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<span>Definition</span> </div> </a> <button aria-controls="toc-Definition-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Definition subsection</span> </button> <ul id="toc-Definition-sublist" class="vector-toc-list"> <li id="toc-Example" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Example"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Example</span> </div> </a> <ul id="toc-Example-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Assumptions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Assumptions"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Assumptions</span> </div> </a> <ul id="toc-Assumptions-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Estimating_heritability" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Estimating_heritability"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Estimating heritability</span> </div> </a> <button aria-controls="toc-Estimating_heritability-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Estimating heritability subsection</span> </button> <ul id="toc-Estimating_heritability-sublist" class="vector-toc-list"> <li id="toc-Regression/correlation_methods_of_estimation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Regression/correlation_methods_of_estimation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Regression/correlation methods of estimation</span> </div> </a> <ul id="toc-Regression/correlation_methods_of_estimation-sublist" class="vector-toc-list"> <li id="toc-Comparison_of_close_relatives" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Comparison_of_close_relatives"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>Comparison of close relatives</span> </div> </a> <ul id="toc-Comparison_of_close_relatives-sublist" class="vector-toc-list"> <li id="toc-Parent-offspring_regression" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Parent-offspring_regression"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1.1</span> <span>Parent-offspring regression</span> </div> </a> <ul id="toc-Parent-offspring_regression-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sibling_comparison" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Sibling_comparison"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1.2</span> <span>Sibling comparison</span> </div> </a> <ul id="toc-Sibling_comparison-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Twin_studies" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Twin_studies"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1.3</span> <span>Twin studies</span> </div> </a> <ul id="toc-Twin_studies-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Analysis_of_variance_methods_of_estimation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Analysis_of_variance_methods_of_estimation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Analysis of variance methods of estimation</span> </div> </a> <ul id="toc-Analysis_of_variance_methods_of_estimation-sublist" class="vector-toc-list"> <li id="toc-Basic_model" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Basic_model"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.1</span> <span>Basic model</span> </div> </a> <ul id="toc-Basic_model-sublist" class="vector-toc-list"> <li id="toc-Intraclass_correlations" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Intraclass_correlations"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.1.1</span> <span>Intraclass correlations</span> </div> </a> <ul id="toc-Intraclass_correlations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_ANOVA" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#The_ANOVA"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.1.2</span> <span>The ANOVA</span> </div> </a> <ul id="toc-The_ANOVA-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Model_with_additive_and_dominance_terms" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Model_with_additive_and_dominance_terms"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.2</span> <span>Model with additive and dominance terms</span> </div> </a> <ul id="toc-Model_with_additive_and_dominance_terms-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Linear_mixed_models" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Linear_mixed_models"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Linear mixed models</span> </div> </a> <ul id="toc-Linear_mixed_models-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Genomic_heritability" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Genomic_heritability"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Genomic heritability</span> </div> </a> <ul id="toc-Genomic_heritability-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Response_to_selection" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Response_to_selection"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Response to selection</span> </div> </a> <ul id="toc-Response_to_selection-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Controversies" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Controversies"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Controversies</span> </div> </a> <ul id="toc-Controversies-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Heritability</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 31 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-31" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">31 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%88%D8%B1%D9%88%D8%AB%D9%8A%D8%A9" title="وروثية – Arabic" lang="ar" hreflang="ar" data-title="وروثية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Heritabilnost" title="Heritabilnost – Bosnian" lang="bs" hreflang="bs" data-title="Heritabilnost" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Heretabilitat" title="Heretabilitat – Catalan" lang="ca" hreflang="ca" data-title="Heretabilitat" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/D%C4%9Bdivost" title="Dědivost – Czech" lang="cs" hreflang="cs" data-title="Dědivost" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Heritabilit%C3%A4t" title="Heritabilität – German" lang="de" hreflang="de" data-title="Heritabilität" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/P%C3%A4ritavus" title="Päritavus – Estonian" lang="et" hreflang="et" data-title="Päritavus" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Heredabilidad" title="Heredabilidad – Spanish" lang="es" hreflang="es" data-title="Heredabilidad" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Heredeblo" title="Heredeblo – Esperanto" lang="eo" hreflang="eo" data-title="Heredeblo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%88%D8%B1%D8%A7%D8%AB%D8%AA%E2%80%8C%D9%BE%D8%B0%DB%8C%D8%B1%DB%8C" title="وراثت‌پذیری – Persian" lang="fa" hreflang="fa" data-title="وراثت‌پذیری" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/H%C3%A9ritabilit%C3%A9" title="Héritabilité – French" lang="fr" hreflang="fr" data-title="Héritabilité" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BA%D5%A1%D5%BC%D5%A1%D5%B6%D5%A3%D5%A5%D5%AC%D5%AB%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Ժառանգելիություն – Armenian" lang="hy" hreflang="hy" data-title="Ժառանգելիություն" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Nasljednost" title="Nasljednost – Croatian" lang="hr" hreflang="hr" data-title="Nasljednost" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Heritabilitas" title="Heritabilitas – Indonesian" lang="id" hreflang="id" data-title="Heritabilitas" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Ereditabilit%C3%A0" title="Ereditabilità – Italian" lang="it" hreflang="it" data-title="Ereditabilità" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%AA%D7%95%D7%A8%D7%A9%D7%AA%D7%99%D7%95%D7%AA" title="תורשתיות – Hebrew" lang="he" hreflang="he" data-title="תורשתיות" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Heritabiliti" title="Heritabiliti – Malay" lang="ms" hreflang="ms" data-title="Heritabiliti" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Overerfbaarheid" title="Overerfbaarheid – Dutch" lang="nl" hreflang="nl" data-title="Overerfbaarheid" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%81%BA%E4%BC%9D%E7%8E%87" title="遺伝率 – Japanese" lang="ja" hreflang="ja" data-title="遺伝率" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Odziedziczalno%C5%9B%C4%87" title="Odziedziczalność – Polish" lang="pl" hreflang="pl" data-title="Odziedziczalność" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Herdabilidade" title="Herdabilidade – Portuguese" lang="pt" hreflang="pt" data-title="Herdabilidade" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Eritabilitate" title="Eritabilitate – Romanian" lang="ro" hreflang="ro" data-title="Eritabilitate" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9D%D0%B0%D1%81%D0%BB%D0%B5%D0%B4%D1%83%D0%B5%D0%BC%D0%BE%D1%81%D1%82%D1%8C_(%D0%B3%D0%B5%D0%BD%D0%B5%D1%82%D0%B8%D0%BA%D0%B0)" title="Наследуемость (генетика) – Russian" lang="ru" hreflang="ru" data-title="Наследуемость (генетика)" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Heritabilnost" title="Heritabilnost – Serbian" lang="sr" hreflang="sr" data-title="Heritabilnost" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Heritabilnost" title="Heritabilnost – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Heritabilnost" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Heritabiliteetti" title="Heritabiliteetti – Finnish" lang="fi" hreflang="fi" data-title="Heritabiliteetti" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Heritabilitet" title="Heritabilitet – Swedish" lang="sv" hreflang="sv" data-title="Heritabilitet" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AD%E0%B8%B1%E0%B8%95%E0%B8%A3%E0%B8%B2%E0%B8%9E%E0%B8%B1%E0%B8%99%E0%B8%98%E0%B8%B8%E0%B8%81%E0%B8%A3%E0%B8%A3%E0%B8%A1" title="อัตราพันธุกรรม – Thai" lang="th" hreflang="th" data-title="อัตราพันธุกรรม" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A3%D1%81%D0%BF%D0%B0%D0%B4%D0%BA%D0%BE%D0%B2%D1%83%D0%B2%D0%B0%D0%BD%D1%96%D1%81%D1%82%D1%8C" title="Успадковуваність – Ukrainian" lang="uk" hreflang="uk" data-title="Успадковуваність" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%E1%BB%87_s%E1%BB%91_di_truy%E1%BB%81n" title="Hệ số di truyền – Vietnamese" lang="vi" hreflang="vi" data-title="Hệ số di truyền" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%81%BA%E5%82%B3%E5%BA%A6" title="遺傳度 – 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.hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/Heredity" title="Heredity">heredity</a>.</div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Critique_of_the_Theory_of_Evolution_Fig_076.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Critique_of_the_Theory_of_Evolution_Fig_076.jpg/160px-Critique_of_the_Theory_of_Evolution_Fig_076.jpg" decoding="async" width="160" height="229" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Critique_of_the_Theory_of_Evolution_Fig_076.jpg/240px-Critique_of_the_Theory_of_Evolution_Fig_076.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Critique_of_the_Theory_of_Evolution_Fig_076.jpg/320px-Critique_of_the_Theory_of_Evolution_Fig_076.jpg 2x" data-file-width="597" data-file-height="856" /></a><figcaption>Studies of heritability ask questions such as to what extent do genetic factors influence <i>differences</i> in height between people. This is not the same as asking to what extent do genetic factors influence height in any one person.</figcaption></figure> <p><b>Heritability</b> is a <a href="/wiki/Statistic" title="Statistic">statistic</a> used in the fields of <a href="/wiki/Animal_husbandry" title="Animal husbandry">breeding</a> and <a href="/wiki/Genetics" title="Genetics">genetics</a> that estimates the degree of <i>variation</i> in a <a href="/wiki/Phenotypic_trait" title="Phenotypic trait">phenotypic trait</a> in a <a href="/wiki/Population" title="Population">population</a> that is due to <a href="/wiki/Genetic_variation" title="Genetic variation">genetic variation</a> between individuals in that population.<sup id="cite_ref-scitable-estimating_1-0" class="reference"><a href="#cite_note-scitable-estimating-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The concept of heritability can be expressed in the form of the following question: "What is the proportion of the variation in a given trait within a population that is <i>not</i> explained by the environment or random chance?"<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Other causes of measured variation in a trait are characterized as <a href="/wiki/Environment_(biophysical)" class="mw-redirect" title="Environment (biophysical)">environmental factors</a>, including <a href="/wiki/Observational_error" title="Observational error">observational error</a>. In human studies of heritability these are often apportioned into factors from "shared environment" and "non-shared environment" based on whether they tend to result in persons brought up in the same household being more or less similar to persons who were not. </p><p>Heritability is estimated by comparing individual phenotypic variation among related individuals in a population, by examining the association between individual phenotype and genotype data,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:0_4-0" class="reference"><a href="#cite_note-:0-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> or even by modeling summary-level data from genome-wide association studies (GWAS).<sup id="cite_ref-:1_5-0" class="reference"><a href="#cite_note-:1-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Heritability is an important concept in <a href="/wiki/Quantitative_genetics" title="Quantitative genetics">quantitative genetics</a>, particularly in <a href="/wiki/Selective_breeding" title="Selective breeding">selective breeding</a> and <a href="/wiki/Behavior_genetics" class="mw-redirect" title="Behavior genetics">behavior genetics</a> (for instance, <a href="/wiki/Twin_study" title="Twin study">twin studies</a>). It is the source of much confusion because its technical definition is different from its commonly-understood folk definition. Therefore, its use conveys the incorrect impression that behavioral traits are "inherited" or specifically passed down through the genes.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Behavioral geneticists also conduct heritability analyses based on the assumption that genes and environments contribute in a separate, additive manner to behavioral traits.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Heritability measures the fraction of phenotype variability that can be attributed to <a href="/wiki/Genetic_variation" title="Genetic variation">genetic variation</a>. This is not the same as saying that this fraction of an individual phenotype is caused by genetics. For example, it is incorrect to say that since the heritability of personality traits is about 0.6, that means that 60% of your personality is inherited from your parents and 40% comes from the environment. In addition, heritability can change without any genetic change occurring, such as when the environment starts contributing to more variation. As a case in point, consider that both <a href="/wiki/Gene" title="Gene">genes</a> and environment have the potential to influence intelligence. Heritability could increase if genetic variation increases, causing individuals to show more phenotypic variation, like showing different levels of intelligence. On the other hand, heritability might also increase if the environmental variation decreases, causing individuals to show less phenotypic variation, like showing more similar levels of intelligence. Heritability increases when genetics are contributing more variation or because non-genetic factors are contributing less variation; what matters is the relative contribution. Heritability is specific to a particular population in a particular environment. High heritability of a trait, consequently, does not necessarily mean that the trait is not very susceptible to environmental influences.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Heritability can also change as a result of changes in the environment, migration, <a href="/wiki/Inbreeding" title="Inbreeding">inbreeding</a>, or how heritability itself is measured in the population under study.<sup id="cite_ref-VisscherHillWray_9-0" class="reference"><a href="#cite_note-VisscherHillWray-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> The heritability of a trait should not be interpreted as a measure of the extent to which said trait is genetically determined in an individual.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>The extent of dependence of phenotype on environment can also be a function of the genes involved. Matters of heritability are complicated because genes may <a href="/wiki/Canalization_(genetics)" class="mw-redirect" title="Canalization (genetics)">canalize</a> a phenotype, making its expression almost inevitable in all occurring environments. Individuals with the same genotype can also exhibit different phenotypes through a mechanism called <a href="/wiki/Phenotypic_plasticity" title="Phenotypic plasticity">phenotypic plasticity</a>, which makes heritability difficult to measure in some cases. Recent insights in molecular biology have identified changes in <a href="/wiki/Transcription_(genetics)" class="mw-redirect" title="Transcription (genetics)">transcriptional</a> activity of individual genes associated with environmental changes. However, there are a large number of genes whose transcription is not affected by the environment.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>Estimates of heritability use <a href="/wiki/Statistical_analyses" class="mw-redirect" title="Statistical analyses">statistical analyses</a> to help to identify the causes of differences between individuals. Since heritability is concerned with variance, it is necessarily an account of the differences between individuals in a population. Heritability can be <a href="/wiki/Univariate" title="Univariate">univariate</a> – examining a single trait – or multivariate – examining the genetic and environmental associations between multiple traits at once. This allows a test of the genetic overlap between different phenotypes: for instance <a href="/wiki/Hair_color" class="mw-redirect" title="Hair color">hair color</a> and <a href="/wiki/Eye_color" title="Eye color">eye color</a>. Environment and genetics may also interact, and heritability analyses can test for and examine these interactions (GxE models). </p><p>A prerequisite for heritability analyses is that there is some population variation to account for. This last point highlights the fact that heritability cannot take into account the effect of factors which are invariant in the population. Factors may be invariant if they are absent and do not exist in the population, such as no one having access to a particular <a href="/wiki/Antibiotic" title="Antibiotic">antibiotic</a>, or because they are omnipresent, like if everyone is drinking <a href="/wiki/Coffee" title="Coffee">coffee</a>. In practice, all human behavioral traits vary and almost all traits show some heritability.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=2" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Any particular phenotype can be <a href="/wiki/Statistical_model" title="Statistical model">modeled</a> as the sum of genetic and environmental effects:<sup id="cite_ref-Kempthorne_1957_14-0" class="reference"><a href="#cite_note-Kempthorne_1957-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <dl><dd>Phenotype (<i>P</i>) = Genotype (<i>G</i>) + Environment (<i>E</i>).</dd></dl> <p>Likewise the phenotypic variance in the trait – Var (P) – is the sum of effects as follows: </p> <dl><dd>Var(<i>P</i>) = Var(<i>G</i>) + Var(<i>E</i>) + 2 Cov(<i>G</i>,<i>E</i>).</dd></dl> <p>In a planned experiment Cov(<i>G</i>,<i>E</i>) can be controlled and held at 0. In this case, heritability, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H^{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd48070c64ac225a925024eb9cf2b16135c81d05" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.805ex; height:3.009ex;" alt="{\displaystyle H^{2},}"></span> is defined as<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H^{2}={\frac {\mathrm {Var} (G)}{\mathrm {Var} (P)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>P</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H^{2}={\frac {\mathrm {Var} (G)}{\mathrm {Var} (P)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8cde8b845913645a027bec0bde9111f2ba586815" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:14.545ex; height:6.509ex;" alt="{\displaystyle H^{2}={\frac {\mathrm {Var} (G)}{\mathrm {Var} (P)}}}"></span></dd></dl> <p><i>H</i><sup>2</sup> is the broad-sense heritability. This reflects all the genetic contributions to a population's phenotypic variance including additive, <a href="/wiki/Dominance_relationship" class="mw-redirect" title="Dominance relationship">dominant</a>, and <a href="/wiki/Epistasis" title="Epistasis">epistatic</a> (multi-genic interactions), as well as <a href="/wiki/Maternal_effect" title="Maternal effect">maternal and paternal effects</a>, where individuals are directly affected by their parents' phenotype, such as with <a href="/wiki/Milk" title="Milk">milk</a> production in mammals. </p><p>A particularly important component of the genetic variance is the additive variance, Var(A), which is the variance due to the average effects (additive effects) of the <a href="/wiki/Allele" title="Allele">alleles</a>. Since each parent passes a single allele per <a href="/wiki/Locus_(genetics)" title="Locus (genetics)">locus</a> to each offspring, parent-offspring resemblance depends upon the average effect of single alleles. Additive variance represents, therefore, the genetic component of variance responsible for parent-offspring resemblance. The additive genetic portion of the phenotypic variance is known as Narrow-sense heritability and is defined as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h^{2}={\frac {\mathrm {Var} (A)}{\mathrm {Var} (P)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>P</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h^{2}={\frac {\mathrm {Var} (A)}{\mathrm {Var} (P)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84ffb39d6dbf22c323638cbdbf2c7007719a27d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:13.7ex; height:6.509ex;" alt="{\displaystyle h^{2}={\frac {\mathrm {Var} (A)}{\mathrm {Var} (P)}}}"></span></dd></dl> <p>An upper case <i>H</i><sup>2</sup> is used to denote broad sense, and lower case <i>h</i><sup>2</sup> for narrow sense. </p><p>For traits which are not continuous but dichotomous such as an additional toe or certain diseases, the contribution of the various alleles can be considered to be a sum, which past a threshold, manifests itself as the trait, giving the <a href="/wiki/Threshold_model#Liability_threshold_model" title="Threshold model">liability threshold model</a> in which heritability can be estimated and selection modeled. </p><p>Additive variance is important for <a href="/wiki/Natural_selection" title="Natural selection">selection</a>. If a selective pressure such as improving livestock is exerted, the response of the trait is directly related to narrow-sense heritability. The mean of the trait will increase in the next generation as a function of how much the mean of the selected parents differs from the mean of the population from which the selected parents were chosen. The observed <i>response to selection</i> leads to an estimate of the narrow-sense heritability (called <b>realized heritability</b>). This is the principle underlying <a href="/wiki/Artificial_selection" class="mw-redirect" title="Artificial selection">artificial selection</a> or breeding. </p> <div class="mw-heading mw-heading3"><h3 id="Example">Example</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=3" title="Edit section: Example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Additive_and_Dominance_Effects.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Additive_and_Dominance_Effects.png/250px-Additive_and_Dominance_Effects.png" decoding="async" width="250" height="254" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Additive_and_Dominance_Effects.png/375px-Additive_and_Dominance_Effects.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/Additive_and_Dominance_Effects.png/500px-Additive_and_Dominance_Effects.png 2x" data-file-width="1255" data-file-height="1273" /></a><figcaption>Figure 1. Relationship of phenotypic values to additive and dominance effects using a completely dominant locus.</figcaption></figure> <p>The simplest genetic model involves a single locus with two alleles (b and B) affecting one quantitative phenotype. </p><p>The number of <b>B</b> alleles can be 0, 1, or 2. For any genotype, (<i>B</i><sub>i</sub>,<i>B</i><sub>j</sub>), where <i>B</i><sub>i</sub> and <i>B</i><sub>j</sub> are either 0 or 1, the expected phenotype can then be written as the sum of the overall mean, a linear effect, and a dominance deviation (one can think of the dominance term as an <i>interaction</i> between <i>B</i><sub>i</sub> and <i>B</i><sub>j</sub>): </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}P_{ij}&=\mu +\alpha \,(B_{i}+B_{j})+\delta \,(B_{i}B_{j})\\&={\text{Population mean}}+{\text{Additive Effect }}(a_{ij}=\alpha (B_{i}+B_{j}))+{\text{Dominance Deviation }}(d_{ij}=\delta (B_{i}B_{j})).\\\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>μ</mi> <mo>+</mo> <mi>α</mi> <mspace width="thinmathspace" /> <mo stretchy="false">(</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <mi>δ</mi> <mspace width="thinmathspace" /> <mo stretchy="false">(</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Population mean</mtext> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Additive Effect </mtext> </mrow> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mi>α</mi> <mo stretchy="false">(</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>Dominance Deviation </mtext> </mrow> <mo stretchy="false">(</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mi>δ</mi> <mo stretchy="false">(</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}P_{ij}&=\mu +\alpha \,(B_{i}+B_{j})+\delta \,(B_{i}B_{j})\\&={\text{Population mean}}+{\text{Additive Effect }}(a_{ij}=\alpha (B_{i}+B_{j}))+{\text{Dominance Deviation }}(d_{ij}=\delta (B_{i}B_{j})).\\\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02f61d0b96fab1a9611e760c65bf71eeae3ed006" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.311ex; margin-bottom: -0.194ex; width:103.245ex; height:6.176ex;" alt="{\displaystyle {\begin{aligned}P_{ij}&=\mu +\alpha \,(B_{i}+B_{j})+\delta \,(B_{i}B_{j})\\&={\text{Population mean}}+{\text{Additive Effect }}(a_{ij}=\alpha (B_{i}+B_{j}))+{\text{Dominance Deviation }}(d_{ij}=\delta (B_{i}B_{j})).\\\end{aligned}}}"></span> </p><p>The additive genetic variance at this locus is the <a href="/wiki/Weighted_mean" class="mw-redirect" title="Weighted mean">weighted average</a> of the squares of the additive effects: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Var} (A)=f(bb)a_{bb}^{2}+f(Bb)a_{Bb}^{2}+f(BB)a_{BB}^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>b</mi> <mi>b</mi> <mo stretchy="false">)</mo> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> <mi>b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>B</mi> <mi>b</mi> <mo stretchy="false">)</mo> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>B</mi> <mi>B</mi> <mo stretchy="false">)</mo> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Var} (A)=f(bb)a_{bb}^{2}+f(Bb)a_{Bb}^{2}+f(BB)a_{BB}^{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5471b22fa13529923542a6ba5991dd9586c3c5d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:44.588ex; height:3.176ex;" alt="{\displaystyle \mathrm {Var} (A)=f(bb)a_{bb}^{2}+f(Bb)a_{Bb}^{2}+f(BB)a_{BB}^{2},}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(bb)a_{bb}+f(Bb)a_{Bb}+f(BB)a_{BB}=0.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>b</mi> <mi>b</mi> <mo stretchy="false">)</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> <mi>b</mi> </mrow> </msub> <mo>+</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>B</mi> <mi>b</mi> <mo stretchy="false">)</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>b</mi> </mrow> </msub> <mo>+</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>B</mi> <mi>B</mi> <mo stretchy="false">)</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>B</mi> </mrow> </msub> <mo>=</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(bb)a_{bb}+f(Bb)a_{Bb}+f(BB)a_{BB}=0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f64f6ec2c028e43330532959a62596b69e59f162" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.381ex; height:2.843ex;" alt="{\displaystyle f(bb)a_{bb}+f(Bb)a_{Bb}+f(BB)a_{BB}=0.}"></span> </p><p>There is a similar relationship for the variance of dominance deviations: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Var} (D)=f(bb)d_{bb}^{2}+f(Bb)d_{Bb}^{2}+f(BB)d_{BB}^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>D</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>b</mi> <mi>b</mi> <mo stretchy="false">)</mo> <msubsup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> <mi>b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>B</mi> <mi>b</mi> <mo stretchy="false">)</mo> <msubsup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>B</mi> <mi>B</mi> <mo stretchy="false">)</mo> <msubsup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>B</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Var} (D)=f(bb)d_{bb}^{2}+f(Bb)d_{Bb}^{2}+f(BB)d_{BB}^{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e76b35b6abf41b05f3f5c50c486bf912f91790c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:44.707ex; height:3.176ex;" alt="{\displaystyle \mathrm {Var} (D)=f(bb)d_{bb}^{2}+f(Bb)d_{Bb}^{2}+f(BB)d_{BB}^{2},}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(bb)d_{bb}+f(Bb)d_{Bb}+f(BB)d_{BB}=0.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>b</mi> <mi>b</mi> <mo stretchy="false">)</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> <mi>b</mi> </mrow> </msub> <mo>+</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>B</mi> <mi>b</mi> <mo stretchy="false">)</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>b</mi> </mrow> </msub> <mo>+</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>B</mi> <mi>B</mi> <mo stretchy="false">)</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>B</mi> </mrow> </msub> <mo>=</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(bb)d_{bb}+f(Bb)d_{Bb}+f(BB)d_{BB}=0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb29837ad1ab1236769d9facd1812c29f8eb0ddb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.319ex; height:2.843ex;" alt="{\displaystyle f(bb)d_{bb}+f(Bb)d_{Bb}+f(BB)d_{BB}=0.}"></span> </p><p>The <a href="/wiki/Linear_regression" title="Linear regression">linear regression</a> of phenotype on genotype is shown in Figure 1. </p> <div class="mw-heading mw-heading3"><h3 id="Assumptions">Assumptions</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=4" title="Edit section: Assumptions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Estimates of the total heritability of human traits assume the absence of epistasis, which has been called the "assumption of additivity". Although some researchers have cited such estimates in support of the existence of "<a href="/wiki/Missing_heritability" class="mw-redirect" title="Missing heritability">missing heritability</a>" unaccounted for by known genetic loci, the assumption of additivity may render these estimates invalid.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> There is also some empirical evidence that the additivity assumption is frequently violated in behavior genetic studies of adolescent intelligence and <a href="/wiki/Academic_achievement" title="Academic achievement">academic achievement</a>.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Estimating_heritability">Estimating heritability</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=5" title="Edit section: Estimating heritability"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Since only <i>P</i> can be observed or measured directly, heritability must be estimated from the similarities observed in subjects varying in their level of genetic or environmental similarity. The <a href="/wiki/Statistics" title="Statistics">statistical</a> analyses required to estimate the <a href="/wiki/Genetics" title="Genetics">genetic</a> and <a href="/wiki/Environment_(biophysical)" class="mw-redirect" title="Environment (biophysical)">environmental</a> components of variance depend on the sample characteristics. Briefly, better estimates are obtained using data from individuals with widely varying levels of genetic relationship - such as <a href="/wiki/Twins" class="mw-redirect" title="Twins">twins</a>, siblings, parents and offspring, rather than from more distantly related (and therefore less similar) subjects. The <a href="/wiki/Standard_error_(statistics)" class="mw-redirect" title="Standard error (statistics)">standard error</a> for heritability estimates is improved with large sample sizes. </p><p>In non-human populations it is often possible to collect information in a controlled way. For example, among farm animals it is easy to arrange for a bull to produce offspring from a large number of cows and to control environments. Such <a href="/wiki/Experimental_control" class="mw-redirect" title="Experimental control">experimental control</a> is generally not possible when gathering human data, relying on naturally occurring relationships and environments. </p><p>In classical quantitative genetics, there were two schools of thought regarding estimation of heritability. </p><p>One <a href="/wiki/School_(discipline)" class="mw-redirect" title="School (discipline)">school of thought</a> was developed by <a href="/wiki/Sewall_Wright" title="Sewall Wright">Sewall Wright</a> at <a href="/wiki/University_of_Chicago" title="University of Chicago">The University of Chicago</a>, and further popularized by <a href="/wiki/C._C._Li" title="C. C. Li">C. C. Li</a> (<a href="/wiki/University_of_Chicago" title="University of Chicago">University of Chicago</a>) and <a href="/wiki/Jay_Laurence_Lush" title="Jay Laurence Lush">J. L. Lush</a> (<a href="/wiki/Iowa_State_University" title="Iowa State University">Iowa State University</a>). It is based on the analysis of correlations and, by extension, regression. <a href="/wiki/Path_analysis_(statistics)" title="Path analysis (statistics)">Path Analysis</a> was developed by <a href="/wiki/Sewall_Wright" title="Sewall Wright">Sewall Wright</a> as a way of estimating heritability. </p><p>The second was originally developed by <a href="/wiki/Ronald_Fisher" title="Ronald Fisher">R. A. Fisher</a> and expanded at <a href="/wiki/University_of_Edinburgh" title="University of Edinburgh">The University of Edinburgh</a>, <a href="/wiki/Iowa_State_University" title="Iowa State University">Iowa State University</a>, and <a href="/wiki/North_Carolina_State_University" title="North Carolina State University">North Carolina State University</a>, as well as other schools. It is based on the <a href="/wiki/Analysis_of_variance" title="Analysis of variance">analysis of variance</a> of breeding studies, using the intraclass correlation of relatives. Various methods of estimating components of variance (and, hence, heritability) from <a href="/wiki/Analysis_of_variance" title="Analysis of variance">ANOVA</a> are used in these analyses. </p><p>Today, heritability can be estimated from general pedigrees using <a href="/wiki/Best_linear_unbiased_prediction" title="Best linear unbiased prediction">linear mixed models</a> and from <a href="/wiki/Genome-wide_complex_trait_analysis" title="Genome-wide complex trait analysis">genomic relatedness</a> estimated from genetic markers. </p><p>Studies of human heritability often utilize adoption study designs, often with <a href="/wiki/Twin" title="Twin">identical twins</a> who have been separated early in life and raised in different environments. Such individuals have identical genotypes and can be used to separate the effects of genotype and environment. A limit of this design is the common prenatal environment and the relatively low numbers of twins reared apart. A second and more common design is the <a href="/wiki/Twin_study" title="Twin study">twin study</a> in which the similarity of identical and fraternal twins is used to estimate heritability. These studies can be limited by the fact that identical twins are <a href="/wiki/Twin#Genetic_and_epigenetic_similarity" title="Twin">not completely genetically identical</a>, potentially resulting in an underestimation of heritability. </p><p>In <a href="/wiki/Observational_study" title="Observational study">observational studies</a>, or because of evocative effects (where a genome evokes environments by its effect on them), G and E may covary: <a href="/wiki/Gene_environment_correlation" class="mw-redirect" title="Gene environment correlation">gene environment correlation</a>. Depending on the methods used to estimate heritability, correlations between genetic factors and shared or non-shared environments may or may not be confounded with heritability.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Regression/correlation_methods_of_estimation"><span id="Regression.2Fcorrelation_methods_of_estimation"></span>Regression/correlation methods of estimation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=6" title="Edit section: Regression/correlation methods of estimation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The first school of estimation uses regression and correlation to estimate heritability. </p> <div class="mw-heading mw-heading4"><h4 id="Comparison_of_close_relatives">Comparison of close relatives</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=7" title="Edit section: Comparison of close relatives"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the comparison of relatives, we find that in general, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h^{2}={\frac {b}{r}}={\frac {t}{r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>b</mi> <mi>r</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>t</mi> <mi>r</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h^{2}={\frac {b}{r}}={\frac {t}{r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb26a946c71392904bac032a718dbbdd3cb7cdb5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.36ex; height:5.343ex;" alt="{\displaystyle h^{2}={\frac {b}{r}}={\frac {t}{r}}}"></span></dd></dl> <p>where <i>r</i> can be thought of as the <a href="/wiki/Coefficient_of_relationship" title="Coefficient of relationship">coefficient of relatedness</a>, <i>b</i> is the coefficient of regression and <i>t</i> is the coefficient of correlation. </p> <div class="mw-heading mw-heading5"><h5 id="Parent-offspring_regression">Parent-offspring regression</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=8" title="Edit section: Parent-offspring regression"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Galton_experiment.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Galton_experiment.png/200px-Galton_experiment.png" decoding="async" width="200" height="132" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Galton_experiment.png/300px-Galton_experiment.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/49/Galton_experiment.png/400px-Galton_experiment.png 2x" data-file-width="2030" data-file-height="1336" /></a><figcaption>Figure 2. <a href="/wiki/Francis_Galton" title="Francis Galton">Francis Galton</a>'s (1889) data showing the relationship between offspring height (928 individuals) as a function of mean parent height (205 sets of parents).</figcaption></figure> <p>Heritability may be estimated by comparing parent and offspring traits (as in Fig. 2). The slope of the line (0.57) approximates the heritability of the trait when offspring values are regressed against the average trait in the parents. If only one parent's value is used then heritability is twice the slope. (This is the source of the term "<a href="/wiki/Regression_analysis" title="Regression analysis">regression</a>," since the offspring values always tend to <a href="/wiki/Regression_toward_the_mean" title="Regression toward the mean">regress to the mean</a> value for the population, <i>i.e.</i>, the slope is always less than one). This regression effect also underlies the <a href="/wiki/DeFries%E2%80%93Fulker_regression" title="DeFries–Fulker regression">DeFries–Fulker method</a> for analyzing twins selected for one member being affected.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading5"><h5 id="Sibling_comparison">Sibling comparison</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=9" title="Edit section: Sibling comparison"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A basic approach to heritability can be taken using full-Sib designs: comparing similarity between siblings who share both a biological mother and a father.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> When there is only additive gene action, this sibling phenotypic correlation is an index of <i>familiarity</i> – the sum of half the additive genetic variance plus full effect of the common environment. It thus places an upper limit on additive heritability of twice the full-Sib phenotypic correlation. Half-Sib designs compare phenotypic traits of siblings that share one parent with other sibling groups. </p> <div class="mw-heading mw-heading5"><h5 id="Twin_studies">Twin studies</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=10" title="Edit section: Twin studies"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Twin_study" title="Twin study">Twin study</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Twin-concordances.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Twin-concordances.jpg/300px-Twin-concordances.jpg" decoding="async" width="300" height="230" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/c/cf/Twin-concordances.jpg 1.5x" data-file-width="404" data-file-height="310" /></a><figcaption>Figure 3. Twin concordances for seven psychological traits (sample size shown inside bars), with DZ being fraternal and MZ being identical twins.</figcaption></figure> <p>Heritability for traits in humans is most frequently estimated by comparing resemblances between twins. "The advantage of twin studies, is that the total variance can be split up into genetic, shared or common environmental, and unique environmental components, enabling an accurate estimation of heritability".<sup id="cite_ref-pmid18157630_21-0" class="reference"><a href="#cite_note-pmid18157630-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> Fraternal or dizygotic (DZ) twins on average share half their genes (assuming there is no <a href="/wiki/Assortative_mating" title="Assortative mating">assortative mating</a> for the trait), and so identical or monozygotic (MZ) twins on average are twice as genetically similar as DZ twins. A crude estimate of heritability, then, is approximately twice the difference in <a href="/wiki/Correlation" title="Correlation">correlation</a> between MZ and DZ twins, i.e. <a href="/wiki/Falconer%27s_formula" title="Falconer's formula">Falconer's formula</a> <i>H</i><sup>2</sup>=2(r(MZ)-r(DZ)). </p><p>The effect of shared environment, <i>c</i><sup>2</sup>, contributes to similarity between siblings due to the commonality of the environment they are raised in. Shared environment is approximated by the DZ correlation minus half heritability, which is the degree to which DZ twins share the same genes, <i>c</i><sup>2</sup>=DZ-1/2<i>h</i><sup>2</sup>. Unique environmental variance, <i>e</i><sup>2</sup>, reflects the degree to which identical twins raised together are dissimilar, <i>e</i><sup>2</sup>=1-r(MZ). </p> <div class="mw-heading mw-heading3"><h3 id="Analysis_of_variance_methods_of_estimation">Analysis of variance methods of estimation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=11" title="Edit section: Analysis of variance methods of estimation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The second set of methods of estimation of heritability involves ANOVA and estimation of variance components. </p> <div class="mw-heading mw-heading4"><h4 id="Basic_model">Basic model</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=12" title="Edit section: Basic model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>We use the basic discussion of Kempthorne.<sup id="cite_ref-Kempthorne_1957_14-1" class="reference"><a href="#cite_note-Kempthorne_1957-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Considering only the most basic of genetic models, we can look at the quantitative contribution of a single locus with genotype <b>G<sub>i</sub></b> as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y_{i}=\mu +g_{i}+e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mi>μ</mi> <mo>+</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y_{i}=\mu +g_{i}+e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d15d580aa1ec667772a332f7a0fecb8085ba097a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.112ex; height:2.509ex;" alt="{\displaystyle y_{i}=\mu +g_{i}+e}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ce36142a0a1c6660e82bdf3ef3f1551317efe0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.909ex; height:2.009ex;" alt="{\displaystyle g_{i}}"></span> is the effect of genotype <b>G<sub>i</sub></b> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd253103f0876afc68ebead27a5aa9867d927467" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle e}"></span> is the environmental effect. </p><p>Consider an experiment with a group of sires and their progeny from random dams. Since the progeny get half of their genes from the father and half from their (random) mother, the progeny equation is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z_{i}=\mu +{\frac {1}{2}}g_{i}+e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mi>μ</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z_{i}=\mu +{\frac {1}{2}}g_{i}+e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ee37544e32d99d16432abc7e9557a1f39d15d17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.053ex; height:5.176ex;" alt="{\displaystyle z_{i}=\mu +{\frac {1}{2}}g_{i}+e}"></span></dd></dl> <div class="mw-heading mw-heading5"><h5 id="Intraclass_correlations">Intraclass correlations</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=13" title="Edit section: Intraclass correlations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Consider the experiment above. We have two groups of progeny we can compare. The first is comparing the various progeny for an individual sire (called <i>within sire group</i>). The variance will include terms for genetic variance (since they did not all get the same genotype) and environmental variance. This is thought of as an <i>error</i> term. </p><p>The second group of progeny are comparisons of means of half sibs with each other (called <i>among sire group</i>). In addition to the <a href="/wiki/Errors_and_residuals_in_statistics" class="mw-redirect" title="Errors and residuals in statistics">error term</a> as in the within sire groups, we have an addition term due to the differences among different means of half sibs. The intraclass correlation is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {corr} (z,z')=\mathrm {corr} (\mu +{\frac {1}{2}}g+e,\mu +{\frac {1}{2}}g+e')={\frac {1}{4}}V_{g}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>z</mi> <mo>,</mo> <msup> <mi>z</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>μ</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>g</mi> <mo>+</mo> <mi>e</mi> <mo>,</mo> <mi>μ</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>g</mi> <mo>+</mo> <msup> <mi>e</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {corr} (z,z')=\mathrm {corr} (\mu +{\frac {1}{2}}g+e,\mu +{\frac {1}{2}}g+e')={\frac {1}{4}}V_{g}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d732930e1e6727ea47845f960efc0db853c175b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:50.404ex; height:5.176ex;" alt="{\displaystyle \mathrm {corr} (z,z')=\mathrm {corr} (\mu +{\frac {1}{2}}g+e,\mu +{\frac {1}{2}}g+e')={\frac {1}{4}}V_{g}}"></span> ,</dd></dl> <p>since environmental effects are independent of each other. </p> <div class="mw-heading mw-heading5"><h5 id="The_ANOVA">The ANOVA</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=14" title="Edit section: The ANOVA"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In an experiment with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> sires and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> progeny per sire, we can calculate the following ANOVA, using <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{g}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{g}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77a0524780b4abb2046b3107a25b05089a443b55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.377ex; height:2.843ex;" alt="{\displaystyle V_{g}}"></span> as the genetic variance and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{e}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{e}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b2a644ac0daba577205f3ca031bffafc702da5c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.354ex; height:2.509ex;" alt="{\displaystyle V_{e}}"></span> as the environmental variance: </p> <table class="wikitable"> <caption>Table 1: ANOVA for Sire experiment </caption> <tbody><tr> <th>Source </th> <th>d.f. </th> <th>Mean Square </th> <th>Expected Mean Square </th></tr> <tr> <td>Between sire groups </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbd0b0f32b28f51962943ee9ede4fb34198a2521" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle n-1}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {3}{4}}V_{g}+V_{e}+r({{\frac {1}{4}}V_{g}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> <mo>+</mo> <mi>r</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {3}{4}}V_{g}+V_{e}+r({{\frac {1}{4}}V_{g}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b8e95ef5f591de5f4bae715fee40ad042e92eea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.643ex; height:5.176ex;" alt="{\displaystyle {\frac {3}{4}}V_{g}+V_{e}+r({{\frac {1}{4}}V_{g}})}"></span> </td></tr> <tr> <td>Within sire groups </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(r-1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(r-1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cef0cd200e3fb8a27afabd62974da81282d47481" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.256ex; height:2.843ex;" alt="{\displaystyle n(r-1)}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle W}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54a9c4c547f4d6111f81946cad242b18298d70b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.435ex; height:2.176ex;" alt="{\displaystyle W}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {3}{4}}V_{g}+V_{e}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {3}{4}}V_{g}+V_{e}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d402bc40cdac5a7771cc76dac6342b9605288eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.569ex; height:5.176ex;" alt="{\displaystyle {\frac {3}{4}}V_{g}+V_{e}}"></span> </td></tr></tbody></table> <p>The <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{4}}V_{g}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{4}}V_{g}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15ecce236978d62df2d6e220329914b60c99cb58" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:4.375ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{4}}V_{g}}"></span> term is the <a href="/wiki/Intraclass_correlation" title="Intraclass correlation">intraclass correlation</a> between half sibs. We can easily calculate <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H^{2}={\frac {V_{g}}{V_{g}+V_{e}}}={\frac {4(S-W)}{S+(r-1)W}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> <mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>g</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mo stretchy="false">(</mo> <mi>S</mi> <mo>−</mo> <mi>W</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>S</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mi>r</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mi>W</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H^{2}={\frac {V_{g}}{V_{g}+V_{e}}}={\frac {4(S-W)}{S+(r-1)W}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bfc79c65a2baa7ca292afe9cbc065cd34b8bcb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:32.233ex; height:6.509ex;" alt="{\displaystyle H^{2}={\frac {V_{g}}{V_{g}+V_{e}}}={\frac {4(S-W)}{S+(r-1)W}}}"></span>. The expected mean square is calculated from the relationship of the individuals (progeny within a sire are all half-sibs, for example), and an understanding of intraclass correlations. </p><p>The use of ANOVA to calculate heritability often fails to account for the presence of <a href="/wiki/Gene%E2%80%93environment_interaction" title="Gene–environment interaction">gene–-environment interactions</a>, because ANOVA has a much lower <a href="/wiki/Statistical_power" class="mw-redirect" title="Statistical power">statistical power</a> for testing for interaction effects than for direct effects.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Model_with_additive_and_dominance_terms">Model with additive and dominance terms</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=15" title="Edit section: Model with additive and dominance terms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For a model with additive and dominance terms, but not others, the equation for a single locus is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y_{ij}=\mu +\alpha _{i}+\alpha _{j}+d_{ij}+e,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mi>μ</mi> <mo>+</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>+</mo> <mi>e</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y_{ij}=\mu +\alpha _{i}+\alpha _{j}+d_{ij}+e,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11da5f9daa94b91de7de39f2adbb30f7580f6ba2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:27.579ex; height:2.843ex;" alt="{\displaystyle y_{ij}=\mu +\alpha _{i}+\alpha _{j}+d_{ij}+e,}"></span></dd></dl> <p>where </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b1fb627423abe4988b7ed88d4920bf1ec074790" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.287ex; height:2.009ex;" alt="{\displaystyle \alpha _{i}}"></span> is the additive effect of the i<sup>th</sup> allele, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha _{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha _{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/293a364991ab1ee55c25b0f60fd9e52af7b7dbde" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.397ex; height:2.343ex;" alt="{\displaystyle \alpha _{j}}"></span> is the additive effect of the j<sup>th</sup> allele, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d_{ij}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d_{ij}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8b0116346390c7dcd72d9ed714177a9b6c81e57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.686ex; height:2.843ex;" alt="{\displaystyle d_{ij}}"></span> is the dominance deviation for the ij<sup>th</sup> genotype, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd253103f0876afc68ebead27a5aa9867d927467" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle e}"></span> is the environment. </p><p>Experiments can be run with a similar setup to the one given in Table 1. Using different relationship groups, we can evaluate different intraclass correlations. Using <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26205fe6c67ed47c72959a921fe7fd9c1c250ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.457ex; height:2.509ex;" alt="{\displaystyle V_{a}}"></span> as the additive genetic variance and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V_{d}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{d}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f251c8864c15077e36834891fed39440bb3daf3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.447ex; height:2.509ex;" alt="{\displaystyle V_{d}}"></span> as the dominance deviation variance, intraclass correlations become <a href="/wiki/Linear_function" title="Linear function">linear functions</a> of these parameters. In general, </p> <dl><dd>Intraclass correlation<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle =rV_{a}+\theta V_{d},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mi>r</mi> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>+</mo> <mi>θ</mi> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =rV_{a}+\theta V_{d},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70ff881a3c409f46926967552fb1299b9f979888" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.984ex; height:2.509ex;" alt="{\displaystyle =rV_{a}+\theta V_{d},}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> are found as </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/393a2f33573f9dc329c1efb8987d3e49242a3e26" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.502ex; height:1.676ex;" alt="{\displaystyle r=}"></span>P[ <a href="/wiki/Alleles" class="mw-redirect" title="Alleles">alleles</a> drawn at random from the relationship pair are <a href="/wiki/Identity_by_descent" title="Identity by descent">identical by descent</a>], and </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta =}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta =}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9cdf817a63d001b9c002aacbbc5fecb60bc86527" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.544ex; height:2.176ex;" alt="{\displaystyle \theta =}"></span>P[ <a href="/wiki/Genotypes" class="mw-redirect" title="Genotypes">genotypes</a> drawn at random from the relationship pair are <a href="/wiki/Identity_by_descent" title="Identity by descent">identical by descent</a>]. </p><p>Some common relationships and their coefficients are given in Table 2. </p> <table class="wikitable"> <caption>Table 2: Coefficients for calculating variance components </caption> <tbody><tr> <th>Relationship </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> </th></tr> <tr> <td>Identical Twins </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span> </td></tr> <tr> <td>Parent-Offspring </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a11cfb2fdb143693b1daf78fcb5c11a023cb1c55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{2}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 0}"></span> </td></tr> <tr> <td>Half Siblings </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2dfb63ee75ec084f2abb25d248bc151a2687508" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{4}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 0}"></span> </td></tr> <tr> <td>Full Siblings </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a11cfb2fdb143693b1daf78fcb5c11a023cb1c55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{2}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2dfb63ee75ec084f2abb25d248bc151a2687508" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{4}}}"></span> </td></tr> <tr> <td>First Cousins </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{8}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>8</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{8}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3f20dc5ae5815ab8628a1294c40639574e0c88e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{8}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 0}"></span> </td></tr> <tr> <td>Double First Cousins </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2dfb63ee75ec084f2abb25d248bc151a2687508" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:1.999ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{4}}}"></span> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{16}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>16</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{16}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a1e485c900bbf76f88efd89fcaea882dbfa17ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.161ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{16}}}"></span> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Linear_mixed_models">Linear mixed models</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=16" title="Edit section: Linear mixed models"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A wide variety of approaches using linear mixed models have been reported in literature. Via these methods, phenotypic variance is partitioned into genetic, environmental and experimental design variances to estimate heritability. Environmental variance can be explicitly modeled by studying individuals across a broad range of environments, although inference of genetic variance from phenotypic and environmental variance may lead to underestimation of heritability due to the challenge of capturing the full range of environmental influence affecting a trait. Other methods for calculating heritability use data from <a href="/wiki/Genome-wide_association_studies" class="mw-redirect" title="Genome-wide association studies">genome-wide association studies</a> to estimate the influence on a trait by genetic factors, which is reflected by the rate and influence of putatively associated genetic loci (usually <a href="/wiki/Single-nucleotide_polymorphisms" class="mw-redirect" title="Single-nucleotide polymorphisms">single-nucleotide polymorphisms</a>) on the trait. This can lead to underestimation of heritability, however. This discrepancy is referred to as "missing heritability" and reflects the challenge of accurately modeling both genetic and environmental variance in heritability models.<sup id="cite_ref-pmid27382152_23-0" class="reference"><a href="#cite_note-pmid27382152-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>When a large, complex pedigree or another aforementioned type of data is available, heritability and other quantitative genetic parameters can be estimated by <a href="/wiki/Restricted_maximum_likelihood" title="Restricted maximum likelihood">restricted maximum likelihood</a> (REML) or <a href="/wiki/Bayesian_statistics" title="Bayesian statistics">Bayesian methods</a>. The <a href="/wiki/Raw_data" title="Raw data">raw data</a> will usually have three or more data points for each individual: a code for the sire, a code for the dam and one or several trait values. Different trait values may be for different traits or for different time points of measurement. </p><p>The currently popular methodology relies on high degrees of certainty over the identities of the sire and dam; it is not common to treat the sire identity probabilistically. This is not usually a problem, since the methodology is rarely applied to wild populations (although it has been used for several wild ungulate and bird populations), and sires are invariably known with a very high degree of certainty in breeding programmes. There are also algorithms that account for uncertain paternity. </p><p>The pedigrees can be viewed using programs such as Pedigree Viewer <a rel="nofollow" class="external autonumber" href="http://www-personal.une.edu.au/~bkinghor/pedigree.htm">[1]</a>, and analyzed with programs such as <a href="/wiki/ASReml" title="ASReml">ASReml</a>, VCE <a rel="nofollow" class="external autonumber" href="https://web.archive.org/web/20070312053650/http://vce.tzv.fal.de/index.pl">[2]</a>, WOMBAT <a rel="nofollow" class="external autonumber" href="https://web.archive.org/web/20061128123632/http://agbu.une.edu.au/~kmeyer/wombat.html">[3]</a>, MCMCglmm within the R environment <a rel="nofollow" class="external autonumber" href="https://www.rdocumentation.org/packages/MCMCglmm/versions/2.29/topics/MCMCglmm-package">[4]</a> or the <a href="/wiki/BLUPF90" title="BLUPF90">BLUPF90</a> family of programs <a rel="nofollow" class="external autonumber" href="http://nce.ads.uga.edu/~ignacy/programs.html">[5]</a>. </p><p>Pedigree models are helpful for untangling confounds such as <a href="/wiki/Reverse_causality" class="mw-redirect" title="Reverse causality">reverse causality</a>, <a href="/wiki/Maternal_effects" class="mw-redirect" title="Maternal effects">maternal effects</a> such as the <a href="/w/index.php?title=Prenatal_environment&action=edit&redlink=1" class="new" title="Prenatal environment (page does not exist)">prenatal environment</a>, and confounding of <a href="/wiki/Genetic_dominance" class="mw-redirect" title="Genetic dominance">genetic dominance</a>, shared environment, and maternal gene effects.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-VisscherHillWray_9-1" class="reference"><a href="#cite_note-VisscherHillWray-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Genomic_heritability">Genomic heritability</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=17" title="Edit section: Genomic heritability"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When genome-wide genotype data and phenotypes from large population samples are available, one can estimate the relationships between individuals based on their genotypes and use a linear mixed model to estimate the variance explained by the genetic markers. This gives a genomic heritability estimate based on the variance captured by common genetic variants.<sup id="cite_ref-:0_4-1" class="reference"><a href="#cite_note-:0-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> There are multiple methods that make different adjustments for allele frequency and <a href="/wiki/Linkage_disequilibrium" title="Linkage disequilibrium">linkage disequilibrium</a>. Particularly, the method called High-Definition Likelihood (HDL) can estimate genomic heritability using only GWAS summary statistics,<sup id="cite_ref-:1_5-1" class="reference"><a href="#cite_note-:1-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> making it easier to incorporate large sample size available in various GWAS meta-analysis. </p> <div class="mw-heading mw-heading2"><h2 id="Response_to_selection">Response to selection</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=18" title="Edit section: Response to selection"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Response_to_selection.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Response_to_selection.jpg/200px-Response_to_selection.jpg" decoding="async" width="200" height="169" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Response_to_selection.jpg/300px-Response_to_selection.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Response_to_selection.jpg/400px-Response_to_selection.jpg 2x" data-file-width="498" data-file-height="422" /></a><figcaption>Figure 4. Strength of selection (S) and response to selection (R) in an artificial selection experiment, <i>h</i><sup>2</sup>=R/S.</figcaption></figure> <p>In <a href="/wiki/Selective_breeding" title="Selective breeding">selective breeding</a> of plants and animals, the expected response to selection of a trait with known narrow-sense heritability <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (h^{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (h^{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec12ce13c16e2e8410387a43734858a9fb015596" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.203ex; height:3.176ex;" alt="{\displaystyle (h^{2})}"></span> can be estimated using the <i>breeder's equation</i>:<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R=h^{2}S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R=h^{2}S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/67253d83c1aaa90139742b2f4fa610c5880ed744" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.755ex; height:2.676ex;" alt="{\displaystyle R=h^{2}S}"></span></dd></dl> <p>In this equation, the Response to Selection (R) is defined as the realized average difference between the parent generation and the next generation, and the Selection Differential (S) is defined as the average difference between the parent generation and the selected parents.<sup id="cite_ref-Kempthorne_1957_14-2" class="reference"><a href="#cite_note-Kempthorne_1957-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 1957">: 1957 </span></sup><sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p><p>For example, imagine that a plant breeder is involved in a selective breeding project with the aim of increasing the number of kernels per ear of corn. For the sake of argument, let us assume that the average ear of corn in the parent generation has 100 kernels. Let us also assume that the selected parents produce corn with an average of 120 kernels per ear. If h<sup>2</sup> equals 0.5, then the next generation will produce corn with an average of 0.5(120-100) = 10 additional kernels per ear. Therefore, the total number of kernels per ear of corn will equal, on average, 110. </p><p>Observing the response to selection in an artificial selection experiment will allow calculation of realized heritability as in Fig. 4. </p><p>Heritability in the above equation is equal to the ratio <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Var} (A)/\mathrm {Var} (P)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">V</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> </mrow> <mo stretchy="false">(</mo> <mi>P</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Var} (A)/\mathrm {Var} (P)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40227e530bcf678d528947a7260ec4bb51f71758" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.904ex; height:2.843ex;" alt="{\displaystyle \mathrm {Var} (A)/\mathrm {Var} (P)}"></span> only if the genotype and the environmental noise follow <a href="/wiki/Gaussian_distributions" class="mw-redirect" title="Gaussian distributions">Gaussian distributions</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Controversies">Controversies</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=19" title="Edit section: Controversies"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Unbalanced_section plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span class="skin-invert-image" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Unbalanced_scales.svg/45px-Unbalanced_scales.svg.png" decoding="async" width="45" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Unbalanced_scales.svg/68px-Unbalanced_scales.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Unbalanced_scales.svg/90px-Unbalanced_scales.svg.png 2x" data-file-width="400" data-file-height="354" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>may be <a href="/wiki/Wikipedia:DUE" class="mw-redirect" title="Wikipedia:DUE">unbalanced</a> towards certain viewpoints</b>.<span class="hide-when-compact"> Please <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Heritability&action=edit">improve the article</a> or discuss the issue on the <a href="/wiki/Talk:Heritability" title="Talk:Heritability">talk page</a>.</span> <span class="date-container"><i>(<span class="date">August 2016</span>)</i></span></div></td></tr></tbody></table> <p>Heritability estimates' prominent critics, such as <a href="/wiki/Steven_Rose" title="Steven Rose">Steven Rose</a>,<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Jay_Joseph" title="Jay Joseph">Jay Joseph</a>,<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Richard_Bentall" title="Richard Bentall">Richard Bentall</a>, focus largely on heritability estimates in <a href="/wiki/Behavioral_sciences" class="mw-redirect" title="Behavioral sciences">behavioral sciences</a> and <a href="/wiki/Social_sciences" class="mw-redirect" title="Social sciences">social sciences</a>. Bentall has claimed that such heritability scores are typically calculated counterintuitively to derive numerically high scores, that heritability is misinterpreted as <a href="/wiki/Genetic_determinism" class="mw-redirect" title="Genetic determinism">genetic determination</a>, and that this alleged bias distracts from other factors that researches have found more causally important, such as childhood abuse causing later psychosis.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> Heritability estimates are also inherently limited because they do not convey any information regarding whether genes or environment play a larger role in the development of the trait under study. For this reason, <a href="/wiki/David_S._Moore_(psychologist)" class="mw-redirect" title="David S. Moore (psychologist)">David Moore</a> and <a href="/wiki/David_Shenk" title="David Shenk">David Shenk</a> describe the term "heritability" in the context of behavior genetics as "...one of the most misleading in the history of science" and argue that it has no value except in very rare cases.<sup id="cite_ref-moore_31-0" class="reference"><a href="#cite_note-moore-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> When studying complex human traits, it is impossible to use heritability analysis to determine the relative contributions of genes and environment, as such traits result from multiple causes interacting.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> In particular, <a href="/wiki/Marcus_Feldman" title="Marcus Feldman">Feldman</a> and <a href="/wiki/Richard_C._Lewontin" class="mw-redirect" title="Richard C. Lewontin">Lewontin</a> emphasize that heritability is itself a function of environmental variation.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> However, some researchers argue that it is possible to disentangle the two.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p><p>The controversy over heritability estimates is largely via their basis in <a href="/wiki/Twin_studies" class="mw-redirect" title="Twin studies">twin studies</a>. The scarce success of <a href="/wiki/Genome-wide_complex_trait_analysis" title="Genome-wide complex trait analysis">molecular-genetic</a> studies to corroborate such <a href="/wiki/Quantitative_genetics" title="Quantitative genetics">population-genetic</a> studies' conclusions is the <a href="/wiki/Missing_heritability_problem" title="Missing heritability problem"><i>missing heritability</i> problem</a>.<sup id="cite_ref-Turkheimer2011_35-0" class="reference"><a href="#cite_note-Turkheimer2011-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> Eric Turkheimer has argued that newer molecular methods have vindicated the conventional interpretation of twin studies,<sup id="cite_ref-Turkheimer2011_35-1" class="reference"><a href="#cite_note-Turkheimer2011-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> although it remains mostly unclear how to explain the relations between genes and behaviors.<sup id="cite_ref-pmid26413946_36-0" class="reference"><a href="#cite_note-pmid26413946-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> According to Turkheimer, both genes and environment are heritable, genetic contribution varies by environment, and a focus on heritability distracts from other important factors.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> Overall, however, <i>heritability</i> is a concept widely applicable.<sup id="cite_ref-VisscherHillWray_9-2" class="reference"><a href="#cite_note-VisscherHillWray-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=20" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Behavioral_genetics" class="mw-redirect" title="Behavioral genetics">Behavioral genetics</a></li> <li><a href="/wiki/Heredity" title="Heredity">Heredity</a></li> <li><a href="/wiki/Heritability_of_IQ" title="Heritability of IQ">Heritability of IQ</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=21" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-scitable-estimating-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-scitable-estimating_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFWrayVisscher2008" class="citation journal cs1">Wray N, Visscher P (2008). <a rel="nofollow" class="external text" href="http://www.nature.com/scitable/topicpage/estimating-trait-heritability-46889">"Estimating Trait Heritability"</a>. <i>Nature Education</i>. <b>1</b> (1): 29. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150802043009/http://www.nature.com/scitable/topicpage/estimating-trait-heritability-46889">Archived</a> from the original on 2 August 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">24 July</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+Education&rft.atitle=Estimating+Trait+Heritability&rft.volume=1&rft.issue=1&rft.pages=29&rft.date=2008&rft.aulast=Wray&rft.aufirst=Naomi&rft.au=Visscher%2C+Peter&rft_id=http%3A%2F%2Fwww.nature.com%2Fscitable%2Ftopicpage%2Festimating-trait-heritability-46889&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeritability" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGazzanigaHeathertonHalpern2015" class="citation book cs1">Gazzaniga MS, Heatherton TF, Halpern DF (February 2015). <i>Psychological science</i> (5th ed.). 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Essex: Longman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-582-24302-6" title="Special:BookSources/978-0-582-24302-6"><bdi>978-0-582-24302-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+quantitative+genetics&rft.place=Essex&rft.edition=4th&rft.pub=Longman&rft.date=1998&rft.isbn=978-0-582-24302-6&rft.aulast=Falconer&rft.aufirst=DS&rft.au=Mackay%2C+TF&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fintroductiontoqu00falc&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeritability" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRose2006" class="citation journal cs1"><a href="/wiki/Steven_Rose" title="Steven Rose">Rose SP</a> (June 2006). <a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fije%2Fdyl064">"Commentary: heritability estimates--long past their sell-by date"</a>. <i>International Journal of Epidemiology</i>. <b>35</b> (3): <span class="nowrap">525–</span>7. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fije%2Fdyl064">10.1093/ije/dyl064</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16645027">16645027</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Epidemiology&rft.atitle=Commentary%3A+heritability+estimates--long+past+their+sell-by+date&rft.volume=35&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E525-%3C%2Fspan%3E7&rft.date=2006-06&rft_id=info%3Adoi%2F10.1093%2Fije%2Fdyl064&rft_id=info%3Apmid%2F16645027&rft.aulast=Rose&rft.aufirst=SP&rft_id=https%3A%2F%2Fdoi.org%2F10.1093%252Fije%252Fdyl064&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeritability" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJoseph2004" class="citation book cs1">Joseph J (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=D4S13LYI9egC&pg=PA141">"Chapter 5"</a>. <a href="/wiki/The_Gene_Illusion" title="The Gene Illusion"><i>The Gene Illusion</i></a>. New York: <a href="/wiki/Algora" title="Algora">Algora</a>. p. 141. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-898059-47-9" title="Special:BookSources/978-1-898059-47-9"><bdi>978-1-898059-47-9</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170719214127/https://books.google.com/books?id=D4S13LYI9egC&pg=PA141">Archived</a> from the original on 2017-07-19<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-04-02</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+5&rft.btitle=The+Gene+Illusion&rft.place=New+York&rft.pages=141&rft.pub=Algora&rft.date=2004&rft.isbn=978-1-898059-47-9&rft.aulast=Joseph&rft.aufirst=Jay&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DD4S13LYI9egC%26pg%3DPA141&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeritability" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBentall2009" class="citation book cs1">Bentall RP (2009). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=V2ahyDKjMykC&pg=PA123"><i>Doctoring the Mind: Is Our Current Treatment of Mental Illness Really Any Good?</i></a>. New York: <a href="/wiki/New_York_University_Press" title="New York University Press">New York University Press</a>. pp. <span class="nowrap">123–</span>127. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8147-8723-6" title="Special:BookSources/978-0-8147-8723-6"><bdi>978-0-8147-8723-6</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20201005031501/https://books.google.com/books?id=V2ahyDKjMykC&pg=PA123">Archived</a> from the original on 2020-10-05<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-04-02</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Doctoring+the+Mind%3A+Is+Our+Current+Treatment+of+Mental+Illness+Really+Any+Good%3F&rft.place=New+York&rft.pages=%3Cspan+class%3D%22nowrap%22%3E123-%3C%2Fspan%3E127&rft.pub=New+York+University+Press&rft.date=2009&rft.isbn=978-0-8147-8723-6&rft.aulast=Bentall&rft.aufirst=Richard+P.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DV2ahyDKjMykC%26pg%3DPA123&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeritability" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcGrath2009" class="citation news cs1">McGrath M (5 July 2009). <a rel="nofollow" class="external text" href="https://www.telegraph.co.uk/culture/books/5712151/Doctoring-the-Mind-Why-Psychiatric-Treatments-Fail-by-Richard-Bentall-review.html">"Doctoring the Mind: Review"</a>. <i><a href="/wiki/The_Telegraph_(newspaper)" class="mw-redirect" title="The Telegraph (newspaper)">The Telegraph</a></i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110928055412/http://www.telegraph.co.uk/culture/books/5712151/Doctoring-the-Mind-Why-Psychiatric-Treatments-Fail-by-Richard-Bentall-review.html">Archived</a> from the original on 28 September 2011<span class="reference-accessdate">. Retrieved <span class="nowrap">4 April</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Telegraph&rft.atitle=Doctoring+the+Mind%3A+Review&rft.date=2009-07-05&rft.aulast=McGrath&rft.aufirst=Melanie&rft_id=https%3A%2F%2Fwww.telegraph.co.uk%2Fculture%2Fbooks%2F5712151%2FDoctoring-the-Mind-Why-Psychiatric-Treatments-Fail-by-Richard-Bentall-review.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeritability" class="Z3988"></span></span> </li> <li id="cite_note-moore-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-moore_31-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMooreShenk2017" class="citation journal cs1">Moore DS, Shenk D (January 2017). "The heritability fallacy". <i>Wiley Interdisciplinary Reviews: Cognitive Science</i>. <b>8</b> (<span class="nowrap">1–</span>2): e1400. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fwcs.1400">10.1002/wcs.1400</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/27906501">27906501</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Wiley+Interdisciplinary+Reviews%3A+Cognitive+Science&rft.atitle=The+heritability+fallacy&rft.volume=8&rft.issue=%3Cspan+class%3D%22nowrap%22%3E1%E2%80%93%3C%2Fspan%3E2&rft.pages=e1400&rft.date=2017-01&rft_id=info%3Adoi%2F10.1002%2Fwcs.1400&rft_id=info%3Apmid%2F27906501&rft.aulast=Moore&rft.aufirst=DS&rft.au=Shenk%2C+D&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeritability" class="Z3988"></span></span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFeldmanRamachandran2018" class="citation journal cs1">Feldman MW, Ramachandran S (April 2018). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5812976">"Missing compared to what? Revisiting heritability, genes and culture"</a>. <i>Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences</i>. <b>373</b> (1743): 20170064. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frstb.2017.0064">10.1098/rstb.2017.0064</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5812976">5812976</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/29440529">29440529</a>. <q>...all complex human traits result from a combination of causes. If these causes interact, it is impossible to assign quantitative values to the fraction of a trait due to each, just as we cannot say how much of the area of a rectangle is due, separately, to each of its two dimensions. Thus, in the analyses of complex human phenotypes...we cannot actually find 'the relative importance of genes and environment in the determination of phenotype'.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions+of+the+Royal+Society+of+London.+Series+B%2C+Biological+Sciences&rft.atitle=Missing+compared+to+what%3F+Revisiting+heritability%2C+genes+and+culture&rft.volume=373&rft.issue=1743&rft.pages=20170064&rft.date=2018-04&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC5812976%23id-name%3DPMC&rft_id=info%3Apmid%2F29440529&rft_id=info%3Adoi%2F10.1098%2Frstb.2017.0064&rft.aulast=Feldman&rft.aufirst=MW&rft.au=Ramachandran%2C+S&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC5812976&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeritability" class="Z3988"></span></span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMarcus_W._FeldmanRichard_C._Lewontin1975" class="citation journal cs1">Marcus W. 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Lewontin (1975). <a rel="nofollow" class="external text" href="https://www.science.org/doi/10.1126/science.1198102">"The Heritability Hang–Up"</a>. <i>Science</i>. <b>190</b> (4220): <span class="nowrap">1163–</span>1168. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1975Sci...190.1163F">1975Sci...190.1163F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.1198102">10.1126/science.1198102</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/1198102">1198102</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:6797128">6797128</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210520091923/https://science.sciencemag.org/content/190/4220/1163">Archived</a> from the original on 20 May 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">20 May</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=The+Heritability+Hang%E2%80%93Up&rft.volume=190&rft.issue=4220&rft.pages=%3Cspan+class%3D%22nowrap%22%3E1163-%3C%2Fspan%3E1168&rft.date=1975&rft_id=info%3Adoi%2F10.1126%2Fscience.1198102&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A6797128%23id-name%3DS2CID&rft_id=info%3Apmid%2F1198102&rft_id=info%3Abibcode%2F1975Sci...190.1163F&rft.au=Marcus+W.+Feldman&rft.au=Richard+C.+Lewontin&rft_id=https%3A%2F%2Fwww.science.org%2Fdoi%2F10.1126%2Fscience.1198102&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeritability" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text">Tredoux, Gavan. "The Nature and Nurture of Rectangles." (2019).</span> </li> <li id="cite_note-Turkheimer2011-35"><span class="mw-cite-backlink">^ <a href="#cite_ref-Turkheimer2011_35-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Turkheimer2011_35-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTurkheimer2011" class="citation journal cs1">Turkheimer E (2011). "Still missing". <i>Research in Human Development</i>. <b>8</b> (<span class="nowrap">3–</span>4): <span class="nowrap">227–</span>241. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F15427609.2011.625321">10.1080/15427609.2011.625321</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:14737438">14737438</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Research+in+Human+Development&rft.atitle=Still+missing&rft.volume=8&rft.issue=%3Cspan+class%3D%22nowrap%22%3E3%E2%80%93%3C%2Fspan%3E4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E227-%3C%2Fspan%3E241&rft.date=2011&rft_id=info%3Adoi%2F10.1080%2F15427609.2011.625321&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A14737438%23id-name%3DS2CID&rft.aulast=Turkheimer&rft.aufirst=Eric&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeritability" class="Z3988"></span></span> </li> <li id="cite_note-pmid26413946-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-pmid26413946_36-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTurkheimer2015" class="citation journal cs1">Turkheimer E (2015). "Genetic Prediction". <i>The Hastings Center Report</i>. <b>45</b> (5 Suppl): S32–8. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fhast.496">10.1002/hast.496</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/26413946">26413946</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Hastings+Center+Report&rft.atitle=Genetic+Prediction&rft.volume=45&rft.issue=5+Suppl&rft.pages=S32-8&rft.date=2015&rft_id=info%3Adoi%2F10.1002%2Fhast.496&rft_id=info%3Apmid%2F26413946&rft.aulast=Turkheimer&rft.aufirst=E&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeritability" class="Z3988"></span></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJoseph2014" class="citation book cs1">Joseph J (2014). <a rel="nofollow" class="external text" href="http://jayjoseph.net/yahoo_site_admin/assets/docs/The_Trouble_with_Twin_Studies_Chapter_Summaries.329211842.pdf"><i>The Trouble with Twin Studies: A Reassessment of Twin Research in the Social and Behavioral Sciences</i></a> <span class="cs1-format">(PDF)</span>. New York: Routledge. p. 81. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-317-60590-4" title="Special:BookSources/978-1-317-60590-4"><bdi>978-1-317-60590-4</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160404081310/http://jayjoseph.net/yahoo_site_admin/assets/docs/The_Trouble_with_Twin_Studies_Chapter_Summaries.329211842.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2016-04-04<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-04-02</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Trouble+with+Twin+Studies%3A+A+Reassessment+of+Twin+Research+in+the+Social+and+Behavioral+Sciences&rft.place=New+York&rft.pages=81&rft.pub=Routledge&rft.date=2014&rft.isbn=978-1-317-60590-4&rft.aulast=Joseph&rft.aufirst=Jay&rft_id=http%3A%2F%2Fjayjoseph.net%2Fyahoo_site_admin%2Fassets%2Fdocs%2FThe_Trouble_with_Twin_Studies_Chapter_Summaries.329211842.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeritability" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=22" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLynchWalsh1998" class="citation book cs1">Lynch M, Walsh B (1998). <i>Genetics and analysis of quantitative traits</i>. Sunderland, Mass.: Sinauer Assoc. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-87893-481-2" title="Special:BookSources/978-0-87893-481-2"><bdi>978-0-87893-481-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Genetics+and+analysis+of+quantitative+traits&rft.place=Sunderland%2C+Mass.&rft.pub=Sinauer+Assoc.&rft.date=1998&rft.isbn=978-0-87893-481-2&rft.aulast=Lynch&rft.aufirst=Michael&rft.au=Walsh%2C+Bruce&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeritability" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJohnsonPenkeSpinath2011" class="citation journal cs1">Johnson W, Penke L, Spinath FM (2011). "Understanding Heritability: What it is and What it is Not". <i>European Journal of Personality</i>. <b>25</b> (4): <span class="nowrap">287–</span>294. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fper.835">10.1002/per.835</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0890-2070">0890-2070</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:41842465">41842465</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=European+Journal+of+Personality&rft.atitle=Understanding+Heritability%3A+What+it+is+and+What+it+is+Not&rft.volume=25&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E287-%3C%2Fspan%3E294&rft.date=2011&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A41842465%23id-name%3DS2CID&rft.issn=0890-2070&rft_id=info%3Adoi%2F10.1002%2Fper.835&rft.aulast=Johnson&rft.aufirst=Wendy&rft.au=Penke%2C+Lars&rft.au=Spinath%2C+Frank+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHeritability" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heritability&action=edit&section=23" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/heredity/">Stanford Encyclopedia of Philosophy entry on Heredity and Heritability</a></li> <li><a rel="nofollow" class="external text" href="http://nitro.biosci.arizona.edu/zbook/book.html">Quantitative Genetics Resources website, including the two volume book by Lynch and Walsh. Free access</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060206232157/http://nitro.biosci.arizona.edu/zbook/book.html">Archived</a> 2006-02-06 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul 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size">Effective population size</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related Topics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Population_genetics" title="Population genetics">Population genetics</a></li> <li><a href="/wiki/Genomics" title="Genomics">Genomics</a></li> <li><a href="/wiki/Evolutionary_biology" title="Evolutionary biology">Evolutionary biology</a></li> <li><a href="/wiki/Heredity" title="Heredity">Heredity</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Population_genetics292" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2" style="text-align:center;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Population_genetics" title="Template:Population genetics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Population_genetics" title="Template talk:Population genetics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Population_genetics" title="Special:EditPage/Template:Population genetics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Population_genetics292" style="font-size:114%;margin:0 4em"><a href="/wiki/Population_genetics" title="Population genetics">Population genetics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Key concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Hardy%E2%80%93Weinberg_principle" title="Hardy–Weinberg principle">Hardy–Weinberg principle</a></li> <li><a href="/wiki/Genetic_linkage" title="Genetic linkage">Genetic linkage</a></li> <li><a href="/wiki/Identity_by_descent" title="Identity by descent">Identity by descent</a></li> <li><a href="/wiki/Linkage_disequilibrium" title="Linkage disequilibrium">Linkage disequilibrium</a></li> <li><a href="/wiki/Fisher%27s_fundamental_theorem_of_natural_selection" title="Fisher's fundamental theorem of natural selection">Fisher's fundamental theorem</a></li> <li><a href="/wiki/Neutral_theory_of_molecular_evolution" title="Neutral theory of molecular evolution">Neutral theory</a></li> <li><a href="/wiki/Shifting_balance_theory" title="Shifting balance theory">Shifting balance theory</a></li> <li><a href="/wiki/Price_equation" title="Price equation">Price equation</a></li> <li><a href="/wiki/Coefficient_of_inbreeding" title="Coefficient of inbreeding">Coefficient of inbreeding</a></li> <li><a href="/wiki/Coefficient_of_relationship" title="Coefficient of relationship">Coefficient of relationship</a></li> <li><a href="/wiki/Selection_coefficient" title="Selection coefficient">Selection coefficient</a></li> <li><a href="/wiki/Fitness_(biology)" title="Fitness (biology)">Fitness</a></li> <li><a class="mw-selflink selflink">Heritability</a></li> <li><a href="/wiki/Population_structure_(genetics)" title="Population structure (genetics)">Population structure</a></li> <li><a href="/wiki/Constructive_neutral_evolution" title="Constructive neutral evolution">Constructive neutral evolution</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Natural_selection" title="Natural selection">Selection</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Natural_selection" title="Natural selection">Natural</a></li> <li><a href="/wiki/Selective_breeding" title="Selective breeding">Artificial</a></li> <li><a href="/wiki/Sexual_selection" title="Sexual selection">Sexual</a></li> <li><a href="/wiki/Ecological_selection" class="mw-redirect" title="Ecological selection">Ecological</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0; line-height:1.1em;">Effects of selection<br />on genomic variation</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Genetic_hitchhiking" title="Genetic hitchhiking">Genetic hitchhiking</a></li> <li><a href="/wiki/Negative_selection_(natural_selection)" title="Negative selection (natural selection)">Background selection</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%"><a href="/wiki/Genetic_drift" title="Genetic drift">Genetic drift</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Small_population_size" title="Small population size">Small population size</a></li> <li><a href="/wiki/Population_bottleneck" title="Population bottleneck">Population bottleneck</a></li> <li><a href="/wiki/Founder_effect" title="Founder effect">Founder effect</a></li> <li><a href="/wiki/Coalescent_theory" title="Coalescent theory">Coalescence</a></li> <li><a href="/wiki/Balding%E2%80%93Nichols_model" title="Balding–Nichols model">Balding–Nichols model</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Founders</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ronald_Fisher" title="Ronald Fisher">R. A. Fisher</a></li> <li><a href="/wiki/J._B._S._Haldane" title="J. B. S. Haldane">J. B. S. Haldane</a></li> <li><a href="/wiki/Sewall_Wright" title="Sewall Wright">Sewall Wright</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align:center;;width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Biogeography" title="Biogeography">Biogeography</a></li> <li><a href="/wiki/Evolution" title="Evolution">Evolution</a></li> <li><a href="/wiki/Evolutionary_game_theory" title="Evolutionary game theory">Evolutionary game theory</a></li> <li><a href="/wiki/Fitness_landscape" title="Fitness landscape">Fitness landscape</a></li> <li><a href="/wiki/Genetic_genealogy" title="Genetic genealogy">Genetic genealogy</a></li> <li><a href="/wiki/Landscape_genetics" title="Landscape genetics">Landscape genetics</a> and <a href="/wiki/Landscape_genomics" title="Landscape genomics">genomics</a></li> <li><a href="/wiki/Microevolution" title="Microevolution">Microevolution</a></li> <li><a href="/wiki/Population_genomics" title="Population genomics">Population genomics</a></li> <li><a href="/wiki/Phylogeography" title="Phylogeography">Phylogeography</a></li> <li><a href="/wiki/Quantitative_genetics" title="Quantitative genetics">Quantitative genetics</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="text-align:center;"><div> <ul><li><a href="/wiki/Index_of_evolutionary_biology_articles" title="Index of evolutionary biology articles">Index of evolutionary biology articles</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="The_development_of_phenotype252" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Genarch" title="Template:Genarch"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Genarch" title="Template talk:Genarch"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Genarch" title="Special:EditPage/Template:Genarch"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="The_development_of_phenotype252" style="font-size:114%;margin:0 4em">The <a href="/wiki/Morphogenesis" title="Morphogenesis">development</a> of <a href="/wiki/Phenotype" title="Phenotype">phenotype</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Key concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Genotype%E2%80%93phenotype_distinction" title="Genotype–phenotype distinction">Genotype–phenotype distinction</a></li> <li><a href="/wiki/Reaction_norm" title="Reaction norm">Reaction norm</a></li> <li><a href="/wiki/Gene%E2%80%93environment_interaction" title="Gene–environment interaction">Gene–environment interaction</a></li> <li><a href="/wiki/Gene%E2%80%93environment_correlation" title="Gene–environment correlation">Gene–environment correlation</a></li> <li><a href="/wiki/Operon" title="Operon">Operon</a></li> <li><a class="mw-selflink selflink">Heritability</a></li> <li><a href="/wiki/Quantitative_genetics" title="Quantitative genetics">Quantitative genetics</a></li> <li><a href="/wiki/Heterochrony" title="Heterochrony">Heterochrony</a> <ul><li><a href="/wiki/Neoteny" title="Neoteny">Neoteny</a></li></ul></li> <li><a href="/wiki/Heterotopy" title="Heterotopy">Heterotopy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Genetic_architecture" title="Genetic architecture">Genetic architecture</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Canalisation_(genetics)" title="Canalisation (genetics)">Canalisation</a></li> <li><a href="/wiki/Genetic_assimilation" title="Genetic assimilation">Genetic assimilation</a></li> <li><a href="/wiki/Dominance_(genetics)" title="Dominance (genetics)">Dominance</a></li> <li><a href="/wiki/Epistasis" title="Epistasis">Epistasis</a></li> <li><a href="/wiki/Fitness_landscape" title="Fitness landscape">Fitness landscape</a>/<a href="/wiki/Evolutionary_landscape" title="Evolutionary landscape">evolutionary landscape</a></li> <li><a href="/wiki/Pleiotropy" title="Pleiotropy">Pleiotropy</a></li> <li><a href="/wiki/Phenotypic_plasticity" title="Phenotypic plasticity">Plasticity</a></li> <li><a href="/wiki/Polygenic_inheritance" class="mw-redirect" title="Polygenic inheritance">Polygenic inheritance</a></li> <li><a href="/wiki/Transgressive_segregation" title="Transgressive segregation">Transgressive segregation</a></li> <li><a href="/wiki/Sequence_space_(evolution)" title="Sequence space (evolution)">Sequence space</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Non-genetic influences</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Epigenetics" title="Epigenetics">Epigenetics</a></li> <li><a href="/wiki/Maternal_effect" title="Maternal effect">Maternal effect</a></li> <li><a href="/wiki/Genomic_imprinting" title="Genomic imprinting">Genomic imprinting</a></li> <li><a href="/wiki/Dual_inheritance_theory" title="Dual inheritance theory">Dual inheritance theory</a></li> <li><a href="/wiki/Polyphenism" title="Polyphenism">Polyphenism</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Developmental architecture</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Developmental_biology" title="Developmental biology">Developmental biology</a></li> <li><a href="/wiki/Morphogenesis" title="Morphogenesis">Morphogenesis</a> <ul><li><a href="/wiki/Eyespot_(mimicry)" title="Eyespot (mimicry)">Eyespot</a></li> <li><a href="/wiki/Pattern_formation" title="Pattern formation">Pattern formation</a></li></ul></li> <li><a href="/wiki/Segmentation_(biology)" title="Segmentation (biology)">Segmentation</a></li> <li><a href="/wiki/Metamerism_(biology)" title="Metamerism (biology)">Metamerism</a></li> <li><a href="/wiki/Modularity_(biology)" title="Modularity (biology)">Modularity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Evolution of genetic systems</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Evolvability" title="Evolvability">Evolvability</a></li> <li><a href="/wiki/Robustness_(evolution)" title="Robustness (evolution)">Robustness</a></li> <li><a href="/wiki/Neutral_network_(evolution)" title="Neutral network (evolution)">Neutral networks</a></li> <li><a href="/wiki/Evolution_of_sexual_reproduction" title="Evolution of sexual reproduction">Evolution of sexual reproduction</a></li> <li><a href="/wiki/Evolutionary_tinkering" title="Evolutionary tinkering">Tinkering</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Control of development</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Systems</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Regulation_of_gene_expression" title="Regulation of gene expression">Regulation of gene expression</a></li> <li><a href="/wiki/Gene_regulatory_network" title="Gene regulatory network">Gene regulatory network</a></li> <li><a href="/wiki/Evo-devo_gene_toolkit" title="Evo-devo gene toolkit">Evo-devo gene toolkit</a></li> <li><a href="/wiki/Evolutionary_developmental_biology" title="Evolutionary developmental biology">Evolutionary developmental biology</a></li> <li><a href="/wiki/Homeobox" title="Homeobox">Homeobox</a></li> <li><a href="/wiki/Hedgehog_signaling_pathway" title="Hedgehog signaling pathway">Hedgehog signaling pathway</a></li> <li><a href="/wiki/Notch_signaling_pathway" title="Notch signaling pathway">Notch signaling pathway</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Elements</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Homeotic_gene" title="Homeotic gene">Homeotic gene</a></li> <li><a href="/wiki/Hox_gene" title="Hox gene">Hox gene</a></li> <li><a href="/wiki/Pax_genes" title="Pax genes">Pax genes</a> <ul><li><a href="/wiki/PAX6" title="PAX6">eyeless gene</a></li></ul></li> <li><a href="/wiki/DLX_gene_family" title="DLX gene family">Distal-less</a></li> <li><a href="/wiki/Engrailed_(gene)" title="Engrailed (gene)">Engrailed</a></li> <li><a href="/wiki/Cis-regulatory_element" title="Cis-regulatory element">cis-regulatory element</a></li> <li><a href="/wiki/Ligand_(biochemistry)" title="Ligand (biochemistry)">Ligand</a></li> <li><a href="/wiki/Morphogen" title="Morphogen">Morphogen</a></li> <li><a href="/wiki/Receptor_(biochemistry)" title="Receptor (biochemistry)">Cell surface receptor</a></li> <li><a href="/wiki/Transcription_factor" title="Transcription factor">Transcription factor</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Influential figures</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/C._H._Waddington" title="C. H. Waddington">C. H. Waddington</a></li> <li><a href="/wiki/Richard_Lewontin" title="Richard Lewontin">Richard Lewontin</a></li> <li><a href="/wiki/Fran%C3%A7ois_Jacob" title="François Jacob">François Jacob</a> + <a href="/wiki/Jacques_Monod" title="Jacques Monod">Jacques Monod</a> <ul><li><a href="/wiki/Lac_operon" title="Lac operon">Lac operon</a></li></ul></li> <li><a href="/wiki/Eric_F._Wieschaus" title="Eric F. Wieschaus">Eric F. Wieschaus</a></li> <li><a href="/wiki/Christiane_N%C3%BCsslein-Volhard" title="Christiane Nüsslein-Volhard">Christiane Nüsslein-Volhard</a></li> <li><a href="/wiki/William_McGinnis" title="William McGinnis">William McGinnis</a></li> <li><a href="/wiki/Michael_Levine_(biologist)" title="Michael Levine (biologist)">Mike Levine</a></li> <li><a href="/wiki/Sean_B._Carroll" title="Sean B. Carroll">Sean B. Carroll</a> <ul><li><i><a href="/wiki/Endless_Forms_Most_Beautiful_(book)" title="Endless Forms Most Beautiful (book)">Endless Forms Most Beautiful</a></i></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Debates</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nature_versus_nurture" title="Nature versus nurture">Nature versus nurture</a></li> <li><a href="/wiki/Morphogenetic_field" title="Morphogenetic field">Morphogenetic field</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><a href="/wiki/Index_of_evolutionary_biology_articles" title="Index of evolutionary biology articles">Index of evolutionary biology articles</a></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Lysenkoism58" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Lysenkoism" title="Template:Lysenkoism"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Lysenkoism" title="Template talk:Lysenkoism"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Lysenkoism" title="Special:EditPage/Template:Lysenkoism"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Lysenkoism58" style="font-size:114%;margin:0 4em"><a href="/wiki/Lysenkoism" title="Lysenkoism">Lysenkoism</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Lysenkoists</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Trofim_Lysenko" title="Trofim Lysenko">Trofim Lysenko</a></li> <li><a href="/wiki/J._D._Bernal" title="J. D. Bernal">J. D. Bernal</a></li> <li><a href="/wiki/Nikita_Khrushchev" title="Nikita Khrushchev">Nikita Khrushchev</a></li> <li><a href="/wiki/Joseph_Stalin" title="Joseph Stalin">Joseph Stalin</a></li> <li><a href="/wiki/VASKhNIL" title="VASKhNIL">VASKhNIL</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Dissidents</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Wac%C5%82aw_Gajewski" title="Wacław Gajewski">Wacław Gajewski</a></li> <li><a href="/wiki/Georgii_Karpechenko" title="Georgii Karpechenko">Georgii Karpechenko</a></li> <li><a href="/wiki/Zhores_Medvedev" title="Zhores Medvedev">Zhores Medvedev</a></li> <li><a href="/wiki/Georgii_Nadson" title="Georgii Nadson">Georgii Nadson</a></li> <li><a href="/wiki/Hans_Stubbe" title="Hans Stubbe">Hans Stubbe</a></li> <li><a href="/wiki/Tan_Jiazhen" title="Tan Jiazhen">Tan Jiazhen</a></li> <li><a href="/wiki/Nikolai_Vavilov" title="Nikolai Vavilov">Nikolai Vavilov</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Heredity" title="Heredity">Heredity</a></li> <li><a class="mw-selflink selflink">Heritability</a></li> <li><a href="/wiki/Hybrid_(biology)" title="Hybrid (biology)">Hybridization</a></li> <li><a href="/wiki/Inheritance_of_acquired_characteristics" class="mw-redirect" title="Inheritance of acquired characteristics">Inheritance of acquired characteristics</a></li> <li><a href="/wiki/Lamarckism" title="Lamarckism">Lamarckism</a></li> <li><a href="/wiki/Mendelian_inheritance" title="Mendelian inheritance">Mendelian inheritance</a></li> <li><a href="/wiki/Vernalization" title="Vernalization">Vernalization</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Soviet policies</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bourgeois_pseudoscience" title="Bourgeois pseudoscience">Bourgeois pseudoscience</a></li> <li><a href="/wiki/Collectivization_in_the_Soviet_Union" title="Collectivization in the Soviet Union">Collectivization in the Soviet Union</a></li> <li><a href="/wiki/Pavlovian_session" title="Pavlovian session">Pavlovian session</a></li> <li><a href="/wiki/Suppressed_research_in_the_Soviet_Union" class="mw-redirect" title="Suppressed research in the Soviet Union">Suppressed research in the Soviet Union</a></li> <li><a href="/wiki/Politicization_of_science" title="Politicization of science">Politicization of science</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox authority-control" aria-label="Navbox391" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: National <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q1503548#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4311919-0">Germany</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; 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