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{{short description|Mathematical guess about inbreeding}}
{{redirect|Relatedness|relatedness in semantics|Semantic relatedness|relatedness in psychology|Self-determination theory}}
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{{Technical|date=December 2019}}
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The '''coefficient of relationship''' is a measure of the degree of [[consanguinity]] (or biological relationship) between two individuals. The term [[coefficient]] of relationship was defined by [[Sewall Wright]] in 1922, and was derived from his definition of the coefficient of [[inbreeding]] of 1921. The measure is most commonly used in [[genetics]] and [[genealogy]]. A [[coefficient of inbreeding]] can be calculated for an individual, and is typically one-half the coefficient of relationship between the parents.
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==Coefficient of relationship==
The coefficient of relationship (
:<math>p_{AO} = 2^{-n} \cdot \sqrt{
where
The coefficient of relationship
:<math>r_{BC} = \sum{p_{AB} \cdot p_{AC}}</math>
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To give an (artificial) example:
Assuming that two individuals share the same 32 ancestors of ''n'' = 5 generations ago, but do not have any common ancestors at four or fewer generations ago, their coefficient of relationship would be
:<math display="inline">r = 2^n \cdot 2^{-2n} = 2^{-n}</math>, which for n = 5, is, <math display="inline">2^{-5} = \frac{1}{32}</math>,
Individuals for which the same situation applies for their 1024 ancestors of ten generations ago would have a coefficient of ''r'' = 2<sup>−10</sup> = 0.1%.
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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.{{efn|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 [[Elizabeth II]] is fully known for a depth of six generations, but becomes difficult to trace in the seventh generation.<!--parents of Francis Webb. d. 1814; mother of Mary Lister; parents of Pierre Roland and Hyacinthe Gabrielle Varis. -->}}
A first-degree relative (FDR) is a person's [[parent]] (father or mother), [[full sibling]] (brother or sister) or [[offspring]].<ref>{{cite book|last1=Talley|first1=Nicholas|title=Gastroenterology and Hepatology: A Clinical Handbook|date=2007|page=200}}</ref> It constitutes a category of family members that largely overlaps with the term [[nuclear family]], but without spouses.<ref>{{cite book|last1=Reiss|first1=David|title=The Family's Construction of Reality|url=https://archive.org/details/familysconstruct00reis|url-access=registration|date=1981|page=276|publisher=Harvard University Press |isbn=9780674294158 }}</ref> If the persons are [[Consanguinity|related by blood]], 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.<ref>{{cite book |last1=Ginsburg |first1=Geoffrey |title=Genomic and Personalized Medicine, Volumes 1-2|date=2008|page=482}}</ref>
A second-degree relative (SDR) is someone who shares 25% of a person's genes. It includes [[uncle]]s, [[aunt]]s, [[nephew]]s, [[niece]]s, [[grandparent]]s, [[grandchild]]ren, [[half-sibling]]s, and [[double cousin]]s.<ref name=cdc>{{cite web|work=Center for Disease Control|title=Breast and Ovarian Cancer and Family History Risk Categories|url=https://www.cdc.gov/genomics/resources/diseases/breast_ovarian_cancer/risk_categories.htm}}</ref><ref name=bcbs>{{cite web|work=Blue Cross Blue Shield|title=First, Second and Third Degree Relative|url=https://www.bcbst.com/mpmanual/First_and_Second_Degree_Relative.htm}}</ref><ref name=cancergov>{{cite web|url=http://www.cancer.gov/publications/dictionaries/genetics-dictionary?cdrid=485395|work=Cancer.gov|title=NCI Dictionary of Genetics Terms}}</ref>
Third-degree relatives are a segment of the [[extended family]] and includes first cousins, great-grandparents and great-grandchildren.<ref>{{cite web|title=First, Second and Third Degree Relative|url=https://www.bcbst.com/mpmanual/First_and_Second_Degree_Relative.htm|website=bcbst.com|publisher=Blue Cross Blue Shield of Tennessee|accessdate=18 August 2016}}</ref> 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.<ref>{{cite book|last1=Ludman|first1=Mark|title=The Encyclopedia of Genetic Disorders and Birth Defects|url=https://books.google.com/books?id=kXaMjwItP0oC|date=2009|page=101|publisher=Infobase |isbn=9781438120959}}</ref> The category includes [[great-grandparents]], [[great-grandchildren]], [[great-uncles|grand-uncles]], grand-aunts, [[first cousins]],<ref>{{Cite web|url=https://www.law.cornell.edu/cfr/text/29/1635.3|title = 29 CFR § 1635.3 - Definitions specific to GINA}}</ref> [[half-uncle]]s, half-aunts, [[half-niece]]s and [[half-nephew]]s.
{|class="wikitable"
!Degree of <br>relationship!!Relationship!!Coefficient of <br>relationship (r)▼
|-
|0|| identical twins; clones || 100%{{efn|By replacement in the definition of the notion of "generation" by "[[meiosis]]". Since identical twins are not separated by meiosis, there are no "generations" between them, hence ''n''{{=}}0 and ''r''{{=}}1. See: <ref>[http://www.genetic-genealogy.co.uk/Toc115570135.html genetic-genealogy.co.uk].</ref>}} (1)▼
|-▼
▲|0|| identical twins; clones || 100%
|-
|1|| mother / father / daughter / son <ref>{{cite web|url=http://taumoda.com/web/PD/library/kin.html|title=Kin Selection|publisher=Benjamin/Cummings|access-date=2007-11-25}}</ref> || 50% (2<sup>−1</sup>)
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|9|| third cousin once removed || 0.390625% (2⋅2<sup>−9</sup>)
|-
|10|| fourth cousin || 0.1953125% (2⋅2<sup>−10</sup>)
▲|-
|}
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|-
| half-sister / half-brother || 1/8
|-
| double cousins || 1/8
|-
|colspan=2|<small>Several of the most common family relationships and their corresponding kinship coefficient.</small>
|}
The coefficient of relatedness is equal to twice the kinship coefficient.<ref>{{cite journal | last1 = Wright | first1 = Sewall | author-link = Sewall Wright | year = 1921 | title =Systems of Mating | url =http://www.genetics.org/content/143/4/1499.full.pdf | journal = Genetics | volume = 6 | issue = 2 | pages = 111–178 | doi = 10.1093/genetics/6.2.111 | pmid = 17245958 | pmc = 1200510 }}</ref>
===Calculation===
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 [[Ploidy|diploid]], 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.<ref>{{cite book|last1=Lange|first1=Kenneth|title=Mathematical and statistical methods for genetic analysis|date=2003|publisher=Springer|pages=81–83}}</ref><ref>{{cite book|last1=Jacquard|first1=Albert|title=The genetic structure of populations|date=1974|publisher=Springer-Verlag|isbn=978-3-642-88415-3}}</ref>
==See also==
{{Portal|Evolutionary biology}}
{{div col|colwidth=25em}}
*[[Accidental incest]]
*[[Effective population size]]
*[[F-statistics]]
*[[Genetic distance]]
*[[Genetic diversity]]
*[[Genetic sexual attraction]]
*[[Inbreeding]]
*[[Inbreeding avoidance]]
*[[Inbreeding depression]]
*[[Incest]]
*[[Incest taboo]]
*[[Legality of incest]]
*[[Malecot's method of coancestry]]
*[[Pedigree collapse]]
*[[Phylogenetics]]
*[[Prohibited degree of kinship]]
*[[Proximity of blood]]
{{div col end}}
==Notes==
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==References==
{{reflist
==Bibliography==
*{{cite journal | last1 = Wright | first1 = Sewall | author-link = Sewall Wright | year = 1921 | title =Systems of Mating | url =http://www.genetics.org/content/143/4/1499.full.pdf | journal = Genetics | volume = 6 | issue = 2 | pages = 111–178 | doi = 10.1093/genetics/6.2.111 | pmid = 17245958 | pmc = 1200510 }} five papers:
** I) The biometric relations between offspring and parent
** II) The effects of inbreeding on the genetic composition of a population
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** V) General considerations
* {{cite journal | last1 = Wright | first1 = Sewall | author-link = Sewall Wright | year = 1922 | title = Coefficients of inbreeding and relationship | url = https://zenodo.org/record/1431365| journal = [[American Naturalist]] | volume = 56 | issue = 645| pages = 330–338 | doi=10.1086/279872| s2cid = 83865141 }}
* [[Gustave Malécot|Malécot, G.]] (1948) ''Les mathématiques de
* Lange, K. (1997) ''Mathematical and statistical methods for genetic analysis'', Springer-Verlag, New-York.
* {{cite journal|last=Oliehoek|first=Pieter |author2=Jack J. Windig |author3=Johan A. M. van Arendonk |author4=Piter Bijma |title=Estimating Relatedness Between Individuals in General Populations With a Focus on Their Use in Conservation Programs|journal=Genetics|date=May 2006|volume=173|issue=1 |pages=483–496|doi=10.1534/genetics.105.049940|pmc=1461426|pmid=16510792}}
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