbel Raul Aspilcueta-Borquis" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>Rusbel Raul Aspilcueta-Borquis</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>Universidade Tecnológica Federal do Paraná – UFTPR, Dois Vizinhos, Paraná</span> </span></div></dd></div><div data-test-author="Humberto Tonhati" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>Humberto Tonhati</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>Faculdade de Ciências Agrárias e Veterinárias de Jaboticabal – UNESP, Jaboticabal, São Paulo, Brazil</span> </span></div></dd></div> <div class="row" data-v-2edb8da6><dt class="col-sm-2 col-12 title" data-v-2edb8da6> * </dt> <dd class="col content" data-v-2edb8da6><div class="row" data-v-2edb8da6><div class="d-sm-flex d-inline flex-sm-1 flex-sm-wrap" data-v-2edb8da6><div class="d-inline" data-v-2edb8da6><span data-v-2edb8da6><div class="corresp"><span class="bold">Corresponding author:</span> F. R. Araujo Neto; Email: <a href="mailto:francisco.neto@ifgoiano.edu.br">francisco.neto@ifgoiano.edu.br</a></div></span></div></div></div></dd></div> <hr aria-hidden="true" class="separator default" data-v-7036083a data-v-2edb8da6></dl></div></div> <div id="app-tabs" class="tabs" data-v-1d90c6ce data-v-01274b1d><div id="app-tabs-wrapper" class="tabs__wrapper" data-v-1d90c6ce><div role="navigation" aria-label="tab navigation" class="container" data-v-1d90c6ce><a data-toggle="collapse" href="#appTabs" role="button" aria-expanded="false" aria-controls="appTabs" class="tabs__collapse collapsed d-sm-none d-print-none" data-v-1d90c6ce><span data-v-1d90c6ce></span> <span class="tabs-arrow-up" data-v-1d90c6ce></span> <span class="tabs-arrow-down" data-v-1d90c6ce></span></a> <ul id="appTabs" role="tablist" class="nav nav-tabs tabs__list collapse show" data-v-1d90c6ce><li role="none" class="tabs__tab" data-v-1d90c6ce><a aria-selected="true" href="#article-tab" role="tab" aria-controls="article-tab" 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class="list__item__link"><span class="toc-title">Abstract</span></a></li> <li class="list__item"><a href="#sec1" class="list__item__link"> <span>Introduction</span></a></li><li class="list__item"><a href="#sec2" class="list__item__link"> <span>Materials and methods</span></a></li><li class="list__item"><a href="#sec3" class="list__item__link"> <span>Results</span></a></li><li class="list__item"><a href="#sec4" class="list__item__link"> <span>Discussion</span></a></li><li class="list__item"><a href="#sec-nts1" class="list__item__link"> <span>Authors’ contributions</span></a></li><li class="list__item"><a href="#sec-fs1" class="list__item__link"> <span>Funding statement</span></a></li><li class="list__item"><a href="#sec-ci1" class="list__item__link"> <span>Competing interests</span></a></li><li class="list__item"><a href="#sec-nts2" class="list__item__link"> <span>Ethical standards</span></a></li>  <li class="list__item"><a href="#references-list" class="list__item__link"><span 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target="_blank" href="https://s100.copyright.com/AppDispatchServlet?publisherName=CUP&publication=AGS&title=Comparison%20of%20single-step%20methods%20for%20genomic%20prediction%20of%20age%20at%20first%20calving%20in%20dairy%20buffaloes&publicationDate=14%20November%202024&author=Jessica%20Cristina%20Gon%C3%A7alves%20dos%20Santos%2C%20Francisco%20Ribeiro%20de%20Ara%C3%BAjo%20Neto%2C%20Gabriela%20Stefani%20Fernandez%2C%20Daniel%20Jordan%20de%20Abreu%20Santos%2C%20Felipe%20Pereira%20Cunha%2C%20Rusbel%20Raul%20Aspilcueta-Borquis%2C%20Humberto%20Tonhati©right=Copyright%20%C2%A9%20The%20Author(s)%2C%202024.%20Published%20by%20Cambridge%20University%20Press&contentID=10.1017%2FS0021859624000364&startPage=1&endPage=7&orderBeanReset=True&volumeNum=&issueNum=&oa=" data-test-id="buttonRightLink" class="app-link rights-link d-print-none app-link__text-icon app-link--accent" data-v-63dfaf6e data-v-92ee52a2 data-v-43a4d572><img src="/core/page-component/img/rights-icon.d4a677c.svg" alt="" class="app-icon icon rights" data-v-d2c09870 data-v-63dfaf6e><span class="text" data-v-63dfaf6e>Rights & Permissions </span> <span class="sr-only" data-v-63dfaf6e>[Opens in a new window]</span></a></div> <hr aria-hidden="true" class="separator default" data-v-7036083a></div> <div class="share-modal-overlay" style="display:none;" data-v-43a4d572></div> <div data-spy="scroll" data-target="#toc" class="scrollspy-content" data-v-43a4d572> <div id="sec0" class="col article-abstract sec" data-v-2fa8b348 data-v-43a4d572><div class="abstract-text-container" data-v-2fa8b348><div lang="en"><h2>Abstract</h2>  <div class="abstract-content"><div class="abstract" data-abstract-type="normal"><p>The age at first calving (AFC) is an important trait to be considered in breeding programmes of dairy buffaloes, where new approaches and technologies, such as genomic selection, are constantly applied. Thus, the objective of this study was to compare the predictive ability of different genomic single-step methods using AFC information from Murrah buffaloes. From a pedigree file containing 3320 buffaloes, 2247 cows had AFC records and 553 animals were genotyped. The following models were performed: pedigree-based BLUP (PBLUP), single-step GBLUP (ssGBLUP), weighted single-step GBLUP (WssGBLUP), and single-step Bayesian regression methods (ssBR-BayesA, BayesBπ, BayesCπ, Bayes-Lasso, and BayesRR). To compare the methodologies, the accuracy and dispersion of (G)EBVs were assessed using the LR method. Accuracy estimates for the genotyped animals ranged from 0.30 (PBLUP) to 0.39 (WssGBLUP). Predictions with the traditional model (PBLUP) were very dispersed from what was expected, while BayesCπ (0.99) and WssGBLUP (1.00) obtained the lowest dispersion. The results indicate that the use of genomic information can improve the genetic gain for AFC by increasing the accuracy and reducing inflation/deflation of predictions compared to the traditional pedigree-based model. In addition, among all genomic single-step models studied, WssGBLUP and single-step BayesA were the most advantageous methods to be used in the genomic evaluation of AFC of buffaloes from this population.</p></div></div> <hr aria-hidden="true" class="abstract-divider separator default" data-v-7036083a></div></div>   </div>  <div class="keywords" data-v-86c27100 data-v-43a4d572><h2 data-v-86c27100>Keywords</h2> <div class="row keywords__pills" data-v-86c27100><a href="/core/search?filters[keywords]=Bayesian inference" data-v-f0b31360 data-v-86c27100><span data-v-f0b31360 data-v-86c27100>Bayesian inference</span></a><a href="/core/search?filters[keywords]=Bubalus bubalis" data-v-f0b31360 data-v-86c27100><span data-v-f0b31360 data-v-86c27100>Bubalus bubalis</span></a><a href="/core/search?filters[keywords]=genomic selection" data-v-f0b31360 data-v-86c27100><span data-v-f0b31360 data-v-86c27100>genomic selection</span></a><a href="/core/search?filters[keywords]=reproductive traits" data-v-f0b31360 data-v-86c27100><span data-v-f0b31360 data-v-86c27100>reproductive traits</span></a></div> <hr aria-hidden="true" class="separator default" data-v-7036083a data-v-86c27100></div>  <dl class="article-details" data-v-6e32a161 data-v-43a4d572><div class="row" data-v-6e32a161><dt class="col-12 col-sm-3 col-md-2_5 title" data-v-6e32a161> Type </dt> <dd class="col content" data-v-6e32a161>Animal Research Paper</dd></div> <div class="row" data-v-6e32a161><dt class="col-12 col-sm-3 col-md-2_5 title" data-v-6e32a161> Information </dt> <dd class="col content" data-v-6e32a161><div class="content__journal" data-v-6e32a161><a href="/core/journals/journal-of-agricultural-science" class="app-link app-link__text app-link--underlined" data-v-63dfaf6e data-v-6e32a161><span class="text" data-v-63dfaf6e>The Journal of Agricultural Science </span> </a> <span data-v-6e32a161> , <a href="/core/journals/journal-of-agricultural-science/firstview" class="app-link app-link__text app-link--underlined" data-v-63dfaf6e data-v-6e32a161><span class="text" data-v-63dfaf6e>First View </span> </a></span>  <span data-v-6e32a161>, pp. 1 - 7</span> </div> <div class="doi-data" data-v-6e32a161><div data-v-6e32a161>DOI: <a target="_blank" href="https://doi.org/10.1017/S0021859624000364" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-6e32a161><span class="text" data-v-63dfaf6e>https://doi.org/10.1017/S0021859624000364 </span> <span class="sr-only" data-v-63dfaf6e>[Opens in a new window]</span></a></div> <a data-target="crossmark" aria-label="Check for updates" href="#" class="crossmark-widget" data-v-6e32a161><img src="/core/page-component/img/crossmark-logo.61d5da3.svg" alt="Check for updates" data-v-6e32a161></a></div>  </dd></div>   <div class="row" data-v-6e32a161><dt class="col-12 col-sm-3 col-md-2_5 title" data-v-6e32a161> Copyright </dt> <dd class="col content" data-v-6e32a161><div data-v-6e32a161> Copyright © The Author(s), 2024. Published by Cambridge University Press </div></dd></div></dl>  <div id="content-container" class="content-container" data-v-43a4d572><div class="content-box"><div class="article research-article NLM"> <div class="body"> <div class="sec intro" data-magellan-destination="sec1" id="sec1"><h2 class="A"> Introduction</h2> <p class="p"> Age at first calving (AFC) is an important indicator trait of reproductive efficiency that is genetically monitored by the Milk-Recording Buffalo Program in Brazil (Aspilcueta-Borquis <em class="italic">et al</em>., <a class="xref bibr" href="#ref7"><span class="show-for-sr">Reference Aspilcueta-Borquis, Seno, Araujo Neto, Santos, Hurtado-Lugo and Tonhati</span>2022</a>). It is well known, however, that the genetic progress obtained by direct selection of AFC can be very slow due to the low heritability magnitude of this trait in Buffaloes (Camargo <em class="italic">et al</em>., <a class="xref bibr" href="#ref10"><span class="show-for-sr">Reference Camargo, Aspilcueta-Borquis, Fortes, Porto-Neto, Cardoso, Santos, Lehnert, Reverter, Moore and Tonhati</span>2015</a>). Since genomic selection is more accurate than traditional selection, especially for low-heritability traits (Calus <em class="italic">et al</em>., <a class="xref bibr" href="#ref9"><span class="show-for-sr">Reference Calus, Meuwissen, De Roos and Veerkamp</span>2008</a>), genomic evaluation is the best strategy for predicting breeding values for AFC. Furthermore, Camargo <em class="italic">et al</em>. (<a class="xref bibr" href="#ref10"><span class="show-for-sr">Reference Camargo, Aspilcueta-Borquis, Fortes, Porto-Neto, Cardoso, Santos, Lehnert, Reverter, Moore and Tonhati</span>2015</a>) and Araujo Neto <em class="italic">et al</em>. (<a class="xref bibr" href="#ref3"><span class="show-for-sr">Reference Araujo Neto, Takada, Santos, Aspilcueta-Borquis, Cardoso, Nascimento, Leão, Oliveira and Tonhati</span>2020<em class="italic">a</em></a>) have reported some specific genomic regions highly associated to this trait in GWAS studies in this population, indicating that differential shrinkage models, such as Bayesian alphabet and weighted single-step GBLUP models, would be a reasonable alternative to be explored.</p> <p class="p"> The single-step GBLUP (ssGBLUP) method has become the main methodology used for genomic evaluations in dairy buffaloes (Araujo Neto <em class="italic">et al</em>., <a class="xref bibr" href="#ref3"><span class="show-for-sr">Reference Araujo Neto, Takada, Santos, Aspilcueta-Borquis, Cardoso, Nascimento, Leão, Oliveira and Tonhati</span>2020<em class="italic">a</em></a>, <a class="xref bibr" href="#ref4"><span class="show-for-sr">Reference Araujo Neto, Santos, Fernandes Júnior, Aspilcueta-Borquis, Nascimento, Seno, Tonhati and Oliveira</span>2020<em class="italic">b</em></a>; Cesarani <em class="italic">et al</em>., <a class="xref bibr" href="#ref13"><span class="show-for-sr">Reference Cesarani, Biffani, Garcia, Lourenco, Bertolini, Neglia, Misztal and Macciotta</span>2021</a>; Lázaro <em class="italic">et al</em>., <a class="xref bibr" href="#ref22"><span class="show-for-sr">Reference Lázaro, Tonhati, Oliveira, Silva, Nascimento, Santos, Stefani and Brito</span>2021</a>; Araujo Neto <em class="italic">et al</em>., <a class="xref bibr" href="#ref5"><span class="show-for-sr">Reference Araujo Neto, Santos, Silva Arce, Borquis, Santos, Guimarães, Nascimento, Oliveira and Tonhati</span>2022</a>) given the ease of integrating the relationship matrices, based on pedigree (<strong>A</strong>) and genomic (<strong>G</strong>) information, without major changes in the mixed model equations (Misztal <em class="italic">et al</em>., <a class="xref bibr" href="#ref27"><span class="show-for-sr">Reference Misztal, Lourenco and Legarra</span>2020</a>). Moreover, this methodology allows assigning different weights for each marker, originating the weighted single-step GBLUP method – WssGBLUP (Wang <em class="italic">et al</em>., <a class="xref bibr" href="#ref31"><span class="show-for-sr">Reference Wang, Misztal, Aguilar, Legarra and Muir</span>2012</a>; Zhang <em class="italic">et al</em>., <a class="xref bibr" href="#ref34"><span class="show-for-sr">Reference Zhang, Lourenco, Aguilar, Legarra and Misztal</span>2016</a>).</p> <p class="p"> Subsequently, Fernando <em class="italic">et al</em>. (<a class="xref bibr" href="#ref17"><span class="show-for-sr">Reference Fernando, Dekkers and Garrick</span>2014</a>) proposed single-step methodologies combined to Bayesian regression methods (ssBR), as an option to ssGBLUP. Nonetheless, few studies have been developed comparing the results of the different single-step methodologies (Lee <em class="italic">et al</em>., <a class="xref bibr" href="#ref23"><span class="show-for-sr">Reference Lee, Cheng, Garrick, Golden, Dekkers, Park, Lee and Fernando</span>2017</a>; Gao <em class="italic">et al</em>., <a class="xref bibr" href="#ref18"><span class="show-for-sr">Reference Gao, Koivula, Jensen, Strandén, Madsen, Pitkänen, Aamand and Mäntysaari</span>2018</a>; Zhou <em class="italic">et al</em>., <a class="xref bibr" href="#ref35"><span class="show-for-sr">Reference Zhou, Mrode, Zhang, Zhang, Li and Liu</span>2018</a>). Based on this, it becomes interesting to perform similar analyses in buffalo databases to assist in decision making in breeding programmes that employ genomic technology. Thus, this work was designed with the aim of comparing the predictive ability of different single-step methods using AFC information from Murrah buffaloes.</p> </div> <div class="sec materials" data-magellan-destination="sec2" id="sec2"><h2 class="A"> Materials and methods</h2> <div class="sec" data-magellan-destination="sec2-1" id="sec2-1"><h3 class="B"> Dataset</h3> <p class="p"> The phenotypic dataset consisted of 2,314AFC records of Murrah buffalo cows born between 1995 and 2017. Contemporary groups (CG) were formed considering animals born on the same farm, year and season of birth, which was divided into two (dry and rainy season). Animals with records outside the range between ±3 standard deviations from their CG averages and animals belonging to GCs with less than five individuals were removed.</p> <p class="p"> From a pedigree file containing 3320 buffaloes, 553 animals (539 dams and 14 sires) were genotyped with the Axiom Buffalo Genotyping Array 90 K (Iamartino <em class="italic">et al</em>., <a class="xref bibr" href="#ref21"><span class="show-for-sr">Reference Iamartino, Nicolazzi, Van Tassell, Reecy, Fritz-Waters, Koltes, Biffani, Sonstegard, Schroeder, Ajmone-Marsan, Negrini, Pasquariello, Ramelli, Coletta, Garcia, Ali, Ramunno, Cosenza, Oliveira, Drummond, Bastianetto, Davassi, Pirani, Brew and Williams</span>2017</a>). Only SNPs present on autosomal chromosomes (BBU1-BBU24 referenced by UOA_WB_1 genome assembly), as well as those with call rate > 95%, MAF > 3% and significance level for Hardy Weinberg equilibrium test was 10<sup class="sup">−5</sup> , were remained in the analysis. All samples had a call rate >90%. The database description (phenotypic and genotypic information) after the consistency step is in <a class="xref table" href="#tab01">Table 1</a>. </p><div class="table-wrap" data-magellan-destination="tab01" id="tab01"><div class="caption"><p class="p"><span class="label">Table 1.</span> Description of age at first calving dataset used in this study</p></div> <span> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_tab1.png?pub-status=live" class="aop-lazy-load-image" width="461" height="272" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_tab1.png" data-zoomable="false"></div> </span> </div> </div> <div class="sec" data-magellan-destination="sec2-2" id="sec2-2"><h3 class="B"> PBLUP, ssGBLUP and WssGBLUP models</h3> <p class="p"> This set of methodologies is based on the use of relationship matrices between individuals in mixed model equations, with the differences consisting of the type of information used (pedigree or genomic) and the way these matrices are constructed. The model using pedigree based BLUP (PBLUP) can be described as:</p><div data-mathjax-status="alt-graphic" class="disp-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$$y = {\boldsymbol X}\beta + {\boldsymbol Z}\alpha + e$$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU1.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="124" height="20" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU1.png" data-zoomable="false"></span></div><p class="p continuation">where, <em class="italic">y</em> is the vector of phenotypic records (AFC); <em class="italic">β</em> is the fixed effect vector (CG), <strong><em class="italic">X</em></strong> is the incidence matrix that associates <em class="italic">β</em> with <em class="italic">y</em>; <em class="italic">α</em> is the vector of additive genetic effects, <strong><em class="italic">Z</em></strong> is an incidence matrix associating <em class="italic">α</em> with <em class="italic">y</em> and, <em class="italic">e</em> is the vector of residuals. The following assumptions were made:</p><div data-mathjax-status="alt-graphic" class="disp-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$$E( y ) = {\boldsymbol X}\beta \quad E( \alpha ) = 0\quad E( e ) = 0$$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU2.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="227" height="20" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU2.png" data-zoomable="false"></span></div><div data-mathjax-status="alt-graphic" class="disp-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$${\rm Var}( \alpha ) = A\sigma _\alpha ^2 \quad {\rm Var}( e ) = {\boldsymbol I}_n\sigma _\varepsilon ^2 $$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU3.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="212" height="23" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU3.png" data-zoomable="false"></span></div><p class="p continuation">where <span data-mathjax-status="alt-graphic" class="inline-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$\sigma _\alpha ^2$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline1.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="20" height="22" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline1.png" data-zoomable="false"></span></span> and <span data-mathjax-status="alt-graphic" class="inline-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$\sigma _\varepsilon ^2$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline2.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="18" height="22" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline2.png" data-zoomable="false"></span></span> represent the additive genetic and residual variances; <strong><em class="italic">A</em></strong> and <strong><em class="italic">I</em></strong><sub><em class="italic">n</em></sub> are the pedigree relationship and an identity matrices, respectively.</p> <p class="p"> The single step GBLUP (ssGBLUP) method is an extension of the PBLUP model, in which the pedigree-based (<strong>A</strong>) and genomic (<strong>G</strong>) relationship matrices are combined into a single matrix (<strong>H</strong>), as described by Aguilar <em class="italic">et al</em>. (<a class="xref bibr" href="#ref2"><span class="show-for-sr">Reference Aguilar, Misztal, Johnson, Legarra, Tsuruta and Lawlor</span>2010</a>). So, its inverse can be obtained as:</p><div data-mathjax-status="alt-graphic" class="disp-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$${\boldsymbol H}^{{-}1} = {\boldsymbol A}^{{-}1} + \left[{\matrix{ 0 \hfill & 0 \hfill \cr 0 \hfill & {{\boldsymbol G}^{{-}1}-{\boldsymbol A}_{22}^{{-}1} } \hfill \cr } } \right]$$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU4.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="221" height="43" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU4.png" data-zoomable="false"></span></div><p class="p continuation">where <strong><em class="italic">A</em></strong><sup class="sup">−1</sup> and <strong><em class="italic">G</em></strong><sup class="sup">−1</sup> are the inverse matrices of <strong>A</strong> and <strong>G</strong> respectively, and <span data-mathjax-status="alt-graphic" class="inline-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">${\boldsymbol A}_{22}^{{-}1}$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline3.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="29" height="22" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline3.png" data-zoomable="false"></span></span> is the inverse of the section of <strong>A</strong> related to the genotyped animals. The <strong>G</strong> matrix was obtained according to VanRaden (<a class="xref bibr" href="#ref30a"><span class="show-for-sr">Reference VanRaden</span>2008</a>) as:</p><div data-mathjax-status="alt-graphic" class="disp-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$${\boldsymbol G} = \displaystyle{{{\boldsymbol ZD{Z}^{\prime}}} \over {2\;\sum {\,p_i} ( 1-p_i{) }^{\prime}}}$$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU5.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="142" height="43" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU5.png" data-zoomable="false"></span></div><p class="p continuation">where <em class="italic">p</em> <sub><em class="italic">i</em></sub> is the minor allele frequency (MAF) of SNP <em class="italic">i</em>, <strong><em class="italic">Z</em></strong> is a matrix relating genotypes of each locus centred by allele frequencies, and <strong><em class="italic">D</em></strong> is a diagonal matrix of weights for SNP variances, (with elements <em class="italic">d</em> <sub><em class="italic">i</em></sub> = SNP <em class="italic">i</em> weight). In ssGBLUP model is set <strong><em class="italic">D</em></strong> = <strong><em class="italic">I</em></strong>, so that the weight of all SNPs is equal to 1.</p> <p class="p"> In WssGBLUP method (Wang <em class="italic">et al</em>., <a class="xref bibr" href="#ref31"><span class="show-for-sr">Reference Wang, Misztal, Aguilar, Legarra and Muir</span>2012</a>) markers are assigned with different weights using an iterative process described with the following steps: </p><ol class="list number nomark"> <li class="list-item"><p class="p"><span class="label">1.</span> Set <em class="italic">D</em> <sup class="sup">(<em class="italic">t</em>)</sup> = <em class="italic">I</em>, when <em class="italic">t</em> = 1</p></li> <li class="list-item"><p class="p"><span class="label">2.</span> The genomic relationship matrix is setup for <em class="italic">t</em> as <span data-mathjax-status="alt-graphic" class="inline-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">${\boldsymbol G}^{( t ) } = {\boldsymbol Z}{\boldsymbol D}^{( {\boldsymbol t} ) }{\boldsymbol {Z}^{\prime}}/( 2\;\sum p_i( {1-p_i} )$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline4.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="210" height="23" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline4.png" data-zoomable="false"></span></span></p></li> <li class="list-item"><p class="p"><span class="label">3.</span> The Genomic Breeding Value (GEBV or <span data-mathjax-status="alt-graphic" class="inline-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$\hat{\alpha }$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline5.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="13" height="15" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline5.png" data-zoomable="false"></span></span>) for <em class="italic">t</em> are obtained;</p></li> <li class="list-item"><p class="p"><span class="label">4.</span> 4.The GEBV <span data-mathjax-status="alt-graphic" class="inline-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$\hat{\alpha }^{( t ) }$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline6.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="24" height="18" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline6.png" data-zoomable="false"></span></span>are converted to SNP effects (<span data-mathjax-status="alt-graphic" class="inline-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$\hat{u}$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline7.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="11" height="16" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline7.png" data-zoomable="false"></span></span>) as <span data-mathjax-status="alt-graphic" class="inline-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$\hat{u}^t = {\boldsymbol D}^{( t ) }{\boldsymbol {Z}^{\prime}}( {\boldsymbol G}^{( t ) }) ^{{-}1}\hat{\alpha }^{( t ) }$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline8.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="150" height="21" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline8.png" data-zoomable="false"></span></span></p></li> <li class="list-item"><p class="p"><span class="label">5.</span> The weight of the <em class="italic">i</em>th SNP (the <em class="italic">i</em>th element of <strong>D</strong> or <em class="italic">d</em> <sub><em class="italic">i</em></sub>) is calculated;</p></li> <li class="list-item"><p class="p"><span class="label">6.</span> SNP weights are normalized in <strong><em class="italic">D</em></strong><sup class="sup">(<em class="italic">t</em>+1)</sup> to have constant genetic variances of SNP effects;</p></li> <li class="list-item"><p class="p"><span class="label">7.</span> Loop to step 2 three times and exit.</p></li> </ol> <p class="p"> For the methods mentioned above, the program BLUPF90+ (Misztal <em class="italic">et al</em>., <a class="xref bibr" href="#ref26"><span class="show-for-sr">Reference Misztal, Tsuruta, Lourenço, Masuda, Aguilar, Legarra and Vitezica</span>2014</a>) was used for the estimation of the variance components and for the validation step. The estimation of the effects of the markers and the calculation of the weighting (WssGBLUP) were performed with the program POSTGSF90 (Misztal <em class="italic">et al</em>., <a class="xref bibr" href="#ref26"><span class="show-for-sr">Reference Misztal, Tsuruta, Lourenço, Masuda, Aguilar, Legarra and Vitezica</span>2014</a>). The heritability estimates for AFC were obtained from these estimated variance components.</p> </div> <div class="sec" data-magellan-destination="sec2-3" id="sec2-3"><h3 class="B"> Single-step Bayesian regression models (ssBR)</h3> <p class="p"> The ssBR models combine all available data from genotyped and non-genotyped animals and use imputed marker covariates for animals that are not genotyped (Fernando <em class="italic">et al</em>., <a class="xref bibr" href="#ref17"><span class="show-for-sr">Reference Fernando, Dekkers and Garrick</span>2014</a>), can be described as:</p><div data-mathjax-status="alt-graphic" class="disp-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$$\left[{\matrix{ {y_n} \cr {y_g} \cr } } \right] = \left[{\matrix{ {{\boldsymbol X}_{\boldsymbol n}} \cr {{\boldsymbol X}_g} \cr } } \right]\beta + \left[{\matrix{ {{\boldsymbol Z}_n} & 0 \cr 0 & {{\boldsymbol Z}_g} \cr } } \right]\left[{\matrix{ {{\boldsymbol M}_n\alpha + \epsilon } \cr {{\boldsymbol M}_g\alpha \;\;\;\;\;\;\;} \cr } } \right] + e$$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU6.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="322" height="43" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU6.png" data-zoomable="false"></span></div><p class="p continuation">where vectors and matrices for non-genotyped animals are denoted with the subscript <em class="italic">n</em> and for genotyped animals with the subscript <em class="italic">g</em>. Thus, <em class="italic">y</em> <sub><em class="italic">n</em></sub> and <em class="italic">y</em> <sub><em class="italic">g</em></sub> represent the vectors of phenotypic observations; <em class="italic">β</em> is the vector of systematic effects of GC (equivalent to the fixed effect in frequentist methods); <strong><em class="italic">X</em></strong><sub><em class="italic">n</em></sub> and <strong><em class="italic">X</em></strong><sub><em class="italic">g</em></sub> design matrices for the fixed effects; <strong><em class="italic">Z</em></strong><sub><em class="italic">n</em></sub> and <strong><em class="italic">Z</em></strong><sub><em class="italic">g</em></sub> represent incidence matrices associated with the genomic values of the animals; <em class="italic">α</em>, <span data-mathjax-status="alt-graphic" class="inline-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$\epsilon$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline9.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="10" height="11" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline9.png" data-zoomable="false"></span></span> and <em class="italic">e</em>, represent in this order, the vectors of marker effects, imputation residual and model residual; <strong><em class="italic">M</em></strong><sub><strong><em class="italic">g</em></strong></sub> is the marker matrix for the genotyped animals and <strong><em class="italic">M</em></strong><sub><strong><em class="italic">n</em></strong></sub> is the imputed marker matrix for the non-genotyped animals. The matrix <strong><em class="italic">M</em></strong><sub><strong><em class="italic">n</em></strong></sub> can be obtained as:</p><div data-mathjax-status="alt-graphic" class="disp-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$${\boldsymbol M}_n = {\boldsymbol A}_{ng}{\boldsymbol A}_{22}^{{-}1} {\boldsymbol M}_g$$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU7.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="119" height="23" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU7.png" data-zoomable="false"></span></div><p class="p continuation">where <strong><em class="italic">A</em></strong><sub><strong><em class="italic">ng</em></strong></sub> represents the pedigree-based relationship matrix between genotyped and non-genotyped animals and; <span data-mathjax-status="alt-graphic" class="inline-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">${\boldsymbol A}_{2g2g}^{{-}1}$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline10.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="37" height="25" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline10.png" data-zoomable="false"></span></span> represents the inverse of the pedigree-based relationship matrix between genotyped animals. The following ssBR methods were used: BayesA (ssBA- Meuwissen et al., <a class="xref bibr" href="#ref25"><span class="show-for-sr">Reference Meuwissen, Hayes and Goddard</span>2001</a>), BayesBπ (ssBBπ- Meuwissen <em class="italic">et al</em>., <a class="xref bibr" href="#ref25"><span class="show-for-sr">Reference Meuwissen, Hayes and Goddard</span>2001</a>), BayesCπ (ssBCπ- Habier <em class="italic">et al</em>., <a class="xref bibr" href="#ref19"><span class="show-for-sr">Reference Habier, Fernando, Kizilkaya and Garrick</span>2011</a>), Lasso Bayesian (ssBL- Yi and Xu, <a class="xref bibr" href="#ref32"><span class="show-for-sr">Reference Yi and Xu</span>2008</a>) and Bayesian ridge regression (ssBRR- Campos <em class="italic">et al</em>., <a class="xref bibr" href="#ref11"><span class="show-for-sr">Reference Campos, Hickey, Pong-Wong, Daetwyler and Calus</span>2013</a>), where the assumptions for markers effects are shown in <a class="xref table" href="#tab02">Table 2</a>. The hibayes package (Yin <em class="italic">et al</em>., <a class="xref bibr" href="#ref33"><span class="show-for-sr">Reference Yin, Zhang, Li, Zhao and Liu</span>2022</a>), available for the R program (R Core Team, <a class="xref bibr" href="#ref28">2021</a>), was used to perform the ssBR analyses. A total of 350 000 samples and a burn-in period of 150 000 samples were generated. The convergence was evaluated using graphical analysis. The heritability estimates for AFC were also obtained using these models. </p><div class="table-wrap" data-magellan-destination="tab02" id="tab02"><div class="caption"><p class="p"><span class="label">Table 2.</span> Description of different prior for markers effects used in Bayesian single-step regression methods used for genomic analysis of age at first calving in dairy buffaloes</p></div> <span> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_tab2.png?pub-status=live" class="aop-lazy-load-image" width="461" height="260" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_tab2.png" data-zoomable="false"></div> </span> </div> </div> <div class="sec" data-magellan-destination="sec2-4" id="sec2-4"><h3 class="B"> Validation of (G)EBVs</h3> <p class="p"> The predictive ability of the methods was assessed using accuracy and dispersion statistics proposed by Legarra and Reverter (<a class="xref bibr" href="#ref24"><span class="show-for-sr">Reference Legarra and Reverter</span>2018</a>). This methodology is based on predicting (G)EBV using full (<span data-mathjax-status="alt-graphic" class="inline-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$\hat{u} _w$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline11.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="20" height="18" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline11.png" data-zoomable="false"></span></span>) and a partial <span data-mathjax-status="alt-graphic" class="inline-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$( \hat{u} _p)$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline12.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="28" height="21" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline12.png" data-zoomable="false"></span></span> datasets. The partial dataset (reference group) was obtained by omitting phenotypic records of genotyped animals born after 2010 (validation group). Thus, to assess the prediction ability of the models, only genotyped animals from the validation group were used to calculate the following statistics:</p><div data-mathjax-status="alt-graphic" class="disp-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$$\matrix{ {{\rm Accuracy}} \hfill & {{\rm Dispersion}} \hfill \cr {r_{A\hat{A}} = \sqrt {\displaystyle{{{\rm cov}( {\hat{u}_w, \;\hat{u}_p} ) } \over {( {1-\bar{F}} ) \hat{\sigma }_g^2 }}} } \hfill & {b_{w, p} = \displaystyle{{{\rm cov}( {\hat{u}_w, \;\hat{u}_p} ) } \over {{\rm var}( {\hat{u}_p} ) }}} \hfill \cr } $$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU8.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="275" height="70" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU8.png" data-zoomable="false"></span></div><p class="p continuation">where <span data-mathjax-status="alt-graphic" class="inline-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$\bar{F}$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline13.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="13" height="18" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline13.png" data-zoomable="false"></span></span> is the average inbreeding coefficient of the validation individuals and <span data-mathjax-status="alt-graphic" class="inline-formula"><span class="alternatives"><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$\hat{\sigma }_{g, i}^2$</span></span><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline14.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="24" height="25" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline14.png" data-zoomable="false"></span></span> is the estimate of additive genetic variance.</p> </div> </div> <div class="sec results" data-magellan-destination="sec3" id="sec3"><h2 class="A"> Results</h2> <p class="p"> In this study, the estimated heritability for AFC was 0.17 using BLUP-based methods and 0.16 to 0.18 using ssBR methods and, the estimates of the effects of the markers can be seen in <a class="xref fig" href="#fig01">Figure 1</a>. Accuracy estimates for the genotyped animals ranged from 0.30 (ssBRR) to 0.39 (WssGBLUP) (<a class="xref fig" href="#fig02">Fig. 2</a>). Estimates of accuracy with low magnitude were observed for non-genotyped animals, with values ranging from 0.29 (ssGBLUP) to 0.33 (ssBA). The PBLUP model presented accuracies of 0.30 and 0.29 for genotyped and non-genotyped animals, respectively. </p><section><div class="fig fig" data-magellan-destination="fig01" id="fig01"><div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_fig1.png?pub-status=live" class="aop-lazy-load-image" width="2050" height="2088" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_fig1.png" data-zoomable="true"></div><div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure 1.</span> Estimates of SNP marker effects (Manhattan plot) for the different methods employed (ssBA, Single step Bayes A; ssBπ, Single step Bayes Bπ; ssBCπ, Single step Bayes Cπ; ssBL, Single step Bayes Lasso; ssBRR, Single step Bayes Ridge Regression), and cluster analysis based on similarity between marker effects.</p></div></div></section> <section><div class="fig fig" data-magellan-destination="fig02" id="fig02"><div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_fig2.png?pub-status=live" class="aop-lazy-load-image" width="2050" height="2142" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_fig2.png" data-zoomable="true"></div><div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure 2.</span> Estimates of accuracy and dispersion of genetic and genomic values using different single-step methods (ssBA, Single step Bayes A; ssBπ, Single step Bayes Bπ; ssBCπ, Single step Bayes Cπ; ssBL, Single step Bayes Lasso; ssBRR, Single step Bayes Ridge Regression) for the study of age at first calving in dairy buffaloes (genotyped animals).</p></div></div></section> <p class="p"> Regarding the dispersion of the GEBV prediction (<a class="xref fig" href="#fig02">Fig. 2</a>), ssBCπ (0.99) and WssGBLUP (1.00) obtained the best results considering only genotyped animals, while for non-genotyped animals only WssGBLUP (1.02) showed the best value, although it was also the higher than 1. The PBLUP model had the worst result with values straying 35% below from the reference value (1.0).</p> <p class="p"> In the full dataset, Pearson's correlation between GEBVs and EBVs (predicted via PBLUP) ranged from 0.92 (ssBRR) to 0.93 (ssGBLUP), while for animals with both genotypic and phenotypic information, the correlation between GEBVs and EBVs ranged from 0.71 (ssBRR) to 0.77 (WssGBLUP). The correlations between all GEBVs predicted with the single-step genomic models were higher than 0.95.</p> </div> <div class="sec discussion" data-magellan-destination="sec4" id="sec4"><h2 class="A"> Discussion</h2> <p class="p"> In this study, a heritability estimate obtained for AFC, had magnitude similar to those described in several studies with the buffalo species, with values ranging from 0.13 to 0.19 (Agudelo <em class="italic">et al</em>., <a class="xref bibr" href="#ref1"><span class="show-for-sr">Reference Agudelo-Gomez, Pineda-Sierra and Cerón-Muñoz</span>2015</a>; Thiruvenkadan <em class="italic">et al</em>., <a class="xref bibr" href="#ref29"><span class="show-for-sr">Reference Thiruvenkadan, Panneerselvam and Murali</span>2015</a>; Fernandes <em class="italic">et al</em>., <a class="xref bibr" href="#ref16"><span class="show-for-sr">Reference Fernandes, Marques, de Araujo Neto, de Oliveira, Hurtado-Lugo, Aspilcueta-Borquis and Tonhati</span>2016</a>; Araujo Neto <em class="italic">et al</em>., <a class="xref bibr" href="#ref3"><span class="show-for-sr">Reference Araujo Neto, Takada, Santos, Aspilcueta-Borquis, Cardoso, Nascimento, Leão, Oliveira and Tonhati</span>2020<em class="italic">a</em></a>, <a class="xref bibr" href="#ref4"><span class="show-for-sr">Reference Araujo Neto, Santos, Fernandes Júnior, Aspilcueta-Borquis, Nascimento, Seno, Tonhati and Oliveira</span>2020<em class="italic">b</em></a>). These results show that despite the greater information provided by the markers in the analysis, there was very little influence on the estimation of the genetic parameters, possibly due to the polygenic nature of the trait. There are few reports in the literature on comparison of genomic prediction for reproductive traits, and it is not yet possible to find studies that compared the predictive ability between different single-step methods for AFC. Moreover, several accuracy measures have been reported by different authors, which makes the comparison between their values even more difficult. For instance, Costa <em class="italic">et al</em>. (<a class="xref bibr" href="#ref15"><span class="show-for-sr">Reference Costa, Irano, Diaz, Takada, Hermisdorff, Carvalheiro, Baldi, Oliveira, Tonhati and Albuquerque</span>2019</a>), working only with genotyped Nellore breed animals and considering the correlation between GEBV and adjusted AFC (<em class="italic">r</em> <sub><em class="italic">GEBV</em>,<em class="italic">Y</em>*</sub>), estimated values with magnitudes similar to those found in our study with BayesCπ (0.31) and Bayes-Lasso (0.31), while Toghiani <em class="italic">et al</em>. (<a class="xref bibr" href="#ref30"><span class="show-for-sr">Reference Toghiani, Hay, Sumreddee, Geary, Rekaya and Roberts</span>2017</a>) reported lower values with BayesA (0.148) and BayesCπ (0.15), studying the same breed and using the same type of accuracy. In both cited studies, accuracy estimates were not presented for PBLUP model, which does not allow us to fully contrast with our findings. Possibly, for comparison purposes, checking the accuracy increments in relation to PBLUP is the best approach to discuss our results. Thus, all literature discussed about predictability were made based on the difference in performance between methods also used in our study.</p> <p class="p"> Considering the percentage of accuracy increment in relation to PBLUP predictions in only genotyped animals, we observed three groups of models: increments less than 5% – ssBL and ssBRR; increments close 10% – ssBBπ, ssBCπ and ssGBLUP and; increments greater than 25% – ssBA and WssGBLUP. Estimates of accuracy increments using SNP markers with magnitudes similar to those we have found for AFC, have been described in the literature for productive traits in buffaloes (Cesarani <em class="italic">et al</em>., <a class="xref bibr" href="#ref13"><span class="show-for-sr">Reference Cesarani, Biffani, Garcia, Lourenco, Bertolini, Neglia, Misztal and Macciotta</span>2021</a>; Herrera <em class="italic">et al</em>., <a class="xref bibr" href="#ref20"><span class="show-for-sr">Reference Herrera, Flores, Duijvesteijn, Moghaddar and van der Werf</span>2021</a>).</p> <p class="p"> For milk, fat and protein yield, greater increases in accuracy (<em class="italic">r</em> <sub><em class="italic">GEBV</em>,<em class="italic">Y</em>*</sub>) are presented by Herrera <em class="italic">et al</em>. (<a class="xref bibr" href="#ref20"><span class="show-for-sr">Reference Herrera, Flores, Duijvesteijn, Moghaddar and van der Werf</span>2021</a>) (13.04 to 76.47%) and Cesarani <em class="italic">et al</em>. (<a class="xref bibr" href="#ref13"><span class="show-for-sr">Reference Cesarani, Biffani, Garcia, Lourenco, Bertolini, Neglia, Misztal and Macciotta</span>2021</a>) (15.28 to 33.33%). Aspilcueta-Borquis <em class="italic">et al</em>. (<a class="xref bibr" href="#ref6"><span class="show-for-sr">Reference Aspilcueta-Borquis, Araujo Neto, Santos, Hurtado-Lugo, Silva and Tonhati</span>2015</a>), studying the same population of this study and ssGBLUP model, reported similar increase in the average accuracy (based on prediction error variance) of (G)EBVs, which ranged from 8.52 to 12.05% for several dairy traits. This gain in accuracy observed with the use of genomic information is due to the additional capture of both Mendelian sampling variations and relationships between animals (Christensen <em class="italic">et al</em>., <a class="xref bibr" href="#ref14"><span class="show-for-sr">Reference Christensen, Madsen, Nielsen, Ostersen and Su</span>2012</a>; Cesarani <em class="italic">et al</em>., <a class="xref bibr" href="#ref12"><span class="show-for-sr">Reference Cesarani, Garcia, Hidalgo, Degano, Vicario, Macciotta and Lourenco</span>2020</a>). The similarity in predictive performance between the different single-step genomic methods, however, could be related to the reduced number of animals evaluated, the small subset of genotyped animals analysed, and the polygenic nature of the AFC (Calus, <a class="xref bibr" href="#ref8"><span class="show-for-sr">Reference Calus</span>2010</a>; Campos <em class="italic">et al</em>., <a class="xref bibr" href="#ref11"><span class="show-for-sr">Reference Campos, Hickey, Pong-Wong, Daetwyler and Calus</span>2013</a>).</p> <p class="p"> The proximity between ssBA and GRM-based model observed in this study (by the magnitude of estimated accuracies) may be explained by the polygenic nature of the trait and the robustness of ssBA method for different genetic architectures. Zhou <em class="italic">et al</em>. (<a class="xref bibr" href="#ref35"><span class="show-for-sr">Reference Zhou, Mrode, Zhang, Zhang, Li and Liu</span>2018</a>), studying the effects of QTL number on the accuracy prediction with simulated data, also verified that ssBA method was robust and performed similarly to ssGBLUP in scenarios with a large number of QTL.</p> <p class="p"> The dispersion criterion is related to the degree of inflation or deflation of predictions, which was measured in our validation set as the slope of the regression of the GEBV obtained with the full dataset on GEBV from the partial dataset. Our results showed that the inclusion of genomic information reduces the dispersion of prediction compared to the traditional evaluations (PBLUP), regardless of the single-step model considered. The same improvement in prediction slopes by using genomic information was reported by Lázaro <em class="italic">et al</em>. (<a class="xref bibr" href="#ref22"><span class="show-for-sr">Reference Lázaro, Tonhati, Oliveira, Silva, Nascimento, Santos, Stefani and Brito</span>2021</a>) studying several milk-related traits with random regression models in the same buffalo population, while other authors, such as Gao <em class="italic">et al</em>. (<a class="xref bibr" href="#ref18"><span class="show-for-sr">Reference Gao, Koivula, Jensen, Strandén, Madsen, Pitkänen, Aamand and Mäntysaari</span>2018</a>) also analysing dairy traits in Finnish red dairy cattle, report no benefit. Moreover, the GEBVs predicted with WssGBPUP did not disperse in relation to what was expected for the subset of genotyped animals and presented little deflation for the prediction of non-genotyped animals. The low dispersion of GEBVs predicted with WssGBLUP compared to the predictions from other genomic models is probably due to the self-fitting of the SNP weights to the dataset (weighting steps), which regulates the scale of the additive effect to the full dataset previously (<em class="italic">a priori</em>).</p> <p class="p"> The results indicate that the use of genomic information can improve the genetic gain for AFC by increasing the accuracy and reducing inflation/deflation of predictions of this trait compared to the traditional pedigree-based model. In addition, among all genomic single-step models studied, WssGBLUP and ssBA were the most advantageous models to be used for the genomic evaluation of AFC of buffaloes from this population.</p> </div> </div> <div class="back"><div class="sec other" data-magellan-destination="sec-nts1" id="sec-nts1"><h2 class="A"> Authors’ contributions</h2> <p class="p"> Jessica Cristina Gonçalves dos Santos: Methodology, Analysis , Writing – original draft.; Francisco Ribeiro de Araujo Neto: Conceptualization, Methodology, Statistical analysis, Writing – review; Gabriela Stefani Fernandez: Database; Daniel Jordan de Abreu Santos: Writing – review & editing; Felipe Pereira Cunha: Writing editing; Rusbel Raul Aspilcueta-Borquis: Statistical analysis; Humberto Tonhati: Conceptualization, Database, Supervision.</p> </div> <div class="sec funding-statement" data-magellan-destination="sec-fs1" id="sec-fs1"><h2 class="A"> Funding statement</h2> <p class="p"> This research received no specific grant from any funding agency, commercial or not-for-profit sectors.</p> </div> <div class="sec coi-statement" data-magellan-destination="sec-ci1" id="sec-ci1"><h2 class="A"> Competing interests</h2> <p class="p"> None.</p> </div> <div class="sec other" data-magellan-destination="sec-nts2" id="sec-nts2"><h2 class="A"> Ethical standards</h2> <p class="p"> Not applicable (the work was developed with a database).</p></div> </div> </div></div>   <hr aria-hidden="true" class="list-divider separator default" data-v-7036083a> <div id="references-list" class="circle-list"><h2>References</h2> <div id="ref1" aria-flowto="reference-1-content reference-1-button" class="circle-list__item"> <div class="circle-list__item__indicator"><AppButton icon="up-circle" aria-label="Return to the reference 1 in the content" id="reference-1-button" class="circle-list__item__indicator__up"></AppButton></div> <div aria-hidden="true" data-test-hidden="true" class="circle-list__item__number"> </div> <div 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Available in: <span class="ext-link doi" href="#10.1101/2022.02.12.480230">https://doi.org/10.1101/2022.02.12.480230</span>.<a class='ref-link' target='_blank' aria-label='Google Scholar link for Hibayes: an R package to fit individual-level, summary-level and single-step Bayesian regression models for genomic prediction and genome-wide association studies' href=https://scholar.google.com/scholar_lookup?title=Hibayes%3A+an+R+package+to+fit+individual-level%2C+summary-level+and+single-step+Bayesian+regression+models+for+genomic+prediction+and+genome-wide+association+studies&author=Yin+L&author=Zhang+H&author=Li+X&author=Zhao+S&author=Liu+X&publication+year=2022&journal=bioRxiv>Google Scholar</a></div></div></div><div id="ref34" aria-flowto="reference-35-content reference-35-button" class="circle-list__item"> <div class="circle-list__item__indicator"><AppButton icon="up-circle" aria-label="Return to the reference 35 in the content" id="reference-35-button" class="circle-list__item__indicator__up"></AppButton></div> <div aria-hidden="true" data-test-hidden="true" class="circle-list__item__number"> </div> <div class="circle-list__item__grouped"><div id="reference-35-content" class="circle-list__item__grouped__content"><span class="string-name"><span class="surname">Zhang</span>, <span class="given-names">X</span></span>, <span class="string-name"><span class="surname">Lourenco</span>, <span class="given-names">D</span></span>, <span class="string-name"><span class="surname">Aguilar</span>, <span class="given-names">I</span></span>, <span class="string-name"><span class="surname">Legarra</span>, <span class="given-names">A</span></span> and <span class="string-name"><span class="surname">Misztal</span>, <span class="given-names">I</span></span> (<span class="year">2016</span>) <span class="article-title">Weighting strategies for single-step genomic BLUP: an iterative approach for accurate calculation of GEBV and GWAS</span>. <span class="source">Frontiers in Genetics</span> <span class="volume">7</span>, <span class="fpage">151</span>. <span class="ext-link doi" href="#10.3389/fgene.2016.00151">https://doi.org/10.3389/fgene.2016.00151</span>.<a class='ref-link' target='_blank' aria-label='CrossRef link for Weighting strategies for single-step genomic BLUP: an iterative approach for accurate calculation of GEBV and GWAS' href=https://dx.doi.org/10.3389/fgene.2016.00151>CrossRef</a><a class='ref-link' target='_blank' aria-label='Google Scholar link for Weighting strategies for single-step genomic BLUP: an iterative approach for accurate calculation of GEBV and GWAS' href=https://scholar.google.com/scholar_lookup?title=Weighting+strategies+for+single-step+genomic+BLUP%3A+an+iterative+approach+for+accurate+calculation+of+GEBV+and+GWAS&author=Zhang+X&author=Lourenco+D&author=Aguilar+I&author=Legarra+A&author=Misztal+I&publication+year=2016&journal=Frontiers+in+Genetics&volume=7&doi=10.3389%2Ffgene.2016.00151>Google Scholar</a><a class='ref-link' target='_blank' aria-label='PubMed link for Weighting strategies for single-step genomic BLUP: an iterative approach for accurate calculation of GEBV and GWAS' href=https://www.ncbi.nlm.nih.gov/pubmed/27594861>PubMed</a></div></div></div><div id="ref35" aria-flowto="reference-36-content reference-36-button" class="circle-list__item"> <div class="circle-list__item__indicator"><AppButton icon="up-circle" aria-label="Return to the reference 36 in the content" id="reference-36-button" class="circle-list__item__indicator__up"></AppButton></div> <div aria-hidden="true" data-test-hidden="true" class="circle-list__item__number"> </div> <div class="circle-list__item__grouped"><div id="reference-36-content" class="circle-list__item__grouped__content"><span class="string-name"><span class="surname">Zhou</span>, <span class="given-names">L</span></span>, <span class="string-name"><span class="surname">Mrode</span>, <span class="given-names">R</span></span>, <span class="string-name"><span class="surname">Zhang</span>, <span class="given-names">S</span></span>, <span class="string-name"><span class="surname">Zhang</span>, <span class="given-names">Q</span></span>, <span class="string-name"><span class="surname">Li</span>, <span class="given-names">B</span></span> and <span class="string-name"><span class="surname">Liu</span>, <span class="given-names">JF</span></span> (<span class="year">2018</span>) <span class="article-title">Factors affecting GEBV accuracy with single-step Bayesian models</span>. <span class="source">Heredity</span> <span class="volume">120</span>, <span class="fpage">100</span>–<span class="lpage">109</span>. doi: <span class="pub-id doi">10.1038/s41437-017-0010-9</span>.<a class='ref-link' target='_blank' aria-label='CrossRef link for Factors affecting GEBV accuracy with single-step Bayesian models' href=https://dx.doi.org/10.1038/s41437-017-0010-9>CrossRef</a><a class='ref-link' target='_blank' aria-label='Google Scholar link for Factors affecting GEBV accuracy with single-step Bayesian models' href=https://scholar.google.com/scholar_lookup?title=Factors+affecting+GEBV+accuracy+with+single-step+Bayesian+models&author=Zhou+L&author=Mrode+R&author=Zhang+S&author=Zhang+Q&author=Li+B&author=Liu+JF&publication+year=2018&journal=Heredity&volume=120&doi=10.1038%2Fs41437-017-0010-9&pages=100-109>Google Scholar</a><a class='ref-link' target='_blank' aria-label='PubMed link for Factors affecting GEBV accuracy with single-step Bayesian models' href=https://www.ncbi.nlm.nih.gov/pubmed/29167557>PubMed</a></div></div></div></div></div> </div></div>  <div id="figures-tab" class="figures tab-pane" data-v-241a4b23><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 0" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_tab1.png" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_tab1.png" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Table 1.</span> <span data-v-241a4b23><span class="p">Description of age at first calving dataset used in this study</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 1" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_tab2.png" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_tab2.png" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Table 2.</span> <span data-v-241a4b23><span class="p">Description of different prior for markers effects used in Bayesian single-step regression methods used for genomic analysis of age at first calving in dairy buffaloes</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 2" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241113063400-39867-mediumThumb-png-S0021859624000364_fig1.jpg" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241113063400-64577-optimisedImage-png-S0021859624000364_fig1.jpg" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure 1.</span> <span data-v-241a4b23><span class="p">Estimates of SNP marker effects (Manhattan plot) for the different methods employed (ssBA, Single step Bayes A; ssBπ, Single step Bayes Bπ; ssBCπ, Single step Bayes Cπ; ssBL, Single step Bayes Lasso; ssBRR, Single step Bayes Ridge Regression), and cluster analysis based on similarity between marker effects.</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 3" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241113063400-09770-mediumThumb-png-S0021859624000364_fig2.jpg" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241113063400-39764-optimisedImage-png-S0021859624000364_fig2.jpg" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure 2.</span> <span data-v-241a4b23><span class="p">Estimates of accuracy and dispersion of genetic and genomic values using different single-step methods (ssBA, Single step Bayes A; ssBπ, Single step Bayes Bπ; ssBCπ, Single step Bayes Cπ; ssBL, Single step Bayes Lasso; ssBRR, Single step Bayes Ridge Regression) for the study of age at first calving in dairy buffaloes (genotyped animals).</span></span></p></div> </div></div> </div></div>         <div id="metrics-tab" publication-date="14 November 2024" class="metrics tab-pane" data-v-c41a0c86><div class="app-loader" data-v-c41a0c86></div></div></div></div> </div> <div role="complementary" aria-label="related contents" class="column__main__right" data-v-01274b1d><div class="access-block row access-status" data-v-5fad35b8 data-v-01274b1d><span class="has-access" data-v-5fad35b8><img 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Neto",nameStyle:k,affiliations:[{text:H}],isCorresponding:c,notes:"\u003Cdiv class=\"corresp\"\u003E\u003Cspan class=\"bold\"\u003ECorresponding author:\u003C\u002Fspan\u003E F. R. Araujo Neto; Email: \u003Ca href=\"mailto:francisco.neto@ifgoiano.edu.br\"\u003Efrancisco.neto@ifgoiano.edu.br\u003C\u002Fa\u003E\u003C\u002Fdiv\u003E",isAnonymous:b,fullName:"Francisco Ribeiro de Araújo Neto",searchUrl:"\u002Fcore\u002Fsearch?filters%5BauthorTerms%5D=Francisco%20Ribeiro%20de%20Ara%C3%BAjo%20Neto&eventCode=SE-AU",orcidUrl:"https:\u002F\u002Forcid.org\u002F0000-0003-1064-5614"},{givenNames:"Gabriela Stefani",surname:"Fernandez",nameStyle:k,affiliations:[{text:n}],isCorresponding:b,notes:a,isAnonymous:b,fullName:"Gabriela Stefani Fernandez",searchUrl:"\u002Fcore\u002Fsearch?filters%5BauthorTerms%5D=Gabriela%20Stefani%20Fernandez&eventCode=SE-AU",orcidUrl:g},{givenNames:"Daniel Jordan",surname:"de Abreu Santos",nameStyle:k,affiliations:[{text:n}],isCorresponding:b,notes:a,isAnonymous:b,fullName:"Daniel Jordan de Abreu Santos",searchUrl:"\u002Fcore\u002Fsearch?filters%5BauthorTerms%5D=Daniel%20Jordan%20de%20Abreu%20Santos&eventCode=SE-AU",orcidUrl:g},{givenNames:"Felipe Pereira",surname:"Cunha",nameStyle:k,affiliations:[{text:H}],isCorresponding:b,notes:a,isAnonymous:b,fullName:"Felipe Pereira Cunha",searchUrl:"\u002Fcore\u002Fsearch?filters%5BauthorTerms%5D=Felipe%20Pereira%20Cunha&eventCode=SE-AU",orcidUrl:g},{givenNames:"Rusbel Raul",surname:"Aspilcueta-Borquis",nameStyle:k,affiliations:[{text:"Universidade Tecnológica Federal do Paraná – UFTPR, Dois Vizinhos, Paraná"}],isCorresponding:b,notes:a,isAnonymous:b,fullName:"Rusbel Raul Aspilcueta-Borquis",searchUrl:"\u002Fcore\u002Fsearch?filters%5BauthorTerms%5D=Rusbel%20Raul%20Aspilcueta-Borquis&eventCode=SE-AU",orcidUrl:g},{givenNames:"Humberto",surname:"Tonhati",nameStyle:k,affiliations:[{text:n}],isCorresponding:b,notes:a,isAnonymous:b,fullName:"Humberto Tonhati",searchUrl:"\u002Fcore\u002Fsearch?filters%5BauthorTerms%5D=Humberto%20Tonhati&eventCode=SE-AU",orcidUrl:g}]},translators:{contributors:[],label:"Translated by"}},collections:[],publishedDate:"14 November 2024",keywords:[{url:"\u002Fcore\u002Fsearch?filters[keywords]=Bayesian inference",name:"Bayesian inference"},{url:"\u002Fcore\u002Fsearch?filters[keywords]=Bubalus bubalis",name:"Bubalus bubalis"},{url:"\u002Fcore\u002Fsearch?filters[keywords]=genomic selection",name:"genomic selection"},{url:"\u002Fcore\u002Fsearch?filters[keywords]=reproductive traits",name:"reproductive traits"}],openPracticeBadges:[],doi:{url:"https:\u002F\u002Fdoi.org\u002F10.1017\u002FS0021859624000364",value:"10.1017\u002FS0021859624000364"},copyright:{statement:["Copyright © The Author(s), 2024. Published by Cambridge University Press"],holder:["The Author(s)"],year:[2024]},creativeCommons:g,acceptedManuscript:b,type:"research-article",pageRange:{range:"1 - 7",firstPage:"1",lastPage:I},typeDescription:"Animal Research Paper",resultTypes:[],commentsCount:B,topicsAndSubtopics:g},journal:{id:J,title:o,titleSlug:"the-journal-of-agricultural-science",mnemonic:"AGS",titleHistory:[],isFirstView:c,journalSlug:"journal-of-agricultural-science",isCompanion:b,parentCompanionJournalName:o,associatedParentCollection:g,paymentInfo:{prices:{"£":{price:26,sku:p,skuNew:m,currency:"£"},"€":{price:31,sku:p,skuNew:m,currency:"€"},US$:{price:36,sku:p,skuNew:m,currency:"US$"},AU$:{price:51,sku:p,skuNew:m,currency:"AU$"}}},url:K,firstViewUrl:L,coverUrl:"https:\u002F\u002Fstatic.cambridge.org\u002Fcovers\u002FAGS_0_0_0\u002Fthe-journal-of-agricultural-science.jpg",submitMaterialsUrl:"\u002Fcore\u002Fjournals\u002Fjournal-of-agricultural-science\u002Finformation\u002Fauthor-instructions\u002Fsubmitting-your-materials",hasHistory:b,latestTitle:o,latestId:J,hasPastTitle:b},abstract:{textAbstracts:[{title:"Abstract",content:"\u003Cdiv class=\"abstract\" data-abstract-type=\"normal\"\u003E\u003Cp\u003EThe age at first calving (AFC) is an important trait to be considered in breeding programmes of dairy buffaloes, where new approaches and technologies, such as genomic selection, are constantly applied. Thus, the objective of this study was to compare the predictive ability of different genomic single-step methods using AFC information from Murrah buffaloes. From a pedigree file containing 3320 buffaloes, 2247 cows had AFC records and 553 animals were genotyped. The following models were performed: pedigree-based BLUP (PBLUP), single-step GBLUP (ssGBLUP), weighted single-step GBLUP (WssGBLUP), and single-step Bayesian regression methods (ssBR-BayesA, BayesBπ, BayesCπ, Bayes-Lasso, and BayesRR). To compare the methodologies, the accuracy and dispersion of (G)EBVs were assessed using the LR method. Accuracy estimates for the genotyped animals ranged from 0.30 (PBLUP) to 0.39 (WssGBLUP). Predictions with the traditional model (PBLUP) were very dispersed from what was expected, while BayesCπ (0.99) and WssGBLUP (1.00) obtained the lowest dispersion. The results indicate that the use of genomic information can improve the genetic gain for AFC by increasing the accuracy and reducing inflation\u002Fdeflation of predictions compared to the traditional pedigree-based model. In addition, among all genomic single-step models studied, WssGBLUP and single-step BayesA were the most advantageous methods to be used in the genomic evaluation of AFC of buffaloes from this population.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E",lang:M}]},content:{html:"\u003Cdiv class=\"article research-article NLM\"\u003E\n\n\u003Cdiv class=\"body\"\u003E\n\u003Cdiv class=\"sec intro\" data-magellan-destination=\"sec1\" id=\"sec1\"\u003E\u003Ch2 class=\"A\"\u003E Introduction\u003C\u002Fh2\u003E\n\u003Cp class=\"p\"\u003E Age at first calving (AFC) is an important indicator trait of reproductive efficiency that is genetically monitored by the Milk-Recording Buffalo Program in Brazil (Aspilcueta-Borquis \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref7\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Aspilcueta-Borquis, Seno, Araujo Neto, Santos, Hurtado-Lugo and Tonhati\u003C\u002Fspan\u003E2022\u003C\u002Fa\u003E). It is well known, however, that the genetic progress obtained by direct selection of AFC can be very slow due to the low heritability magnitude of this trait in Buffaloes (Camargo \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref10\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Camargo, Aspilcueta-Borquis, Fortes, Porto-Neto, Cardoso, Santos, Lehnert, Reverter, Moore and Tonhati\u003C\u002Fspan\u003E2015\u003C\u002Fa\u003E). Since genomic selection is more accurate than traditional selection, especially for low-heritability traits (Calus \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref9\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Calus, Meuwissen, De Roos and Veerkamp\u003C\u002Fspan\u003E2008\u003C\u002Fa\u003E), genomic evaluation is the best strategy for predicting breeding values for AFC. Furthermore, Camargo \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E. (\u003Ca class=\"xref bibr\" href=\"#ref10\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Camargo, Aspilcueta-Borquis, Fortes, Porto-Neto, Cardoso, Santos, Lehnert, Reverter, Moore and Tonhati\u003C\u002Fspan\u003E2015\u003C\u002Fa\u003E) and Araujo Neto \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E. (\u003Ca class=\"xref bibr\" href=\"#ref3\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Araujo Neto, Takada, Santos, Aspilcueta-Borquis, Cardoso, Nascimento, Leão, Oliveira and Tonhati\u003C\u002Fspan\u003E2020\u003Cem class=\"italic\"\u003Ea\u003C\u002Fem\u003E\u003C\u002Fa\u003E) have reported some specific genomic regions highly associated to this trait in GWAS studies in this population, indicating that differential shrinkage models, such as Bayesian alphabet and weighted single-step GBLUP models, would be a reasonable alternative to be explored.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E The single-step GBLUP (ssGBLUP) method has become the main methodology used for genomic evaluations in dairy buffaloes (Araujo Neto \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref3\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Araujo Neto, Takada, Santos, Aspilcueta-Borquis, Cardoso, Nascimento, Leão, Oliveira and Tonhati\u003C\u002Fspan\u003E2020\u003Cem class=\"italic\"\u003Ea\u003C\u002Fem\u003E\u003C\u002Fa\u003E, \u003Ca class=\"xref bibr\" href=\"#ref4\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Araujo Neto, Santos, Fernandes Júnior, Aspilcueta-Borquis, Nascimento, Seno, Tonhati and Oliveira\u003C\u002Fspan\u003E2020\u003Cem class=\"italic\"\u003Eb\u003C\u002Fem\u003E\u003C\u002Fa\u003E; Cesarani \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref13\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Cesarani, Biffani, Garcia, Lourenco, Bertolini, Neglia, Misztal and Macciotta\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E; Lázaro \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref22\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Lázaro, Tonhati, Oliveira, Silva, Nascimento, Santos, Stefani and Brito\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E; Araujo Neto \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref5\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Araujo Neto, Santos, Silva Arce, Borquis, Santos, Guimarães, Nascimento, Oliveira and Tonhati\u003C\u002Fspan\u003E2022\u003C\u002Fa\u003E) given the ease of integrating the relationship matrices, based on pedigree (\u003Cstrong\u003EA\u003C\u002Fstrong\u003E) and genomic (\u003Cstrong\u003EG\u003C\u002Fstrong\u003E) information, without major changes in the mixed model equations (Misztal \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref27\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Misztal, Lourenco and Legarra\u003C\u002Fspan\u003E2020\u003C\u002Fa\u003E). Moreover, this methodology allows assigning different weights for each marker, originating the weighted single-step GBLUP method – WssGBLUP (Wang \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref31\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Wang, Misztal, Aguilar, Legarra and Muir\u003C\u002Fspan\u003E2012\u003C\u002Fa\u003E; Zhang \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref34\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Zhang, Lourenco, Aguilar, Legarra and Misztal\u003C\u002Fspan\u003E2016\u003C\u002Fa\u003E).\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E Subsequently, Fernando \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E. (\u003Ca class=\"xref bibr\" href=\"#ref17\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Fernando, Dekkers and Garrick\u003C\u002Fspan\u003E2014\u003C\u002Fa\u003E) proposed single-step methodologies combined to Bayesian regression methods (ssBR), as an option to ssGBLUP. Nonetheless, few studies have been developed comparing the results of the different single-step methodologies (Lee \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref23\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Lee, Cheng, Garrick, Golden, Dekkers, Park, Lee and Fernando\u003C\u002Fspan\u003E2017\u003C\u002Fa\u003E; Gao \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref18\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Gao, Koivula, Jensen, Strandén, Madsen, Pitkänen, Aamand and Mäntysaari\u003C\u002Fspan\u003E2018\u003C\u002Fa\u003E; Zhou \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref35\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Zhou, Mrode, Zhang, Zhang, Li and Liu\u003C\u002Fspan\u003E2018\u003C\u002Fa\u003E). Based on this, it becomes interesting to perform similar analyses in buffalo databases to assist in decision making in breeding programmes that employ genomic technology. Thus, this work was designed with the aim of comparing the predictive ability of different single-step methods using AFC information from Murrah buffaloes.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec materials\" data-magellan-destination=\"sec2\" id=\"sec2\"\u003E\u003Ch2 class=\"A\"\u003E Materials and methods\u003C\u002Fh2\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"sec2-1\" id=\"sec2-1\"\u003E\u003Ch3 class=\"B\"\u003E Dataset\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E The phenotypic dataset consisted of 2,314AFC records of Murrah buffalo cows born between 1995 and 2017. Contemporary groups (CG) were formed considering animals born on the same farm, year and season of birth, which was divided into two (dry and rainy season). Animals with records outside the range between ±3 standard deviations from their CG averages and animals belonging to GCs with less than five individuals were removed.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E From a pedigree file containing 3320 buffaloes, 553 animals (539 dams and 14 sires) were genotyped with the Axiom Buffalo Genotyping Array 90 K (Iamartino \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref21\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Iamartino, Nicolazzi, Van Tassell, Reecy, Fritz-Waters, Koltes, Biffani, Sonstegard, Schroeder, Ajmone-Marsan, Negrini, Pasquariello, Ramelli, Coletta, Garcia, Ali, Ramunno, Cosenza, Oliveira, Drummond, Bastianetto, Davassi, Pirani, Brew and Williams\u003C\u002Fspan\u003E2017\u003C\u002Fa\u003E). Only SNPs present on autosomal chromosomes (BBU1-BBU24 referenced by UOA_WB_1 genome assembly), as well as those with call rate > 95%, MAF > 3% and significance level for Hardy Weinberg equilibrium test was 10\u003Csup class=\"sup\"\u003E−5\u003C\u002Fsup\u003E , were remained in the analysis. All samples had a call rate >90%. The database description (phenotypic and genotypic information) after the consistency step is in \u003Ca class=\"xref table\" href=\"#tab01\"\u003ETable 1\u003C\u002Fa\u003E.\n\u003C\u002Fp\u003E\u003Cdiv class=\"table-wrap\" data-magellan-destination=\"tab01\" id=\"tab01\"\u003E\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003ETable 1.\u003C\u002Fspan\u003E Description of age at first calving dataset used in this study\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\n\u003Cspan\u003E\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_tab1.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"461\" height=\"272\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_tab1.png\" data-zoomable=\"false\"\u003E\u003C\u002Fdiv\u003E\n\n\u003C\u002Fspan\u003E\n\u003C\u002Fdiv\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"sec2-2\" id=\"sec2-2\"\u003E\u003Ch3 class=\"B\"\u003E PBLUP, ssGBLUP and WssGBLUP models\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E This set of methodologies is based on the use of relationship matrices between individuals in mixed model equations, with the differences consisting of the type of information used (pedigree or genomic) and the way these matrices are constructed. The model using pedigree based BLUP (PBLUP) can be described as:\u003C\u002Fp\u003E\u003Cdiv data-mathjax-status=\"alt-graphic\" class=\"disp-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$$y = {\\boldsymbol X}\\beta + {\\boldsymbol Z}\\alpha + e$$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU1.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"124\" height=\"20\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU1.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp class=\"p continuation\"\u003Ewhere, \u003Cem class=\"italic\"\u003Ey\u003C\u002Fem\u003E is the vector of phenotypic records (AFC); \u003Cem class=\"italic\"\u003Eβ\u003C\u002Fem\u003E is the fixed effect vector (CG), \u003Cstrong\u003E\u003Cem class=\"italic\"\u003EX\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E is the incidence matrix that associates \u003Cem class=\"italic\"\u003Eβ\u003C\u002Fem\u003E with \u003Cem class=\"italic\"\u003Ey\u003C\u002Fem\u003E; \u003Cem class=\"italic\"\u003Eα\u003C\u002Fem\u003E is the vector of additive genetic effects, \u003Cstrong\u003E\u003Cem class=\"italic\"\u003EZ\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E is an incidence matrix associating \u003Cem class=\"italic\"\u003Eα\u003C\u002Fem\u003E with \u003Cem class=\"italic\"\u003Ey\u003C\u002Fem\u003E and, \u003Cem class=\"italic\"\u003Ee\u003C\u002Fem\u003E is the vector of residuals. The following assumptions were made:\u003C\u002Fp\u003E\u003Cdiv data-mathjax-status=\"alt-graphic\" class=\"disp-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$$E( y ) = {\\boldsymbol X}\\beta \\quad E( \\alpha ) = 0\\quad E( e ) = 0$$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU2.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"227\" height=\"20\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU2.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cdiv data-mathjax-status=\"alt-graphic\" class=\"disp-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$${\\rm Var}( \\alpha ) = A\\sigma _\\alpha ^2 \\quad {\\rm Var}( e ) = {\\boldsymbol I}_n\\sigma _\\varepsilon ^2 $$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU3.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"212\" height=\"23\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU3.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp class=\"p continuation\"\u003Ewhere \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$\\sigma _\\alpha ^2$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline1.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"20\" height=\"22\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline1.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E and \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$\\sigma _\\varepsilon ^2$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline2.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"18\" height=\"22\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline2.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E represent the additive genetic and residual variances; \u003Cstrong\u003E\u003Cem class=\"italic\"\u003EA\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E and \u003Cstrong\u003E\u003Cem class=\"italic\"\u003EI\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003Csub\u003E\u003Cem class=\"italic\"\u003En\u003C\u002Fem\u003E\u003C\u002Fsub\u003E are the pedigree relationship and an identity matrices, respectively.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E The single step GBLUP (ssGBLUP) method is an extension of the PBLUP model, in which the pedigree-based (\u003Cstrong\u003EA\u003C\u002Fstrong\u003E) and genomic (\u003Cstrong\u003EG\u003C\u002Fstrong\u003E) relationship matrices are combined into a single matrix (\u003Cstrong\u003EH\u003C\u002Fstrong\u003E), as described by Aguilar \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E. (\u003Ca class=\"xref bibr\" href=\"#ref2\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Aguilar, Misztal, Johnson, Legarra, Tsuruta and Lawlor\u003C\u002Fspan\u003E2010\u003C\u002Fa\u003E). So, its inverse can be obtained as:\u003C\u002Fp\u003E\u003Cdiv data-mathjax-status=\"alt-graphic\" class=\"disp-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$${\\boldsymbol H}^{{-}1} = {\\boldsymbol A}^{{-}1} + \\left[{\\matrix{ 0 \\hfill & 0 \\hfill \\cr 0 \\hfill & {{\\boldsymbol G}^{{-}1}-{\\boldsymbol A}_{22}^{{-}1} } \\hfill \\cr } } \\right]$$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU4.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"221\" height=\"43\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU4.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp class=\"p continuation\"\u003Ewhere \u003Cstrong\u003E\u003Cem class=\"italic\"\u003EA\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003Csup class=\"sup\"\u003E−1\u003C\u002Fsup\u003E and \u003Cstrong\u003E\u003Cem class=\"italic\"\u003EG\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003Csup class=\"sup\"\u003E−1\u003C\u002Fsup\u003E are the inverse matrices of \u003Cstrong\u003EA\u003C\u002Fstrong\u003E and \u003Cstrong\u003EG\u003C\u002Fstrong\u003E respectively, and \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E${\\boldsymbol A}_{22}^{{-}1}$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline3.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"29\" height=\"22\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline3.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E is the inverse of the section of \u003Cstrong\u003EA\u003C\u002Fstrong\u003E related to the genotyped animals. The \u003Cstrong\u003EG\u003C\u002Fstrong\u003E matrix was obtained according to VanRaden (\u003Ca class=\"xref bibr\" href=\"#ref30a\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference VanRaden\u003C\u002Fspan\u003E2008\u003C\u002Fa\u003E) as:\u003C\u002Fp\u003E\u003Cdiv data-mathjax-status=\"alt-graphic\" class=\"disp-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$${\\boldsymbol G} = \\displaystyle{{{\\boldsymbol ZD{Z}^{\\prime}}} \\over {2\\;\\sum {\\,p_i} ( 1-p_i{) }^{\\prime}}}$$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU5.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"142\" height=\"43\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU5.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp class=\"p continuation\"\u003Ewhere \u003Cem class=\"italic\"\u003Ep\u003C\u002Fem\u003E \u003Csub\u003E\u003Cem class=\"italic\"\u003Ei\u003C\u002Fem\u003E\u003C\u002Fsub\u003E is the minor allele frequency (MAF) of SNP \u003Cem class=\"italic\"\u003Ei\u003C\u002Fem\u003E, \u003Cstrong\u003E\u003Cem class=\"italic\"\u003EZ\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E is a matrix relating genotypes of each locus centred by allele frequencies, and \u003Cstrong\u003E\u003Cem class=\"italic\"\u003ED\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E is a diagonal matrix of weights for SNP variances, (with elements \u003Cem class=\"italic\"\u003Ed\u003C\u002Fem\u003E \u003Csub\u003E\u003Cem class=\"italic\"\u003Ei\u003C\u002Fem\u003E\u003C\u002Fsub\u003E = SNP \u003Cem class=\"italic\"\u003Ei\u003C\u002Fem\u003E weight). In ssGBLUP model is set \u003Cstrong\u003E\u003Cem class=\"italic\"\u003ED\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E = \u003Cstrong\u003E\u003Cem class=\"italic\"\u003EI\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E, so that the weight of all SNPs is equal to 1.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E In WssGBLUP method (Wang \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref31\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Wang, Misztal, Aguilar, Legarra and Muir\u003C\u002Fspan\u003E2012\u003C\u002Fa\u003E) markers are assigned with different weights using an iterative process described with the following steps:\n\u003C\u002Fp\u003E\u003Col class=\"list number nomark\"\u003E\n\u003Cli class=\"list-item\"\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E1.\u003C\u002Fspan\u003E Set \u003Cem class=\"italic\"\u003ED\u003C\u002Fem\u003E \u003Csup class=\"sup\"\u003E(\u003Cem class=\"italic\"\u003Et\u003C\u002Fem\u003E)\u003C\u002Fsup\u003E = \u003Cem class=\"italic\"\u003EI\u003C\u002Fem\u003E, when \u003Cem class=\"italic\"\u003Et\u003C\u002Fem\u003E = 1\u003C\u002Fp\u003E\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E2.\u003C\u002Fspan\u003E The genomic relationship matrix is setup for \u003Cem class=\"italic\"\u003Et\u003C\u002Fem\u003E as \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E${\\boldsymbol G}^{( t ) } = {\\boldsymbol Z}{\\boldsymbol D}^{( {\\boldsymbol t} ) }{\\boldsymbol {Z}^{\\prime}}\u002F( 2\\;\\sum p_i( {1-p_i} )$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline4.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"210\" height=\"23\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline4.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003C\u002Fp\u003E\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E3.\u003C\u002Fspan\u003E The Genomic Breeding Value (GEBV or \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$\\hat{\\alpha }$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline5.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"13\" height=\"15\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline5.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E) for \u003Cem class=\"italic\"\u003Et\u003C\u002Fem\u003E are obtained;\u003C\u002Fp\u003E\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E4.\u003C\u002Fspan\u003E 4.The GEBV \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$\\hat{\\alpha }^{( t ) }$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline6.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"24\" height=\"18\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline6.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003Eare converted to SNP effects (\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$\\hat{u}$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline7.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"11\" height=\"16\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline7.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E) as \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$\\hat{u}^t = {\\boldsymbol D}^{( t ) }{\\boldsymbol {Z}^{\\prime}}( {\\boldsymbol G}^{( t ) }) ^{{-}1}\\hat{\\alpha }^{( t ) }$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline8.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"150\" height=\"21\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline8.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003C\u002Fp\u003E\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E5.\u003C\u002Fspan\u003E The weight of the \u003Cem class=\"italic\"\u003Ei\u003C\u002Fem\u003Eth SNP (the \u003Cem class=\"italic\"\u003Ei\u003C\u002Fem\u003Eth element of \u003Cstrong\u003ED\u003C\u002Fstrong\u003E or \u003Cem class=\"italic\"\u003Ed\u003C\u002Fem\u003E \u003Csub\u003E\u003Cem class=\"italic\"\u003Ei\u003C\u002Fem\u003E\u003C\u002Fsub\u003E) is calculated;\u003C\u002Fp\u003E\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E6.\u003C\u002Fspan\u003E SNP weights are normalized in \u003Cstrong\u003E\u003Cem class=\"italic\"\u003ED\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003Csup class=\"sup\"\u003E(\u003Cem class=\"italic\"\u003Et\u003C\u002Fem\u003E+1)\u003C\u002Fsup\u003E to have constant genetic variances of SNP effects;\u003C\u002Fp\u003E\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E7.\u003C\u002Fspan\u003E Loop to step 2 three times and exit.\u003C\u002Fp\u003E\u003C\u002Fli\u003E\n\u003C\u002Fol\u003E\n\u003Cp class=\"p\"\u003E For the methods mentioned above, the program BLUPF90+ (Misztal \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref26\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Misztal, Tsuruta, Lourenço, Masuda, Aguilar, Legarra and Vitezica\u003C\u002Fspan\u003E2014\u003C\u002Fa\u003E) was used for the estimation of the variance components and for the validation step. The estimation of the effects of the markers and the calculation of the weighting (WssGBLUP) were performed with the program POSTGSF90 (Misztal \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref26\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Misztal, Tsuruta, Lourenço, Masuda, Aguilar, Legarra and Vitezica\u003C\u002Fspan\u003E2014\u003C\u002Fa\u003E). The heritability estimates for AFC were obtained from these estimated variance components.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"sec2-3\" id=\"sec2-3\"\u003E\u003Ch3 class=\"B\"\u003E Single-step Bayesian regression models (ssBR)\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E The ssBR models combine all available data from genotyped and non-genotyped animals and use imputed marker covariates for animals that are not genotyped (Fernando \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref17\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Fernando, Dekkers and Garrick\u003C\u002Fspan\u003E2014\u003C\u002Fa\u003E), can be described as:\u003C\u002Fp\u003E\u003Cdiv data-mathjax-status=\"alt-graphic\" class=\"disp-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$$\\left[{\\matrix{ {y_n} \\cr {y_g} \\cr } } \\right] = \\left[{\\matrix{ {{\\boldsymbol X}_{\\boldsymbol n}} \\cr {{\\boldsymbol X}_g} \\cr } } \\right]\\beta + \\left[{\\matrix{ {{\\boldsymbol Z}_n} & 0 \\cr 0 & {{\\boldsymbol Z}_g} \\cr } } \\right]\\left[{\\matrix{ {{\\boldsymbol M}_n\\alpha + \\epsilon } \\cr {{\\boldsymbol M}_g\\alpha \\;\\;\\;\\;\\;\\;\\;} \\cr } } \\right] + e$$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU6.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"322\" height=\"43\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU6.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp class=\"p continuation\"\u003Ewhere vectors and matrices for non-genotyped animals are denoted with the subscript \u003Cem class=\"italic\"\u003En\u003C\u002Fem\u003E and for genotyped animals with the subscript \u003Cem class=\"italic\"\u003Eg\u003C\u002Fem\u003E. Thus, \u003Cem class=\"italic\"\u003Ey\u003C\u002Fem\u003E \u003Csub\u003E\u003Cem class=\"italic\"\u003En\u003C\u002Fem\u003E\u003C\u002Fsub\u003E and \u003Cem class=\"italic\"\u003Ey\u003C\u002Fem\u003E \u003Csub\u003E\u003Cem class=\"italic\"\u003Eg\u003C\u002Fem\u003E\u003C\u002Fsub\u003E represent the vectors of phenotypic observations; \u003Cem class=\"italic\"\u003Eβ\u003C\u002Fem\u003E is the vector of systematic effects of GC (equivalent to the fixed effect in frequentist methods); \u003Cstrong\u003E\u003Cem class=\"italic\"\u003EX\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003Csub\u003E\u003Cem class=\"italic\"\u003En\u003C\u002Fem\u003E\u003C\u002Fsub\u003E and \u003Cstrong\u003E\u003Cem class=\"italic\"\u003EX\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003Csub\u003E\u003Cem class=\"italic\"\u003Eg\u003C\u002Fem\u003E\u003C\u002Fsub\u003E design matrices for the fixed effects; \u003Cstrong\u003E\u003Cem class=\"italic\"\u003EZ\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003Csub\u003E\u003Cem class=\"italic\"\u003En\u003C\u002Fem\u003E\u003C\u002Fsub\u003E and \u003Cstrong\u003E\u003Cem class=\"italic\"\u003EZ\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003Csub\u003E\u003Cem class=\"italic\"\u003Eg\u003C\u002Fem\u003E\u003C\u002Fsub\u003E represent incidence matrices associated with the genomic values of the animals; \u003Cem class=\"italic\"\u003Eα\u003C\u002Fem\u003E, \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$\\epsilon$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline9.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"10\" height=\"11\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline9.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E and \u003Cem class=\"italic\"\u003Ee\u003C\u002Fem\u003E, represent in this order, the vectors of marker effects, imputation residual and model residual; \u003Cstrong\u003E\u003Cem class=\"italic\"\u003EM\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003Csub\u003E\u003Cstrong\u003E\u003Cem class=\"italic\"\u003Eg\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003C\u002Fsub\u003E is the marker matrix for the genotyped animals and \u003Cstrong\u003E\u003Cem class=\"italic\"\u003EM\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003Csub\u003E\u003Cstrong\u003E\u003Cem class=\"italic\"\u003En\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003C\u002Fsub\u003E is the imputed marker matrix for the non-genotyped animals. The matrix \u003Cstrong\u003E\u003Cem class=\"italic\"\u003EM\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003Csub\u003E\u003Cstrong\u003E\u003Cem class=\"italic\"\u003En\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003C\u002Fsub\u003E can be obtained as:\u003C\u002Fp\u003E\u003Cdiv data-mathjax-status=\"alt-graphic\" class=\"disp-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$${\\boldsymbol M}_n = {\\boldsymbol A}_{ng}{\\boldsymbol A}_{22}^{{-}1} {\\boldsymbol M}_g$$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU7.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"119\" height=\"23\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU7.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp class=\"p continuation\"\u003Ewhere \u003Cstrong\u003E\u003Cem class=\"italic\"\u003EA\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003Csub\u003E\u003Cstrong\u003E\u003Cem class=\"italic\"\u003Eng\u003C\u002Fem\u003E\u003C\u002Fstrong\u003E\u003C\u002Fsub\u003E represents the pedigree-based relationship matrix between genotyped and non-genotyped animals and; \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E${\\boldsymbol A}_{2g2g}^{{-}1}$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline10.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"37\" height=\"25\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline10.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E represents the inverse of the pedigree-based relationship matrix between genotyped animals. The following ssBR methods were used: BayesA (ssBA- Meuwissen et al., \u003Ca class=\"xref bibr\" href=\"#ref25\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Meuwissen, Hayes and Goddard\u003C\u002Fspan\u003E2001\u003C\u002Fa\u003E), BayesBπ (ssBBπ- Meuwissen \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref25\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Meuwissen, Hayes and Goddard\u003C\u002Fspan\u003E2001\u003C\u002Fa\u003E), BayesCπ (ssBCπ- Habier \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref19\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Habier, Fernando, Kizilkaya and Garrick\u003C\u002Fspan\u003E2011\u003C\u002Fa\u003E), Lasso Bayesian (ssBL- Yi and Xu, \u003Ca class=\"xref bibr\" href=\"#ref32\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Yi and Xu\u003C\u002Fspan\u003E2008\u003C\u002Fa\u003E) and Bayesian ridge regression (ssBRR- Campos \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref11\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Campos, Hickey, Pong-Wong, Daetwyler and Calus\u003C\u002Fspan\u003E2013\u003C\u002Fa\u003E), where the assumptions for markers effects are shown in \u003Ca class=\"xref table\" href=\"#tab02\"\u003ETable 2\u003C\u002Fa\u003E. The hibayes package (Yin \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref33\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Yin, Zhang, Li, Zhao and Liu\u003C\u002Fspan\u003E2022\u003C\u002Fa\u003E), available for the R program (R Core Team, \u003Ca class=\"xref bibr\" href=\"#ref28\"\u003E2021\u003C\u002Fa\u003E), was used to perform the ssBR analyses. A total of 350 000 samples and a burn-in period of 150 000 samples were generated. The convergence was evaluated using graphical analysis. The heritability estimates for AFC were also obtained using these models.\n\u003C\u002Fp\u003E\u003Cdiv class=\"table-wrap\" data-magellan-destination=\"tab02\" id=\"tab02\"\u003E\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003ETable 2.\u003C\u002Fspan\u003E Description of different prior for markers effects used in Bayesian single-step regression methods used for genomic analysis of age at first calving in dairy buffaloes\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\n\u003Cspan\u003E\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_tab2.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"461\" height=\"260\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_tab2.png\" data-zoomable=\"false\"\u003E\u003C\u002Fdiv\u003E\n\n\u003C\u002Fspan\u003E\n\u003C\u002Fdiv\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"sec2-4\" id=\"sec2-4\"\u003E\u003Ch3 class=\"B\"\u003E Validation of (G)EBVs\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E The predictive ability of the methods was assessed using accuracy and dispersion statistics proposed by Legarra and Reverter (\u003Ca class=\"xref bibr\" href=\"#ref24\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Legarra and Reverter\u003C\u002Fspan\u003E2018\u003C\u002Fa\u003E). This methodology is based on predicting (G)EBV using full (\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$\\hat{u} _w$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline11.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"20\" height=\"18\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline11.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E) and a partial \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$( \\hat{u} _p)$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline12.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"28\" height=\"21\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline12.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E datasets. The partial dataset (reference group) was obtained by omitting phenotypic records of genotyped animals born after 2010 (validation group). Thus, to assess the prediction ability of the models, only genotyped animals from the validation group were used to calculate the following statistics:\u003C\u002Fp\u003E\u003Cdiv data-mathjax-status=\"alt-graphic\" class=\"disp-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$$\\matrix{ {{\\rm Accuracy}} \\hfill & {{\\rm Dispersion}} \\hfill \\cr {r_{A\\hat{A}} = \\sqrt {\\displaystyle{{{\\rm cov}( {\\hat{u}_w, \\;\\hat{u}_p} ) } \\over {( {1-\\bar{F}} ) \\hat{\\sigma }_g^2 }}} } \\hfill & {b_{w, p} = \\displaystyle{{{\\rm cov}( {\\hat{u}_w, \\;\\hat{u}_p} ) } \\over {{\\rm var}( {\\hat{u}_p} ) }}} \\hfill \\cr } $$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU8.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"275\" height=\"70\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_eqnU8.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fdiv\u003E\u003Cp class=\"p continuation\"\u003Ewhere \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$\\bar{F}$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline13.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"13\" height=\"18\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline13.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E is the average inbreeding coefficient of the validation individuals and \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\u003Cspan class=\"alternatives\"\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$\\hat{\\sigma }_{g, i}^2$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline14.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"24\" height=\"25\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_inline14.png\" data-zoomable=\"false\"\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E is the estimate of additive genetic variance.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec results\" data-magellan-destination=\"sec3\" id=\"sec3\"\u003E\u003Ch2 class=\"A\"\u003E Results\u003C\u002Fh2\u003E\n\u003Cp class=\"p\"\u003E In this study, the estimated heritability for AFC was 0.17 using BLUP-based methods and 0.16 to 0.18 using ssBR methods and, the estimates of the effects of the markers can be seen in \u003Ca class=\"xref fig\" href=\"#fig01\"\u003EFigure 1\u003C\u002Fa\u003E. Accuracy estimates for the genotyped animals ranged from 0.30 (ssBRR) to 0.39 (WssGBLUP) (\u003Ca class=\"xref fig\" href=\"#fig02\"\u003EFig. 2\u003C\u002Fa\u003E). Estimates of accuracy with low magnitude were observed for non-genotyped animals, with values ranging from 0.29 (ssGBLUP) to 0.33 (ssBA). The PBLUP model presented accuracies of 0.30 and 0.29 for genotyped and non-genotyped animals, respectively.\n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig fig\" data-magellan-destination=\"fig01\" id=\"fig01\"\u003E\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_fig1.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"2050\" height=\"2088\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_fig1.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure 1.\u003C\u002Fspan\u003E Estimates of SNP marker effects (Manhattan plot) for the different methods employed (ssBA, Single step Bayes A; ssBπ, Single step Bayes Bπ; ssBCπ, Single step Bayes Cπ; ssBL, Single step Bayes Lasso; ssBRR, Single step Bayes Ridge Regression), and cluster analysis based on similarity between marker effects.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\u003Csection\u003E\u003Cdiv class=\"fig fig\" data-magellan-destination=\"fig02\" id=\"fig02\"\u003E\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_fig2.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"2050\" height=\"2142\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241113063331639-0631:S0021859624000364:S0021859624000364_fig2.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure 2.\u003C\u002Fspan\u003E Estimates of accuracy and dispersion of genetic and genomic values using different single-step methods (ssBA, Single step Bayes A; ssBπ, Single step Bayes Bπ; ssBCπ, Single step Bayes Cπ; ssBL, Single step Bayes Lasso; ssBRR, Single step Bayes Ridge Regression) for the study of age at first calving in dairy buffaloes (genotyped animals).\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\u003Cp class=\"p\"\u003E Regarding the dispersion of the GEBV prediction (\u003Ca class=\"xref fig\" href=\"#fig02\"\u003EFig. 2\u003C\u002Fa\u003E), ssBCπ (0.99) and WssGBLUP (1.00) obtained the best results considering only genotyped animals, while for non-genotyped animals only WssGBLUP (1.02) showed the best value, although it was also the higher than 1. The PBLUP model had the worst result with values straying 35% below from the reference value (1.0).\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E In the full dataset, Pearson's correlation between GEBVs and EBVs (predicted via PBLUP) ranged from 0.92 (ssBRR) to 0.93 (ssGBLUP), while for animals with both genotypic and phenotypic information, the correlation between GEBVs and EBVs ranged from 0.71 (ssBRR) to 0.77 (WssGBLUP). The correlations between all GEBVs predicted with the single-step genomic models were higher than 0.95.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec discussion\" data-magellan-destination=\"sec4\" id=\"sec4\"\u003E\u003Ch2 class=\"A\"\u003E Discussion\u003C\u002Fh2\u003E\n\u003Cp class=\"p\"\u003E In this study, a heritability estimate obtained for AFC, had magnitude similar to those described in several studies with the buffalo species, with values ranging from 0.13 to 0.19 (Agudelo \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref1\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Agudelo-Gomez, Pineda-Sierra and Cerón-Muñoz\u003C\u002Fspan\u003E2015\u003C\u002Fa\u003E; Thiruvenkadan \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref29\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Thiruvenkadan, Panneerselvam and Murali\u003C\u002Fspan\u003E2015\u003C\u002Fa\u003E; Fernandes \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref16\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Fernandes, Marques, de Araujo Neto, de Oliveira, Hurtado-Lugo, Aspilcueta-Borquis and Tonhati\u003C\u002Fspan\u003E2016\u003C\u002Fa\u003E; Araujo Neto \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref3\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Araujo Neto, Takada, Santos, Aspilcueta-Borquis, Cardoso, Nascimento, Leão, Oliveira and Tonhati\u003C\u002Fspan\u003E2020\u003Cem class=\"italic\"\u003Ea\u003C\u002Fem\u003E\u003C\u002Fa\u003E, \u003Ca class=\"xref bibr\" href=\"#ref4\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Araujo Neto, Santos, Fernandes Júnior, Aspilcueta-Borquis, Nascimento, Seno, Tonhati and Oliveira\u003C\u002Fspan\u003E2020\u003Cem class=\"italic\"\u003Eb\u003C\u002Fem\u003E\u003C\u002Fa\u003E). These results show that despite the greater information provided by the markers in the analysis, there was very little influence on the estimation of the genetic parameters, possibly due to the polygenic nature of the trait. There are few reports in the literature on comparison of genomic prediction for reproductive traits, and it is not yet possible to find studies that compared the predictive ability between different single-step methods for AFC. Moreover, several accuracy measures have been reported by different authors, which makes the comparison between their values even more difficult. For instance, Costa \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E. (\u003Ca class=\"xref bibr\" href=\"#ref15\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Costa, Irano, Diaz, Takada, Hermisdorff, Carvalheiro, Baldi, Oliveira, Tonhati and Albuquerque\u003C\u002Fspan\u003E2019\u003C\u002Fa\u003E), working only with genotyped Nellore breed animals and considering the correlation between GEBV and adjusted AFC (\u003Cem class=\"italic\"\u003Er\u003C\u002Fem\u003E \u003Csub\u003E\u003Cem class=\"italic\"\u003EGEBV\u003C\u002Fem\u003E,\u003Cem class=\"italic\"\u003EY\u003C\u002Fem\u003E*\u003C\u002Fsub\u003E), estimated values with magnitudes similar to those found in our study with BayesCπ (0.31) and Bayes-Lasso (0.31), while Toghiani \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E. (\u003Ca class=\"xref bibr\" href=\"#ref30\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Toghiani, Hay, Sumreddee, Geary, Rekaya and Roberts\u003C\u002Fspan\u003E2017\u003C\u002Fa\u003E) reported lower values with BayesA (0.148) and BayesCπ (0.15), studying the same breed and using the same type of accuracy. In both cited studies, accuracy estimates were not presented for PBLUP model, which does not allow us to fully contrast with our findings. Possibly, for comparison purposes, checking the accuracy increments in relation to PBLUP is the best approach to discuss our results. Thus, all literature discussed about predictability were made based on the difference in performance between methods also used in our study.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E Considering the percentage of accuracy increment in relation to PBLUP predictions in only genotyped animals, we observed three groups of models: increments less than 5% – ssBL and ssBRR; increments close 10% – ssBBπ, ssBCπ and ssGBLUP and; increments greater than 25% – ssBA and WssGBLUP. Estimates of accuracy increments using SNP markers with magnitudes similar to those we have found for AFC, have been described in the literature for productive traits in buffaloes (Cesarani \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref13\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Cesarani, Biffani, Garcia, Lourenco, Bertolini, Neglia, Misztal and Macciotta\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E; Herrera \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref20\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Herrera, Flores, Duijvesteijn, Moghaddar and van der Werf\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E).\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E For milk, fat and protein yield, greater increases in accuracy (\u003Cem class=\"italic\"\u003Er\u003C\u002Fem\u003E \u003Csub\u003E\u003Cem class=\"italic\"\u003EGEBV\u003C\u002Fem\u003E,\u003Cem class=\"italic\"\u003EY\u003C\u002Fem\u003E*\u003C\u002Fsub\u003E) are presented by Herrera \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E. (\u003Ca class=\"xref bibr\" href=\"#ref20\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Herrera, Flores, Duijvesteijn, Moghaddar and van der Werf\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E) (13.04 to 76.47%) and Cesarani \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E. (\u003Ca class=\"xref bibr\" href=\"#ref13\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Cesarani, Biffani, Garcia, Lourenco, Bertolini, Neglia, Misztal and Macciotta\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E) (15.28 to 33.33%). Aspilcueta-Borquis \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E. (\u003Ca class=\"xref bibr\" href=\"#ref6\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Aspilcueta-Borquis, Araujo Neto, Santos, Hurtado-Lugo, Silva and Tonhati\u003C\u002Fspan\u003E2015\u003C\u002Fa\u003E), studying the same population of this study and ssGBLUP model, reported similar increase in the average accuracy (based on prediction error variance) of (G)EBVs, which ranged from 8.52 to 12.05% for several dairy traits. This gain in accuracy observed with the use of genomic information is due to the additional capture of both Mendelian sampling variations and relationships between animals (Christensen \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref14\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Christensen, Madsen, Nielsen, Ostersen and Su\u003C\u002Fspan\u003E2012\u003C\u002Fa\u003E; Cesarani \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref12\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Cesarani, Garcia, Hidalgo, Degano, Vicario, Macciotta and Lourenco\u003C\u002Fspan\u003E2020\u003C\u002Fa\u003E). The similarity in predictive performance between the different single-step genomic methods, however, could be related to the reduced number of animals evaluated, the small subset of genotyped animals analysed, and the polygenic nature of the AFC (Calus, \u003Ca class=\"xref bibr\" href=\"#ref8\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Calus\u003C\u002Fspan\u003E2010\u003C\u002Fa\u003E; Campos \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E., \u003Ca class=\"xref bibr\" href=\"#ref11\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Campos, Hickey, Pong-Wong, Daetwyler and Calus\u003C\u002Fspan\u003E2013\u003C\u002Fa\u003E).\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E The proximity between ssBA and GRM-based model observed in this study (by the magnitude of estimated accuracies) may be explained by the polygenic nature of the trait and the robustness of ssBA method for different genetic architectures. Zhou \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E. (\u003Ca class=\"xref bibr\" href=\"#ref35\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Zhou, Mrode, Zhang, Zhang, Li and Liu\u003C\u002Fspan\u003E2018\u003C\u002Fa\u003E), studying the effects of QTL number on the accuracy prediction with simulated data, also verified that ssBA method was robust and performed similarly to ssGBLUP in scenarios with a large number of QTL.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E The dispersion criterion is related to the degree of inflation or deflation of predictions, which was measured in our validation set as the slope of the regression of the GEBV obtained with the full dataset on GEBV from the partial dataset. Our results showed that the inclusion of genomic information reduces the dispersion of prediction compared to the traditional evaluations (PBLUP), regardless of the single-step model considered. The same improvement in prediction slopes by using genomic information was reported by Lázaro \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E. (\u003Ca class=\"xref bibr\" href=\"#ref22\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Lázaro, Tonhati, Oliveira, Silva, Nascimento, Santos, Stefani and Brito\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E) studying several milk-related traits with random regression models in the same buffalo population, while other authors, such as Gao \u003Cem class=\"italic\"\u003Eet al\u003C\u002Fem\u003E. (\u003Ca class=\"xref bibr\" href=\"#ref18\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Gao, Koivula, Jensen, Strandén, Madsen, Pitkänen, Aamand and Mäntysaari\u003C\u002Fspan\u003E2018\u003C\u002Fa\u003E) also analysing dairy traits in Finnish red dairy cattle, report no benefit. Moreover, the GEBVs predicted with WssGBPUP did not disperse in relation to what was expected for the subset of genotyped animals and presented little deflation for the prediction of non-genotyped animals. The low dispersion of GEBVs predicted with WssGBLUP compared to the predictions from other genomic models is probably due to the self-fitting of the SNP weights to the dataset (weighting steps), which regulates the scale of the additive effect to the full dataset previously (\u003Cem class=\"italic\"\u003Ea priori\u003C\u002Fem\u003E).\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E The results indicate that the use of genomic information can improve the genetic gain for AFC by increasing the accuracy and reducing inflation\u002Fdeflation of predictions of this trait compared to the traditional pedigree-based model. In addition, among all genomic single-step models studied, WssGBLUP and ssBA were the most advantageous models to be used for the genomic evaluation of AFC of buffaloes from this population.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"back\"\u003E\u003Cdiv class=\"sec other\" data-magellan-destination=\"sec-nts1\" id=\"sec-nts1\"\u003E\u003Ch2 class=\"A\"\u003E Authors’ contributions\u003C\u002Fh2\u003E\n\u003Cp class=\"p\"\u003E Jessica Cristina Gonçalves dos Santos: Methodology, Analysis , Writing – original draft.; Francisco Ribeiro de Araujo Neto: Conceptualization, Methodology, Statistical analysis, Writing – review; Gabriela Stefani Fernandez: Database; Daniel Jordan de Abreu Santos: Writing – review & editing; Felipe Pereira Cunha: Writing editing; Rusbel Raul Aspilcueta-Borquis: Statistical analysis; Humberto Tonhati: Conceptualization, Database, Supervision.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec funding-statement\" data-magellan-destination=\"sec-fs1\" id=\"sec-fs1\"\u003E\u003Ch2 class=\"A\"\u003E Funding statement\u003C\u002Fh2\u003E\n\u003Cp class=\"p\"\u003E This research received no specific grant from any funding agency, commercial or not-for-profit sectors.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec coi-statement\" data-magellan-destination=\"sec-ci1\" id=\"sec-ci1\"\u003E\u003Ch2 class=\"A\"\u003E Competing interests\u003C\u002Fh2\u003E\n\u003Cp class=\"p\"\u003E None.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec other\" data-magellan-destination=\"sec-nts2\" id=\"sec-nts2\"\u003E\u003Ch2 class=\"A\"\u003E Ethical standards\u003C\u002Fh2\u003E\n\u003Cp class=\"p\"\u003E Not applicable (the work was developed with a database).\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E\n\n\u003C\u002Fdiv\u003E\n\u003C\u002Fdiv\u003E",tableOfContent:[{level:h,current:b,title:"\u003Cdiv class=\"toc-title\"\u003EIntroduction\u003C\u002Fdiv\u003E",url:"sec1"},{level:h,current:b,title:"\u003Cdiv class=\"toc-title\"\u003EMaterials and methods\u003C\u002Fdiv\u003E",url:"sec2"},{level:h,current:b,title:"\u003Cdiv class=\"toc-title\"\u003EResults\u003C\u002Fdiv\u003E",url:"sec3"},{level:h,current:b,title:"\u003Cdiv class=\"toc-title\"\u003EDiscussion\u003C\u002Fdiv\u003E",url:"sec4"},{level:h,current:b,title:"\u003Cdiv class=\"toc-title\"\u003EAuthors’ contributions\u003C\u002Fdiv\u003E",url:"sec-nts1"},{level:h,current:b,title:"\u003Cdiv class=\"toc-title\"\u003EFunding statement\u003C\u002Fdiv\u003E",url:"sec-fs1"},{level:h,current:b,title:"\u003Cdiv class=\"toc-title\"\u003ECompeting interests\u003C\u002Fdiv\u003E",url:"sec-ci1"},{level:h,current:b,title:"\u003Cdiv class=\"toc-title\"\u003EEthical standards\u003C\u002Fdiv\u003E",url:"sec-nts2"}],footnotes:[],fulltextNotes:[],references:[{id:"ref1",displayNumber:a,existInContent:c,content:"\u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003EAgudelo-Gomez\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003ED\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003EPineda-Sierra\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003ES\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E and \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003ECerón-Muñoz\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EMF\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E (\u003Cspan class=\"year\"\u003E2015\u003C\u002Fspan\u003E) \u003Cspan class=\"article-title\"\u003EGenetic evaluation of dual-purpose buffaloes (\u003Cem class=\"italic\"\u003EBubalus bubalis\u003C\u002Fem\u003E) in Colombia using principal component analysis\u003C\u002Fspan\u003E. \u003Cspan class=\"source\"\u003EPLoS One\u003C\u002Fspan\u003E \u003Cspan class=\"volume\"\u003E10\u003C\u002Fspan\u003E, \u003Cspan class=\"fpage\"\u003Ee0132811\u003C\u002Fspan\u003E.\u003Ca class='ref-link' target='_blank' aria-label='CrossRef link for Genetic evaluation of dual-purpose buffaloes (Bubalus bubalis) in Colombia using principal component analysis' href=https:\u002F\u002Fdx.doi.org\u002F10.1371\u002Fjournal.pone.0132811\u003ECrossRef\u003C\u002Fa\u003E\u003Ca class='ref-link' target='_blank' aria-label='Google Scholar link for Genetic evaluation of dual-purpose buffaloes (Bubalus bubalis) in Colombia using principal component analysis' href=https:\u002F\u002Fscholar.google.com\u002Fscholar_lookup?title=Genetic+evaluation+of+dual-purpose+buffaloes+(Bubalus+bubalis)+in+Colombia+using+principal+component+analysis&author=Agudelo-Gomez+D&author=Pineda-Sierra+S&author=Cer%C3%B3n-Mu%C3%B1oz+MF&publication+year=2015&journal=PLoS+One&volume=10&doi=10.1371%2Fjournal.pone.0132811\u003EGoogle Scholar\u003C\u002Fa\u003E\u003Ca class='ref-link' target='_blank' aria-label='PubMed link for Genetic evaluation of 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class=\"given-names\"\u003EFR\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003ETakada\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EL\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003ESantos\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EDJA\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003EAspilcueta-Borquis\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003ERR\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003ECardoso\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EDF\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003ENascimento\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EAV\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003ELeão\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EKM\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003EOliveira\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EHN\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E and \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003ETonhati\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EH\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E (\u003Cspan class=\"year\"\u003E2020\u003C\u002Fspan\u003E \u003Cem class=\"italic\"\u003Ea\u003C\u002Fem\u003E) \u003Cspan class=\"article-title\"\u003EIdentification of genomic regions related to age at first calving and first calving interval in water buffalo using single-step GBLUP\u003C\u002Fspan\u003E. \u003Cspan class=\"source\"\u003EReproduction in 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href=https:\u002F\u002Fwww.ncbi.nlm.nih.gov\u002Fpubmed\u002F32853485\u003EPubMed\u003C\u002Fa\u003E",item:[{googleScholarLink:"https:\u002F\u002Fscholar.google.com\u002Fscholar_lookup?title=Identification+of+genomic+regions+related+to+age+at+first+calving+and+first+calving+interval+in+water+buffalo+using+single-step+GBLUP&author=Araujo+Neto+FR&author=Takada+L&author=Santos+DJA&author=Aspilcueta-Borquis+RR&author=Cardoso+DF&author=Nascimento+AV&author=Le%C3%A3o+KM&author=Oliveira+HN&author=Tonhati+H&publication+year=2020&journal=Reproduction+in+Domestic+Animals&volume=55&doi=10.1111%2Frda.13811&pages=1565-1572",openUrlParams:{genre:f,atitle:S,jtitle:s,title:s,volume:"55",artnum:"6734483f1921644800f9eff6",spage:T,epage:"1572",date:t,sid:e,aulast:a,aufirst:a,doi:U,au:a},innerRefId:"cite3",title:S,pubMedId:"32853485",doi:U,crossRefLink:"https:\u002F\u002Fdx.doi.org\u002F10.1111\u002Frda.13811",pubMedLink:"https:\u002F\u002Fwww.ncbi.nlm.nih.gov\u002Fpubmed\u002F32853485"}]},{id:"ref4",displayNumber:a,existInContent:c,content:"\u003Cspan 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class=\"surname\"\u003EKoltes\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EJE\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003EBiffani\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003ES\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003ESonstegard\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003ETS\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003ESchroeder\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003ESG\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003EAjmone-Marsan\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EP\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"string-name\"\u003E\u003Cspan 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class=\"given-names\"\u003ED\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003EAguilar\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EI\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003ELegarra\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EA\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E and \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003EMisztal\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EI\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E (\u003Cspan class=\"year\"\u003E2016\u003C\u002Fspan\u003E) \u003Cspan class=\"article-title\"\u003EWeighting strategies for single-step genomic BLUP: an iterative approach for accurate calculation of GEBV and GWAS\u003C\u002Fspan\u003E. \u003Cspan class=\"source\"\u003EFrontiers in Genetics\u003C\u002Fspan\u003E \u003Cspan 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href=https:\u002F\u002Fscholar.google.com\u002Fscholar_lookup?title=Factors+affecting+GEBV+accuracy+with+single-step+Bayesian+models&author=Zhou+L&author=Mrode+R&author=Zhang+S&author=Zhang+Q&author=Li+B&author=Liu+JF&publication+year=2018&journal=Heredity&volume=120&doi=10.1038%2Fs41437-017-0010-9&pages=100-109\u003EGoogle Scholar\u003C\u002Fa\u003E\u003Ca class='ref-link' target='_blank' aria-label='PubMed link for Factors affecting GEBV accuracy with single-step Bayesian models' href=https:\u002F\u002Fwww.ncbi.nlm.nih.gov\u002Fpubmed\u002F29167557\u003EPubMed\u003C\u002Fa\u003E",item:[{googleScholarLink:"https:\u002F\u002Fscholar.google.com\u002Fscholar_lookup?title=Factors+affecting+GEBV+accuracy+with+single-step+Bayesian+models&author=Zhou+L&author=Mrode+R&author=Zhang+S&author=Zhang+Q&author=Li+B&author=Liu+JF&publication+year=2018&journal=Heredity&volume=120&doi=10.1038%2Fs41437-017-0010-9&pages=100-109",openUrlParams:{genre:f,atitle:bo,jtitle:bp,title:bp,volume:"120",artnum:"6734483f1921644800f9f017",spage:"100",epage:"109",date:E,sid:e,aulast:a,aufirst:a,doi:bq,au:a},innerRefId:"cite35",title:bo,pubMedId:"29167557",doi:bq,crossRefLink:"https:\u002F\u002Fdx.doi.org\u002F10.1038\u002Fs41437-017-0010-9",pubMedLink:"https:\u002F\u002Fwww.ncbi.nlm.nih.gov\u002Fpubmed\u002F29167557"}]}],figures:[{contentId:"tab01",label:"Table 1.",description:"\u003Cspan class=\"p\"\u003EDescription of age at first calving dataset used in this study\u003C\u002Fspan\u003E",thumbnailSrc:br,enlargedSrc:br,attrib:[]},{contentId:"tab02",label:"Table 2.",description:"\u003Cspan class=\"p\"\u003EDescription of different prior for markers effects used in Bayesian single-step regression methods used for genomic analysis of age at first calving in dairy buffaloes\u003C\u002Fspan\u003E",thumbnailSrc:bs,enlargedSrc:bs,attrib:[]},{contentId:"fig01",label:"Figure 1.",description:"\u003Cspan class=\"p\"\u003EEstimates of SNP marker effects (Manhattan plot) for the different methods employed (ssBA, Single step Bayes A; ssBπ, Single step Bayes Bπ; ssBCπ, Single step Bayes Cπ; ssBL, Single step Bayes Lasso; ssBRR, Single step Bayes Ridge Regression), and cluster analysis based on similarity between marker effects.\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241113063400-39867-mediumThumb-png-S0021859624000364_fig1.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241113063400-64577-optimisedImage-png-S0021859624000364_fig1.jpg",attrib:[]},{contentId:"fig02",label:"Figure 2.",description:"\u003Cspan class=\"p\"\u003EEstimates of accuracy and dispersion of genetic and genomic values using different single-step methods (ssBA, Single step Bayes A; ssBπ, Single step Bayes Bπ; ssBCπ, Single step Bayes Cπ; ssBL, Single step Bayes Lasso; ssBRR, Single step Bayes Ridge Regression) for the study of age at first calving in dairy buffaloes (genotyped animals).\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241113063400-09770-mediumThumb-png-S0021859624000364_fig2.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241113063400-39764-optimisedImage-png-S0021859624000364_fig2.jpg",attrib:[]}]},pdf:{standardResolution:{fileUrl:"\u002Fcore\u002Fservices\u002Faop-cambridge-core\u002Fcontent\u002Fview\u002FEE7AD86B2F8357591452CD46DAD1D5EA\u002FS0021859624000364a.pdf\u002Fcomparison-of-single-step-methods-for-genomic-prediction-of-age-at-first-calving-in-dairy-buffaloes.pdf",fileSizeInMb:.34,articleTitle:A,slugTitle:"comparison-of-single-step-methods-for-genomic-prediction-of-age-at-first-calving-in-dairy-buffaloes"},highResolution:g,media:g},classification:[],supplementaryMaterials:[],relations:{corrections:[],correctionsOriginals:[],retractions:[],retractionsOriginals:[],addendums:[],addendumsOriginals:[],hasAnyRelations:b,hasAnyOriginalArticle:b},settings:{hasAccess:c,isOpenAccess:b,displayRightsLink:c,shouldDisplayCrossMark:c,shouldDisplayNasaAds:b,suppressPdf:b,isShareable:c,isAnnotationsEnabled:b,disableArticleCommentary:b,displayArticleCommentaryAsDiscussionLinks:b,isCommentsEnabled:b,hasContent:c,shouldDisplaySubmitContent:b,isResearchDirections:b,isQuestionCollection:b,isMathjaxEnabled:b},citationCount:B,openUrlParams:"?genre=article&atitle=Comparison%20of%20single-step%20methods%20for%20genomic%20prediction%20of%20age%20at%20first%20calving%20in%20dairy%20buffaloes&jtitle=The%20Journal%20of%20Agricultural%20Science&title=The%20Journal%20of%20Agricultural%20Science&spage=1&epage=7&sid=https%3A%2F%2Fwww.cambridge.org%2Fcore&aulast=dos%20Santos&aufirst=Jessica%20Cristina%20Gon%C3%A7alves&doi=10.1017\u002FS0021859624000364",ecommerceProducts:{digitalSku:m,paperBackSku:g,hardBackSku:g},subject:[],permissionUrl:"https:\u002F\u002Fs100.copyright.com\u002FAppDispatchServlet?publisherName=CUP&publication=AGS&title=Comparison%20of%20single-step%20methods%20for%20genomic%20prediction%20of%20age%20at%20first%20calving%20in%20dairy%20buffaloes&publicationDate=14%20November%202024&author=Jessica%20Cristina%20Gon%C3%A7alves%20dos%20Santos%2C%20Francisco%20Ribeiro%20de%20Ara%C3%BAjo%20Neto%2C%20Gabriela%20Stefani%20Fernandez%2C%20Daniel%20Jordan%20de%20Abreu%20Santos%2C%20Felipe%20Pereira%20Cunha%2C%20Rusbel%20Raul%20Aspilcueta-Borquis%2C%20Humberto%20Tonhati&copyright=Copyright%20%C2%A9%20The%20Author(s)%2C%202024.%20Published%20by%20Cambridge%20University%20Press&contentID=10.1017%2FS0021859624000364&startPage=1&endPage=7&orderBeanReset=True&volumeNum=&issueNum=&oa="},breadcrumbs:[{name:"Home",url:"\u002Fcore"},{name:"Journals",url:"\u002Fcore\u002Fpublications\u002Fjournals"},{name:o,url:K},{name:"FirstView",url:L},{name:"Comparison 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of Dairy Science","Genetics","western","Genetics Selection Evolution","S0021859624000364","Faculdade de Ciências Agrárias e Veterinárias de Jaboticabal – UNESP, Jaboticabal, São Paulo, Brazil","The Journal of Agricultural Science","article_ags_ind_pur","PLoS One","2015","Reproduction in Domestic Animals","2020","Journal of Applied Genetics","Animal","2021","12","Frontiers in Genetics","Journal of Animal Science","Comparison of single-step methods for genomic prediction of age at first calving in dairy buffaloes",0,"2022","2008","2018","2017","R: A Language and Environment for Statistical Computing","Instituto Federal de Ciência e Tecnologia Goiano – IFGoiano, Rio Verde, Goiás","7","77EB13D6C66FED2F2E3B34871326A147","\u002Fcore\u002Fjournals\u002Fjournal-of-agricultural-science","\u002Fcore\u002Fjournals\u002Fjournal-of-agricultural-science\u002Ffirstview","en","Genetic evaluation of dual-purpose buffaloes (Bubalus bubalis) in Colombia using principal component analysis","10.1371\u002Fjournal.pone.0132811","Hot topic: a unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score","2010","10.3168\u002Fjds.2009-2730","Identification of genomic regions related to age at first calving and first calving interval in water buffalo using single-step GBLUP","1565","10.1111\u002Frda.13811","Genome-wide association studies for growth traits in buffaloes using the single step genomic BLUP","10.1007\u002Fs13353-019-00528-5","Genomic study of the resilience of buffalo cows to a negative energy balance","10.1007\u002Fs13353-021-00680-x","Multiple-trait genomic evaluation for milk yield and milk quality traits using genomic and phenotypic data in buffalo in Brazil","Genetics and Molecular Research","10.4238\u002F2015.December.22.27","Lifetime productivity: genetic study of longevity and its associations with economically important traits in dairy buffaloes","Livestock Science","10.1016\u002Fj.livsci.2022.104900","Genomic breeding value prediction: methods and procedures","157","10.1017\u002FS1751731109991352","Accuracy of genomic selection using different methods to define haplotypes","10.1534\u002Fgenetics.107.080838","Prospecting major genes in dairy buffaloes","BMC Genomics","10.1186\u002Fs12864-015-1986-2","Whole-genome regression and prediction methods applied to plant and animal breeding","10.1534\u002Fgenetics.112.143313","Genomic information allows for more accurate breeding values for milk ability in dual-purpose Italian Simmental cattle","104","10.3168\u002Fjds.2020-19838","Genomic investigation of milk production in Italian buffalo","Italian Journal of Animal Science","10.1080\u002F1828051X.2021.1902404","Single-step methods for genomic evaluation in pigs","2012","10.1017\u002FS1751731112000742","Prediction of genomic breeding values for reproductive traits in Nellore heifers","Theriogenology","10.1016\u002Fj.theriogenology.2018.10.014","Genetic-quantitative study of the first-service pregnancy probability of Murrah heifers","2016","10.1111\u002Frda.12697","A class of Bayesian methods to combine large numbers of genotyped and non-genotyped animals for whole-genome analyses","50","2014","10.1186\u002F1297-9686-46-50","Short communication: genomic prediction using different single-step methods in the Finnish red dairy cattle population","10.3168\u002Fjds.2018-14913","Extension of the Bayesian alphabet for genomic selection","BMC Bioinformatics","10.1186\u002F1471-2105-12-186","Accuracy of genomic prediction for milk production traits in Philippine dairy buffaloes","10.3389\u002Ffgene.2021.682576","Design and validation of a 90K SNP genotyping assay for the water buffalo (Bubalus bubalis)","10.1371\u002Fjournal.pone.0185220","Genomic studies of milk-related traits in water buffalo (Bubalus bubalis) based on single-step genomic best linear unbiased prediction and random regression models","10.3168\u002Fjds.2020-19534","Comparison of alternative approaches to single-trait genomic prediction using genotyped and non-genotyped Hanwoo beef cattle","49","10.1186\u002Fs12711-016-0279-9","Semi-parametric estimates of population accuracy and bias of predictions of breeding values and future phenotypes using the LR method","10.1186\u002Fs12711-018-0426-6","Prediction of total genetic value using genome-wide dense marker maps","10.1093\u002Fgenetics\u002F157.4.1819","Current status of genomic evaluation","10.1093\u002Fjas\u002Fskaa101","Study on ages at first mating and calving of Murrah buffaloes in hot and humid climate of Tamil Nadu","India. Indian Journal of Animal Research","Genomic prediction of continuous and binary fertility traits of females in a composite beef cattle breed","10.2527\u002Fjas2017.1944","Efficient methods to compute genomic predictions","Journal Dairy Science","10.3168\u002Fjds.2007-0980","Genome-wide association mapping including phenotypes from relatives without genotypes","Genetics Research","10.1017\u002FS0016672312000274","Bayesian LASSO for quantitative trait loci mapping","10.1534\u002Fgenetics.107.085589","Hibayes: an R package to fit individual-level, summary-level and single-step Bayesian regression models for genomic prediction and genome-wide association studies","bioRxiv","Weighting strategies for single-step genomic BLUP: an iterative approach for accurate calculation of GEBV and GWAS","10.3389\u002Ffgene.2016.00151","Factors affecting GEBV accuracy with single-step Bayesian 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