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open-block";}</script><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><section class="mf-section-0" id="mf-section-0"> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .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">"Relatedness" redirects here. For relatedness in semantics, see <a href="/wiki/Semantic_relatedness" class="mw-redirect" title="Semantic relatedness">Semantic relatedness</a>. For relatedness in psychology, see <a href="/wiki/Self-determination_theory" title="Self-determination theory">Self-determination theory</a>.</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 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.ambox{border:none;border-collapse:collapse;background-color:transparent;margin:0 0 0 1.6em!important;padding:0!important;width:auto;display:block}body.mediawiki .mw-parser-output .compact-ambox .ambox.mbox-small-left{font-size:100%;width:auto;margin:0}.mw-parser-output .compact-ambox .ambox .mbox-text{padding:0!important;margin:0!important}.mw-parser-output .compact-ambox .ambox .mbox-text-span{display:list-item;line-height:1.5em;list-style-type:disc}body.skin-minerva .mw-parser-output .multiple-issues-text>.mw-collapsible-toggle,.mw-parser-output .compact-ambox .ambox .mbox-image,.mw-parser-output .compact-ambox .ambox .mbox-imageright,.mw-parser-output .compact-ambox .ambox .mbox-empty-cell,.mw-parser-output .compact-ambox .hide-when-compact{display:none}</style><table class="box-Multiple_issues plainlinks metadata ambox ambox-content ambox-multiple_issues compact-ambox" role="presentation"><tbody><tr><td class="mbox-text"><div class="mbox-text-span"><div class="multiple-issues-text mw-collapsible"><b>This article has multiple issues.</b> Please help <b><a href="/wiki/Special:EditPage/Coefficient_of_relationship" title="Special:EditPage/Coefficient of relationship">improve it</a></b> or discuss these issues on the <b><a href="/wiki/Talk:Coefficient_of_relationship" title="Talk:Coefficient of relationship">talk page</a></b>. <small><i>(<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove these messages</a>)</i></small> <div class="mw-collapsible-content"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Technical plainlinks metadata ambox ambox-style ambox-technical" role="presentation"><tbody><tr><td class="mbox-text"><div class="mbox-text-span">This article <b>may be too technical for most readers to understand</b>.<span class="hide-when-compact"> Please <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Coefficient_of_relationship&action=edit">help improve it</a> to <a href="/wiki/Wikipedia:Make_technical_articles_understandable" title="Wikipedia:Make technical articles understandable">make it understandable to non-experts</a>, without removing the technical details.</span> <span class="date-container"><i>(<span class="date">December 2019</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-More_footnotes_needed plainlinks metadata ambox ambox-style ambox-More_footnotes_needed" role="presentation"><tbody><tr><td class="mbox-text"><div class="mbox-text-span">This article includes a list of <a href="/wiki/Wikipedia:Citing_sources#General_references" title="Wikipedia:Citing sources">general references</a>, but <b>it lacks sufficient corresponding <a href="/wiki/Wikipedia:Citing_sources#Inline_citations" title="Wikipedia:Citing sources">inline citations</a></b>.<span class="hide-when-compact"> Please help to <a href="/wiki/Wikipedia:WikiProject_Reliability" title="Wikipedia:WikiProject Reliability">improve</a> this article by <a href="/wiki/Wikipedia:When_to_cite" title="Wikipedia:When to cite">introducing</a> more precise citations.</span> <span class="date-container"><i>(<span class="date">December 2019</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> </div> </div><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>The <b>coefficient of relationship</b> is a measure of the degree of <a href="/wiki/Consanguinity" title="Consanguinity">consanguinity</a> (or biological relationship) between two individuals. The term <a href="/wiki/Coefficient" title="Coefficient">coefficient</a> of relationship was defined by <a href="/wiki/Sewall_Wright" title="Sewall Wright">Sewall Wright</a> in 1922, and was derived from his definition of the coefficient of <a href="/wiki/Inbreeding" title="Inbreeding">inbreeding</a> of 1921. The measure is most commonly used in <a href="/wiki/Genetics" title="Genetics">genetics</a> and <a href="/wiki/Genealogy" title="Genealogy">genealogy</a>. A <a href="/wiki/Coefficient_of_inbreeding" title="Coefficient of inbreeding">coefficient of inbreeding</a> can be calculated for an individual, and is typically one-half the coefficient of relationship between the parents. </p><p>In general, the higher the level of inbreeding the closer the coefficient of relationship between the parents approaches a value of 1, expressed as a percentage,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> and approaches a value of 0 for individuals with arbitrarily remote common ancestors. </p> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#Coefficient_of_relationship"><span class="tocnumber">1</span> <span class="toctext">Coefficient of relationship</span></a></li> <li class="toclevel-1 tocsection-2"><a href="#Human_relationships"><span class="tocnumber">2</span> <span class="toctext">Human relationships</span></a></li> <li class="toclevel-1 tocsection-3"><a href="#Kinship_coefficient"><span class="tocnumber">3</span> <span class="toctext">Kinship coefficient</span></a> <ul> <li class="toclevel-2 tocsection-4"><a href="#Calculation"><span class="tocnumber">3.1</span> <span class="toctext">Calculation</span></a></li> </ul> </li> <li class="toclevel-1 tocsection-5"><a href="#See_also"><span class="tocnumber">4</span> <span class="toctext">See also</span></a></li> <li class="toclevel-1 tocsection-6"><a href="#Notes"><span class="tocnumber">5</span> <span class="toctext">Notes</span></a></li> <li class="toclevel-1 tocsection-7"><a href="#References"><span class="tocnumber">6</span> <span class="toctext">References</span></a></li> <li class="toclevel-1 tocsection-8"><a href="#Bibliography"><span class="tocnumber">7</span> <span class="toctext">Bibliography</span></a></li> </ul> </div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Coefficient_of_relationship">Coefficient of relationship</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Coefficient_of_relationship&action=edit&section=1" title="Edit section: Coefficient of relationship" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-1 collapsible-block" id="mf-section-1"> <p>The coefficient of relationship (<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><noscript><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}"></noscript><span class="lazy-image-placeholder" style="width: 1.049ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" data-alt="{\displaystyle r}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>) between two individuals B and C is obtained by a summation of coefficients calculated for every line by which they are connected to their <a href="/wiki/Identical_ancestors_point" title="Identical ancestors point">common ancestors</a>. Each such line connects the two individuals via a common ancestor, passing through no individual which is not a common ancestor more than once. A path coefficient between an ancestor A and an offspring O separated by <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><noscript><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}"></noscript><span class="lazy-image-placeholder" style="width: 1.395ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" data-alt="{\displaystyle n}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> generations is given 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 p_{AO}=2^{-n}\cdot {\sqrt {\frac {1+f_{A}}{1+f_{O}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mi>O</mi> </mrow> </msub> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>n</mi> </mrow> </msup> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>O</mi> </mrow> </msub> </mrow> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{AO}=2^{-n}\cdot {\sqrt {\frac {1+f_{A}}{1+f_{O}}}}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/925757570c79ca4d9a035b7dfbd2db3fb7900d97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; margin-left: -0.089ex; width:22.203ex; height:7.509ex;" alt="{\displaystyle p_{AO}=2^{-n}\cdot {\sqrt {\frac {1+f_{A}}{1+f_{O}}}}}"></noscript><span class="lazy-image-placeholder" style="width: 22.203ex;height: 7.509ex;vertical-align: -3.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/925757570c79ca4d9a035b7dfbd2db3fb7900d97" data-alt="{\displaystyle p_{AO}=2^{-n}\cdot {\sqrt {\frac {1+f_{A}}{1+f_{O}}}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></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_{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{A}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4df88573ffd17201a3c77be3bee49037c3f9aa4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.604ex; height:2.509ex;" alt="{\displaystyle f_{A}}"></noscript><span class="lazy-image-placeholder" style="width: 2.604ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4df88573ffd17201a3c77be3bee49037c3f9aa4" data-alt="{\displaystyle f_{A}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></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 f_{O}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>O</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{O}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d42bf56f333df93265ecb1bbccc2e034ac5a163d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.625ex; height:2.509ex;" alt="{\displaystyle f_{O}}"></noscript><span class="lazy-image-placeholder" style="width: 2.625ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d42bf56f333df93265ecb1bbccc2e034ac5a163d" data-alt="{\displaystyle f_{O}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> are the <a href="/wiki/Coefficient_of_inbreeding" title="Coefficient of inbreeding">coefficients of inbreeding</a> for A and O, respectively. </p><p>The coefficient of relationship <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_{BC}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>C</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{BC}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2fe28c53d1e56fd17f456fa735a926ac4209fc59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.777ex; height:2.009ex;" alt="{\displaystyle r_{BC}}"></noscript><span class="lazy-image-placeholder" style="width: 3.777ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2fe28c53d1e56fd17f456fa735a926ac4209fc59" data-alt="{\displaystyle r_{BC}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is now obtained by summing over all path coefficients: </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_{BC}=\sum {p_{AB}\cdot p_{AC}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mi>B</mi> </mrow> </msub> <mo>⋅</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mi>C</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{BC}=\sum {p_{AB}\cdot p_{AC}}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ece79a719218b5f06acec4a9755e13c9906a9b50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:20.062ex; height:3.843ex;" alt="{\displaystyle r_{BC}=\sum {p_{AB}\cdot p_{AC}}}"></noscript><span class="lazy-image-placeholder" style="width: 20.062ex;height: 3.843ex;vertical-align: -1.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ece79a719218b5f06acec4a9755e13c9906a9b50" data-alt="{\displaystyle r_{BC}=\sum {p_{AB}\cdot p_{AC}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>By assuming that the pedigree can be traced back to a sufficiently remote population of perfectly random-bred stock (<i>f</i><sub>A</sub> = 0 for all <i>A</i> in the sum) the definition of <i>r</i> may be simplified to </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_{BC}=\sum _{p}{2^{-L(p)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>L</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r_{BC}=\sum _{p}{2^{-L(p)}}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ad7df42bfb2d4b789b49378c4744be25eac5991" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:16.517ex; height:5.676ex;" alt="{\displaystyle r_{BC}=\sum _{p}{2^{-L(p)}}}"></noscript><span class="lazy-image-placeholder" style="width: 16.517ex;height: 5.676ex;vertical-align: -3.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ad7df42bfb2d4b789b49378c4744be25eac5991" data-alt="{\displaystyle r_{BC}=\sum _{p}{2^{-L(p)}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></dd></dl> <p>where <i>p</i> enumerates all paths connecting B and C with unique common ancestors (i.e. all paths terminate at a common ancestor and may not pass through a common ancestor to a common ancestor's ancestor), and <i>L(p)</i> is the length of the path <i>p</i>. </p><p>To give an (artificial) example: Assuming that two individuals share the same 32 ancestors of <i>n</i> = 5 generations ago, but do not have any common ancestors at four or fewer generations ago, their coefficient of relationship would be </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="{\textstyle r=2^{n}\cdot 2^{-2n}=2^{-n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>⋅</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> <mi>n</mi> </mrow> </msup> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle r=2^{n}\cdot 2^{-2n}=2^{-n}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5aba60974467c7fbb946846e7aff24b7c5d4324e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:19.447ex; height:2.676ex;" alt="{\textstyle r=2^{n}\cdot 2^{-2n}=2^{-n}}"></noscript><span class="lazy-image-placeholder" style="width: 19.447ex;height: 2.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5aba60974467c7fbb946846e7aff24b7c5d4324e" data-alt="{\textstyle r=2^{n}\cdot 2^{-2n}=2^{-n}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, which for n = 5, is, <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="{\textstyle 2^{-5}={\frac {1}{32}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>5</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>32</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle 2^{-5}={\frac {1}{32}}}</annotation> </semantics> </math></span><noscript><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c9531818e8f70a9baf8404111332170907f0387" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:9.074ex; height:3.676ex;" alt="{\textstyle 2^{-5}={\frac {1}{32}}}"></noscript><span class="lazy-image-placeholder" style="width: 9.074ex;height: 3.676ex;vertical-align: -1.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c9531818e8f70a9baf8404111332170907f0387" data-alt="{\textstyle 2^{-5}={\frac {1}{32}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, equal to 0.03125 or approximately 3%.</dd></dl> <p>Individuals for which the same situation applies for their 1024 ancestors of ten generations ago would have a coefficient of <i>r</i> = 2<sup>−10</sup> = 0.1%. If follows that the value of <i>r</i> can be given to an accuracy of a few percent if the family tree of both individuals is known for a depth of five generations, and to an accuracy of a tenth of a percent if the known depth is at least ten generations. The contribution to <i>r</i> from common ancestors of 20 generations ago (corresponding to roughly 500 years in human genealogy, or the contribution from common descent from a <a href="/wiki/Middle_Ages" title="Middle Ages">medieval</a> population) falls below one <a href="/wiki/Parts-per_notation" title="Parts-per notation">part-per-million</a>. </p> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Human_relationships">Human relationships</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Coefficient_of_relationship&action=edit&section=2" title="Edit section: Human relationships" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-2 collapsible-block" id="mf-section-2"> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Coefficient_of_relatedness.png" class="mw-file-description"><noscript><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Coefficient_of_relatedness.png/220px-Coefficient_of_relatedness.png" decoding="async" width="220" height="189" class="mw-file-element" data-file-width="1833" data-file-height="1572"></noscript><span class="lazy-image-placeholder" style="width: 220px;height: 189px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Coefficient_of_relatedness.png/220px-Coefficient_of_relatedness.png" data-width="220" data-height="189" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Coefficient_of_relatedness.png/330px-Coefficient_of_relatedness.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Coefficient_of_relatedness.png/440px-Coefficient_of_relatedness.png 2x" data-class="mw-file-element"> </span></a><figcaption>Diagram of common family relationships, where the area of each colored circle is scaled according to the coefficient of relatedness. All relatives of the same relatedness are included together in one of the gray ellipses. Legal <a href="/wiki/Degree_of_relationship" class="mw-redirect" title="Degree of relationship">degrees of relationship</a> can be found by counting the number of solid-line connections between the self and a relative.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>The coefficient of relationship is sometimes used to express <a href="/wiki/Degrees_of_kinship" class="mw-redirect" title="Degrees of kinship">degrees of kinship</a> in numeric terms in human <a href="/wiki/Genealogy" title="Genealogy">genealogy</a>. </p><p>In human relationships, the value of the coefficient of relationship is usually calculated based on the knowledge of a full family tree extending to a comparatively small number of generations, perhaps of the order of three or four. As explained above, the value for the coefficient of relationship so calculated is thus a lower bound, with an actual value that may be up to a few percent higher. The value is accurate to within 1% if the full family tree of both individuals is known to a depth of seven generations.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>c<span class="cite-bracket">]</span></a></sup> </p><p>A first-degree relative (FDR) is a person's <a href="/wiki/Parent" title="Parent">parent</a> (father or mother), <a href="/wiki/Sibling" title="Sibling">sibling</a> (brother or sister) or <a href="/wiki/Offspring" title="Offspring">child</a> (son or daughter).<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> It constitutes a category of family members that largely overlaps with the term <a href="/wiki/Nuclear_family" title="Nuclear family">nuclear family</a>, but without spouses.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> If the persons are <a href="/wiki/Consanguinity" title="Consanguinity">related by blood</a>, the first degree relatives share approximately 50% of their genes. First-degree relatives are a common measure used to diagnose risks for common diseases by analyzing family history.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>A second-degree relative (SDR) is someone who shares 25% of a person's genes. It includes <a href="/wiki/Uncle" title="Uncle">uncles</a>, <a href="/wiki/Aunt" title="Aunt">aunts</a>, <a href="/wiki/Nephew" class="mw-redirect" title="Nephew">nephews</a>, <a href="/wiki/Niece" class="mw-redirect" title="Niece">nieces</a>, <a href="/wiki/Grandparent" title="Grandparent">grandparents</a>, <a href="/wiki/Grandchild" class="mw-redirect" title="Grandchild">grandchildren</a>, <a href="/wiki/Half-sibling" class="mw-redirect" title="Half-sibling">half-siblings</a> and double-first cousins.<sup id="cite_ref-cdc_7-0" class="reference"><a href="#cite_note-cdc-7"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-bcbs_8-0" class="reference"><a href="#cite_note-bcbs-8"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-cancergov_9-0" class="reference"><a href="#cite_note-cancergov-9"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Third-degree relatives are a segment of the <a href="/wiki/Extended_family" title="Extended family">extended family</a> and includes first cousins, great-grandparents and great-grandchildren.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Third-degree relatives are generally defined by the expected amount of genetic overlap that exists between two people, with the third-degree relatives of an individual sharing approximately 12.5% of their genes.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> The category includes great-grandparents, great-grandchildren, granduncles, grandaunts, grandnephews, grandnieces, first cousins,<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> half-uncles, half-aunts, half-nieces and half-nephews. </p> <table class="wikitable"> <tbody><tr> <th>Degree of<br>relationship</th> <th>Relationship</th> <th>Coefficient of<br>relationship (r) </th></tr> <tr> <td>0</td> <td>self</td> <td>100% (2<sup>0</sup>) </td></tr> <tr> <td>1</td> <td>mother / father / daughter / son<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></td> <td>50% (2<sup>−1</sup>) </td></tr> <tr> <td>1</td> <td>sister / brother</td> <td>50% (2<sup>−1</sup>) </td></tr> <tr> <td>2</td> <td>grandmother / grandfather / granddaughter / grandson</td> <td>25% (2<sup>−2</sup>) </td></tr> <tr> <td>2</td> <td>aunt / uncle / niece / nephew</td> <td>25% (2<sup>−2</sup>) </td></tr> <tr> <td>3</td> <td>first cousin</td> <td>12.5% (2<sup>−3</sup>) </td></tr> <tr> <td>3</td> <td>great-grandmother / great-grandfather / great-granddaughter / great-grandson</td> <td>12.5% (2<sup>−3</sup>) </td></tr> <tr> <td>3</td> <td>grandaunt / granduncle / grandniece / grandnephew</td> <td>12.5% (2<sup>−3</sup>) </td></tr> <tr> <td>4</td> <td>first cousin once removed</td> <td>6.25% (2<sup>−4</sup>) </td></tr> <tr> <td>5</td> <td>second cousin</td> <td>3.125% (2<sup>−5</sup>) </td></tr> <tr> <td>4</td> <td>great-great-grandmother / great-great-grandfather / great-great-granddaughter / great-great-grandson</td> <td>6.25% (2<sup>−4</sup>) </td></tr> <tr> <td>4</td> <td>great-grandaunt / great-granduncle / great-grandniece / great-grandnephew</td> <td>6.25% (2<sup>−4</sup>) </td></tr> <tr> <td>5</td> <td>first cousin twice removed</td> <td>3.125% (2<sup>−5</sup>) </td></tr> <tr> <td>6</td> <td>second cousin once removed</td> <td>1.5625% (2<sup>−6</sup>) </td></tr> <tr> <td>7</td> <td>third cousin</td> <td>0.78125% (2<sup>−7</sup>) </td></tr> <tr> <td>5</td> <td>great-great-great-grandmother / great-great-great-grandfather / great-great-great-granddaughter / great-great-great-grandson</td> <td>3.125% (2<sup>−5</sup>) </td></tr> <tr> <td>5</td> <td>great-great-grandaunt / great-great-granduncle / great-great-grandniece / great-great-grandnephew</td> <td>3.125% (2<sup>−5</sup>) </td></tr> <tr> <td>6</td> <td>first cousin thrice removed</td> <td>1.5625% (2<sup>−6</sup>) </td></tr> <tr> <td>7</td> <td>second cousin twice removed</td> <td>0.78125% (2<sup>−7</sup>) </td></tr> <tr> <td>8</td> <td>third cousin once removed</td> <td>0.390625% (2<sup>−8</sup>) </td></tr> <tr> <td>9</td> <td>fourth cousin</td> <td>0.1953125% (2<sup>−9</sup>) </td></tr> <tr> <td>2</td> <td>half-sister / half-brother</td> <td>25% (2<sup>−2</sup>) </td></tr> <tr> <td>3</td> <td>half-aunt / half-uncle / half-niece / half-nephew</td> <td>12.5% (2<sup>−3</sup>) </td></tr> <tr> <td>4</td> <td>half-first cousin</td> <td>6.25% (2<sup>−4</sup>) </td></tr> <tr> <td>2</td> <td>double-first cousin</td> <td>25% (2<sup>−2</sup>) </td></tr> <tr> <td>4</td> <td>half-grandaunt / half-granduncle / half-grandniece / half-grandnephew</td> <td>6.25% (2<sup>−4</sup>) </td></tr> <tr> <td>5</td> <td>half-first cousin once removed</td> <td>3.125% (2<sup>−5</sup>) </td></tr> <tr> <td>3</td> <td>double-first cousin once removed</td> <td>12.5% (2<sup>−3</sup>) </td></tr> <tr> <td>5</td> <td>half-great-grandaunt / half-great-granduncle / half-great-grandniece / half-great-grandnephew</td> <td>3.125% (2<sup>−5</sup>) </td></tr> <tr> <td>6</td> <td>half-first cousin twice removed</td> <td>1.5625% (2<sup>−6</sup>) </td></tr> <tr> <td>4</td> <td>double-first cousin twice removed</td> <td>6.25% (2<sup>−4</sup>) </td></tr> <tr> <td>6</td> <td>half-great-great-grandaunt / half-great-great-granduncle / half-great-great-grandniece / half-great-great-grandnephew</td> <td>1.5625% (2<sup>−6</sup>) </td></tr> <tr> <td>7</td> <td>half-first cousin thrice removed</td> <td>0.78125% (2<sup>−7</sup>) </td></tr> <tr> <td>5</td> <td>double-first cousin thrice removed</td> <td>3.125% (2<sup>−5</sup>) </td></tr></tbody></table> <p>Most <a href="/wiki/Incest_laws" class="mw-redirect" title="Incest laws">incest laws</a> concern the relationships where <i>r</i> = 25% or higher, although many ignore the rare case of double first cousins. Some jurisdictions also prohibit sexual relations or marriage <a href="/wiki/Cousin_marriage" title="Cousin marriage">between cousins</a> of various degree, or individuals related only through <a href="/wiki/Adoption" title="Adoption">adoption</a> or <a href="/wiki/Affinity_(law)" title="Affinity (law)">affinity</a>. Whether there is any likelihood of conception is generally considered irrelevant. </p> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(3)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Kinship_coefficient">Kinship coefficient</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Coefficient_of_relationship&action=edit&section=3" title="Edit section: Kinship coefficient" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-3 collapsible-block" id="mf-section-3"> <p>The <b>kinship coefficient</b> is a simple measure of relatedness, defined as the <a href="/wiki/Probability" title="Probability">probability</a> that a pair of randomly sampled homologous <a href="/wiki/Alleles" class="mw-redirect" title="Alleles">alleles</a> are <a href="/wiki/Identity_by_descent" title="Identity by descent">identical by descent</a>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> More simply, it is the probability that an allele selected randomly from an individual, i, and an allele selected at the same <a href="/wiki/Autosomal" class="mw-redirect" title="Autosomal">autosomal</a> locus from another individual, j, are identical and from the same ancestor. </p> <table class="wikitable sortable floatright"> <tbody><tr> <th>Relationship</th> <th>Kinship<br>coefficient </th></tr> <tr> <td>self</td> <td>1/2 </td></tr> <tr> <td>mother / father / daughter / son</td> <td>1/4 </td></tr> <tr> <td>sister / brother</td> <td>1/4 </td></tr> <tr> <td>grandmother / grandfather / granddaughter / grandson</td> <td>1/8 </td></tr> <tr> <td>aunt / uncle / niece / nephew</td> <td>1/8 </td></tr> <tr> <td>first cousin</td> <td>1/16 </td></tr> <tr> <td>half-sister / half-brother</td> <td>1/8 </td></tr> <tr> <td>half-first cousin</td> <td>1/32 </td></tr> <tr> <td>double-first cousin</td> <td>1/8 </td></tr> <tr> <td colspan="2"><small>Several of the most common family relationships and their corresponding kinship coefficient.</small> </td></tr></tbody></table> <p>The coefficient of relatedness is equal to twice the kinship coefficient.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Calculation">Calculation</h3><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Coefficient_of_relationship&action=edit&section=4" title="Edit section: Calculation" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <p>The kinship coefficient between two individuals, i and j, is represented as Φ<sub>ij</sub>. The kinship coefficient between a non-inbred individual and itself, Φ<sub>ii</sub>, is equal to 1/2. This is due to the fact that humans are <a href="/wiki/Ploidy" title="Ploidy">diploid</a>, meaning the only way for the randomly chosen alleles to be identical by descent is if the same allele is chosen twice (probability 1/2). Similarly, the relationship between a parent and a child is found by the chance that the randomly picked allele in the child is from the parent (probability 1/2) and the probability of the allele that is picked from the parent being the same one passed to the child (probability 1/2). Since these two events are independent of each other, they are multiplied Φ<sub>ij</sub> = 1/2 X 1/2 = 1/4.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(4)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="See_also">See also</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Coefficient_of_relationship&action=edit&section=5" title="Edit section: See also" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section 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<li><a href="/wiki/Genetic_diversity" title="Genetic diversity">Genetic diversity</a></li> <li><a href="/wiki/Genetic_sexual_attraction" title="Genetic sexual attraction">Genetic sexual attraction</a></li> <li><a href="/wiki/Inbreeding" title="Inbreeding">Inbreeding</a></li> <li><a href="/wiki/Coefficient_of_inbreeding" title="Coefficient of inbreeding">Coefficient of inbreeding</a></li> <li><a href="/wiki/Inbreeding_avoidance" title="Inbreeding avoidance">Inbreeding avoidance</a></li> <li><a href="/wiki/Inbreeding_depression" title="Inbreeding depression">Inbreeding depression</a></li> <li><a href="/wiki/Incest" title="Incest">Incest</a></li> <li><a href="/wiki/Incest_taboo" title="Incest taboo">Incest taboo</a></li> <li><a href="/wiki/Legality_of_incest" title="Legality of incest">Legality of incest</a></li> <li><a href="/wiki/Malecot%27s_method_of_coancestry" title="Malecot's method of coancestry">Malecot's method of coancestry</a></li> <li><a href="/wiki/Pedigree_collapse" title="Pedigree collapse">Pedigree collapse</a></li> <li><a href="/wiki/Phylogenetics" title="Phylogenetics">Phylogenetics</a></li> <li><a href="/wiki/Prohibited_degree_of_kinship" title="Prohibited degree of kinship">Prohibited degree of kinship</a></li> <li><a href="/wiki/Proximity_of_blood" title="Proximity of blood">Proximity of blood</a></li></ul> </div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(5)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Notes">Notes</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Coefficient_of_relationship&action=edit&section=6" title="Edit section: Notes" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-5 collapsible-block" id="mf-section-5"> <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 reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">strictly speaking, r=1 for clones and identical twins, but since the definition of r is usually intended to estimate the suitability of two individuals for breeding, they are typically taken to be of opposite sex.</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">For instance, one's sibling connects to one's parent, which connects to one's self (2 lines) while one's aunt/uncle connects to one's grandparent, which connects to one's parent, which connects to one's self (3 lines).</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">A full family tree of seven generations (128 paths to ancestors of the 7th degree) is unreasonable even for members of high nobility. For example, the family tree of Queen <a href="/wiki/Elizabeth_II" title="Elizabeth II">Elizabeth II</a> is fully known for a depth of six generations, but becomes difficult to trace in the seventh generation.</span> </li> </ol></div></div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(6)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="References">References</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Coefficient_of_relationship&action=edit&section=7" title="Edit section: References" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-6 collapsible-block" id="mf-section-6"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</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="CITEREFTalley2007" class="citation book cs1">Talley, Nicholas (2007). <i>Gastroenterology and Hepatology: A Clinical Handbook</i>. p. 200.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Gastroenterology+and+Hepatology%3A+A+Clinical+Handbook&rft.pages=200&rft.date=2007&rft.aulast=Talley&rft.aufirst=Nicholas&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoefficient+of+relationship" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFReiss1981" class="citation book cs1">Reiss, David (1981). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/familysconstruct00reis"><i>The Family's Construction of Reality</i></a></span>. Harvard University Press. p. 276. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780674294158" title="Special:BookSources/9780674294158"><bdi>9780674294158</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Family%27s+Construction+of+Reality&rft.pages=276&rft.pub=Harvard+University+Press&rft.date=1981&rft.isbn=9780674294158&rft.aulast=Reiss&rft.aufirst=David&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ffamilysconstruct00reis&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoefficient+of+relationship" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGinsburg2008" class="citation book cs1">Ginsburg, Geoffrey (2008). <i>Genomic and Personalized Medicine, Volumes 1-2</i>. p. 482.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Genomic+and+Personalized+Medicine%2C+Volumes+1-2&rft.pages=482&rft.date=2008&rft.aulast=Ginsburg&rft.aufirst=Geoffrey&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoefficient+of+relationship" class="Z3988"></span></span> </li> <li id="cite_note-cdc-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-cdc_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.cdc.gov/genomics/resources/diseases/breast_ovarian_cancer/risk_categories.htm">"Breast and Ovarian Cancer and Family History Risk Categories"</a>. <i>Center for Disease Control</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Center+for+Disease+Control&rft.atitle=Breast+and+Ovarian+Cancer+and+Family+History+Risk+Categories&rft_id=https%3A%2F%2Fwww.cdc.gov%2Fgenomics%2Fresources%2Fdiseases%2Fbreast_ovarian_cancer%2Frisk_categories.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoefficient+of+relationship" class="Z3988"></span></span> </li> <li id="cite_note-bcbs-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-bcbs_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.bcbst.com/mpmanual/First_and_Second_Degree_Relative.htm">"First, Second and Third Degree Relative"</a>. <i>Blue Cross Blue Shield</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Blue+Cross+Blue+Shield&rft.atitle=First%2C+Second+and+Third+Degree+Relative&rft_id=https%3A%2F%2Fwww.bcbst.com%2Fmpmanual%2FFirst_and_Second_Degree_Relative.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoefficient+of+relationship" class="Z3988"></span></span> </li> <li id="cite_note-cancergov-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-cancergov_9-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.cancer.gov/publications/dictionaries/genetics-dictionary?cdrid=485395">"NCI Dictionary of Genetics Terms"</a>. <i>Cancer.gov</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Cancer.gov&rft.atitle=NCI+Dictionary+of+Genetics+Terms&rft_id=http%3A%2F%2Fwww.cancer.gov%2Fpublications%2Fdictionaries%2Fgenetics-dictionary%3Fcdrid%3D485395&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoefficient+of+relationship" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.bcbst.com/mpmanual/First_and_Second_Degree_Relative.htm">"First, Second and Third Degree Relative"</a>. <i>bcbst.com</i>. Blue Cross Blue Shield of Tennessee<span class="reference-accessdate">. Retrieved <span class="nowrap">18 August</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=bcbst.com&rft.atitle=First%2C+Second+and+Third+Degree+Relative&rft_id=https%3A%2F%2Fwww.bcbst.com%2Fmpmanual%2FFirst_and_Second_Degree_Relative.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoefficient+of+relationship" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLudman2009" class="citation book cs1">Ludman, Mark (2009). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=kXaMjwItP0oC"><i>The Encyclopedia of Genetic Disorders and Birth Defects</i></a>. Infobase. p. 101. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781438120959" title="Special:BookSources/9781438120959"><bdi>9781438120959</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Encyclopedia+of+Genetic+Disorders+and+Birth+Defects&rft.pages=101&rft.pub=Infobase&rft.date=2009&rft.isbn=9781438120959&rft.aulast=Ludman&rft.aufirst=Mark&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DkXaMjwItP0oC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoefficient+of+relationship" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.law.cornell.edu/cfr/text/29/1635.3">"29 CFR § 1635.3 - Definitions specific to GINA"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=29+CFR+%C2%A7+1635.3+-+Definitions+specific+to+GINA&rft_id=https%3A%2F%2Fwww.law.cornell.edu%2Fcfr%2Ftext%2F29%2F1635.3&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoefficient+of+relationship" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://taumoda.com/web/PD/library/kin.html">"Kin Selection"</a>. Benjamin/Cummings<span class="reference-accessdate">. Retrieved <span class="nowrap">2007-11-25</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Kin+Selection&rft.pub=Benjamin%2FCummings&rft_id=http%3A%2F%2Ftaumoda.com%2Fweb%2FPD%2Flibrary%2Fkin.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoefficient+of+relationship" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLange2003" class="citation book cs1">Lange, Kenneth (2003). <i>Mathematical and statistical methods for genetic analysis</i>. Springer. p. 81. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-21750-5" title="Special:BookSources/978-0-387-21750-5"><bdi>978-0-387-21750-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+and+statistical+methods+for+genetic+analysis&rft.pages=81&rft.pub=Springer&rft.date=2003&rft.isbn=978-0-387-21750-5&rft.aulast=Lange&rft.aufirst=Kenneth&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoefficient+of+relationship" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWright1921" class="citation journal cs1"><a href="/wiki/Sewall_Wright" title="Sewall Wright">Wright, Sewall</a> (1921). <a rel="nofollow" class="external text" href="http://www.genetics.org/content/143/4/1499.full.pdf">"Systems of Mating"</a> <span class="cs1-format">(PDF)</span>. <i>Genetics</i>. <b>6</b> (2): 111–178. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fgenetics%2F6.2.111">10.1093/genetics/6.2.111</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/PMC1200510">1200510</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/17245958">17245958</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Genetics&rft.atitle=Systems+of+Mating&rft.volume=6&rft.issue=2&rft.pages=111-178&rft.date=1921&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1200510%23id-name%3DPMC&rft_id=info%3Apmid%2F17245958&rft_id=info%3Adoi%2F10.1093%2Fgenetics%2F6.2.111&rft.aulast=Wright&rft.aufirst=Sewall&rft_id=http%3A%2F%2Fwww.genetics.org%2Fcontent%2F143%2F4%2F1499.full.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoefficient+of+relationship" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLange2003" class="citation book cs1">Lange, Kenneth (2003). <i>Mathematical and statistical methods for genetic analysis</i>. Springer. pp. 81–83.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+and+statistical+methods+for+genetic+analysis&rft.pages=81-83&rft.pub=Springer&rft.date=2003&rft.aulast=Lange&rft.aufirst=Kenneth&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoefficient+of+relationship" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJacquard1974" class="citation book cs1">Jacquard, Albert (1974). <i>The genetic structure of populations</i>. Springer-Verlag. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-88415-3" title="Special:BookSources/978-3-642-88415-3"><bdi>978-3-642-88415-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+genetic+structure+of+populations&rft.pub=Springer-Verlag&rft.date=1974&rft.isbn=978-3-642-88415-3&rft.aulast=Jacquard&rft.aufirst=Albert&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoefficient+of+relationship" class="Z3988"></span></span> </li> </ol></div></div> </section><div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(7)"><span class="indicator mf-icon mf-icon-expand mf-icon--small"></span><h2 id="Bibliography">Bibliography</h2><span class="mw-editsection"> <a role="button" href="/w/index.php?title=Coefficient_of_relationship&action=edit&section=8" title="Edit section: Bibliography" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div><section class="mf-section-7 collapsible-block" id="mf-section-7"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWright1921" class="citation journal cs1"><a href="/wiki/Sewall_Wright" title="Sewall Wright">Wright, Sewall</a> (1921). <a rel="nofollow" class="external text" href="http://www.genetics.org/content/143/4/1499.full.pdf">"Systems of Mating"</a> <span class="cs1-format">(PDF)</span>. <i>Genetics</i>. <b>6</b> (2): 111–178. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fgenetics%2F6.2.111">10.1093/genetics/6.2.111</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/PMC1200510">1200510</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/17245958">17245958</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Genetics&rft.atitle=Systems+of+Mating&rft.volume=6&rft.issue=2&rft.pages=111-178&rft.date=1921&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1200510%23id-name%3DPMC&rft_id=info%3Apmid%2F17245958&rft_id=info%3Adoi%2F10.1093%2Fgenetics%2F6.2.111&rft.aulast=Wright&rft.aufirst=Sewall&rft_id=http%3A%2F%2Fwww.genetics.org%2Fcontent%2F143%2F4%2F1499.full.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoefficient+of+relationship" class="Z3988"></span> five papers: <ul><li>I) The biometric relations between offspring and parent</li> <li>II) The effects of inbreeding on the genetic composition of a population</li> <li>III) Assortative mating based on somatic resemblance</li> <li>IV) The effects of selection</li> <li>V) General considerations</li></ul></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWright1922" class="citation journal cs1"><a href="/wiki/Sewall_Wright" title="Sewall Wright">Wright, Sewall</a> (1922). <a rel="nofollow" class="external text" href="https://zenodo.org/record/1431365">"Coefficients of inbreeding and relationship"</a>. <i><a href="/wiki/American_Naturalist" class="mw-redirect" title="American Naturalist">American Naturalist</a></i>. <b>56</b> (645): 330–338. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F279872">10.1086/279872</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:83865141">83865141</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Naturalist&rft.atitle=Coefficients+of+inbreeding+and+relationship&rft.volume=56&rft.issue=645&rft.pages=330-338&rft.date=1922&rft_id=info%3Adoi%2F10.1086%2F279872&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A83865141%23id-name%3DS2CID&rft.aulast=Wright&rft.aufirst=Sewall&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1431365&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACoefficient+of+relationship" class="Z3988"></span></li> <li><a href="/wiki/Gustave_Mal%C3%A9cot" title="Gustave Malécot">Malécot, G.</a> (1948) <i>Les mathématiques de l'hérédité</i>, Masson et Cie, Paris.</li> <li>Lange, K. (1997) <i>Mathematical and statistical methods for genetic analysis</i>, Springer-Verlag, New-York.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOliehoekJack_J._WindigJohan_A._M._van_ArendonkPiter_Bijma2006" class="citation journal cs1">Oliehoek, Pieter; Jack J. Windig; Johan A. M. van Arendonk; Piter Bijma (May 2006). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1461426">"Estimating Relatedness Between Individuals in General Populations With a Focus on Their Use in Conservation Programs"</a>. <i>Genetics</i>. <b>173</b> (1): 483–496. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1534%2Fgenetics.105.049940">10.1534/genetics.105.049940</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/PMC1461426">1461426</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/16510792">16510792</a>.</cite><span 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