Inbreeding coefficient

The inbreeding coefficient ( IK or F for short ; see also coefficient : "Beizahl, Vorzahl") calculates the probability that the same (randomly selected) genetic information is found in the offspring of parents who are already closely biologically related as in the last common ancestor of the two parents. The coefficient corresponds to around half of the relationship coefficient of the two parents to one another, because they only inherit 50% of their genetic makeup . The offspring of identical twins or clones (copies) are completely identical in genetic makeup compared to their parents , because these are already genetically identical individuals - consequently they also have an inbreeding coefficient of 1/2 = 50%. In contrast, the statistical probability that any two individuals who are not closely related from the same population group have the same randomly selected genetic information and pass it on to their offspring together is around 3%.

In genetic terms, the inbreeding coefficient makes a mathematical prediction of the extent to which an offspring at any location on a chromosome ( locus ) has inherited two identical states of a gene ( alleles ) from both ancestors (purity: homozygosity ). The calculation was developed in the 1920s by the American geneticist Sewall Wright ( see below ).

Because increased inbreeding coefficient leads to a higher homozygosity of the offspring and most hereditary diseases are inherited receding ( recessive ), it may at regional or social confined populations or populations that are only or mainly to one another mate to hereditary diseases in endogamous populations occur (see also Hereditary diseases in human inbreeding , human genetic counseling ).

Overview

The likelihood of genetic matching increases when the parents are closely related , and decreases the more generations the last common ancestor is . The following table of inbreeding coefficients is calculated from the kinship coefficients divided by 2, because the values refer to the (future) children of the related individuals , i.e. 1 generation forward:

pairing	Relationship Coefficient (R)	Inbreeding coefficient for offspring (F), (IK)
identical twins or two clones	1/1 00= 1.00 00000= 100% match	1/2 00= 50% ...
Parent ∞ child	1/2 00= 0.50 00000= 050% ...	1/4 00= 25% ...
Brother ∞ sister	1/2 00= 0.50 00000= 050% ...	1/4 00= 25% ...
Half brother ∞ half sister	1/4 00= 0.25 00000= 025% ...	1/8 00= 12.50% ...
Grandparent ∞ grandchild	1/4 00= 0.25 00000= 025% ...	1/8 00= 12.50% ...
Uncle, aunt ∞ nephew, niece	1/4 00= 0.25 00000= 025% ...	1/8 00= 12.50% ...
Cousin ∞ cousin (1st degree)	1/8 00= 0.125 0000= 012.5% ...	1/16 0= 06.25% ...
Cousin ∞ cousin (1st degree, 1 generation postponed)	1/16 0= 0.0625 000= 006.25% ...	1/32 0= 03.125% ...
Cousin ∞ 2nd cousin	1/32 0= 0.03125 00= 003.125% ...	1/64 0= 01.56% ...
Cousin ∞ 3rd cousin	1/128 = 0.0078125 = 000.78125% ...	1/256 = 00.39% ...
two random individuals (from the same population group)	00000≈ 0.06 00000≈ 006% statist. Matches	00000≈ 02–4% statistical matches

cousins

The distance between the cousins (1st degree: normal) and the 2nd degree cousins shifts by 2 degrees of relationship: In the direct line of the ancestors, there is 1 generation back to their common ancestors, the great-grandparents (or only to a great-grandparent), and then in the two branches of the family (side lines) again 1 in front of the current generation (see also direct and lateral relationship ). Accordingly, the values of the "distant" cousins are only a quarter of those of the 1st degree. In the case of 3rd degree cousins (2 back, 2 forwards) the values drop well below the statistical average and are negligible. These low values represent the small genetic “holdover” of the original great-grandparents (or a great-grandparent) who gave birth to two children who in turn established the two different sidelines of the third-degree cousins.

Relatives preference

The level of the kinship coefficient also plays a role in explaining selfless acts ( altruism ) in humans and animals or in social succession (see relatives selection ). In sociobiology and psychobiology , the level of the kinship coefficient of individuals allows corresponding predictions to be made about their behavior, which ensures that their own gene is more successful in reproduction .

Estimation procedure

For groups or populations, it is possible to calculate an average over all of their members. In order to be able to calculate their inbreeding coefficient, the degree of consanguinity of their ancestors must be known. Statements are only possible at a certain time depth, because with increasing generations, all calculations due to missing proven ancestors (or loss of ancestors ) become estimates with more or less large statistical errors .

In order to roughly estimate inbreeding coefficients for individuals, social groups or parts of the population, the frequency of surnames of their ancestors can be evaluated: If two parents had the same name before their marriage ( isonymy ), a higher inbreeding coefficient is assumed.

Use in breeding

In animal breeding, there is data for many species and races that show an adverse relationship between the inbreeding coefficient and loss of performance, for example with regard to milk yield, fertility or prize money; this is called inbreeding depression (decreased fitness ). In such cases, breeding is about keeping the inbreeding coefficient as low as possible.

On the other hand, inbreeding to an ancestor with particularly good performance can also lead to an increase in this performance in his offspring, which outweighs the disadvantageous influence of inbreeding depression. In such cases it is a matter of a balance between the inbreeding-related increase in performance and the inbreeding depression that occurs.

In populations that are subject to complete inbreeding recovery ( purging ), there is no longer any connection between the inbreeding coefficient and inbreeding depression .

calculation

Wright's exact method

Inbreeding coefficients can be calculated in several ways. The exact (complex) calculation is provided by the formula of the US geneticist Sewall Wright , which he developed in the 1920s:

${\ displaystyle F_ {I} = \ sum \ left ({\ frac {1} {2}} \ right) ^ {n_ {1} + n_ {2} +1} \ cdot (1 + F_ {A_ {i }})}$

${\ displaystyle n_ {1}}$ = Number of generations from father to common ancestor
${\ displaystyle n_ {2}}$ = Number of generations from mother to common ancestor
${\ displaystyle F_ {A_ {i}}}$ = Inbreeding coefficient of the common ancestor

Calculation using isonomy coefficients

Since the Wright formula includes the inbreeding coefficients of the individual ancestors, a very high computing power is quickly required for the Wright calculation, depending on the number of generations. The following approximation formula therefore exists for a less complex calculation:

${\ displaystyle IK = \ sum {\ frac {1} {2 ^ {n_ {1} + n_ {2} +1}}}}$

${\ displaystyle IK}$ = Isonomy coefficient (approximation of the inbreeding coefficient)
${\ displaystyle n_ {1}}$ = Generations between father and common ancestors
${\ displaystyle n_ {2}}$ = Generations between mother and common ancestors

This is calculated for each recurring ancestor and then totaled. Ancestors are only included more than once if they flow through other ancestors; the parents of multiple ancestors are therefore not included, as these are already part of the ancestor. The inbreeding coefficient of the individual ancestors is not taken into account, which means that the approximate value obtained is rather too low.

Other methods

Other calculation methods, particularly suitable for very large populations (over 100,000 individuals), are the inbreeding calculation according to Quaas (1976), according to Meuwissen (1992), and according to van Raden (1992). Their advantage over Wright's method lies in the significantly faster calculation of good approximations of the inbreeding coefficient even with a very large amount of data.

literature

General:

Horst Kräusslich , Gottfried Brem (Hrsg.): Animal breeding and general agricultural teaching for veterinarians. Enke, Stuttgart 1997, ISBN 3-432-26621-9 .
Adrian Morris Srb, Ray David Owen, Robert Stuart Edgar: General Genetics. 2nd Edition. Freeman, San Francisco / London 1965, Library of Congress 65-19558 (English).

Methods:

Th. Meuwissen, Z. Luo: Computing Inbreeding Coefficients in Large Populations. In: Genet Sel Evol. Volume 24, 1992, pp. 305-313 (English; PMC 2711146 (free full text)).
RL Quaas: Computing the diagonal elements and inverse of a large numerator relationship matrix. In: Biometrics. Volume 32, 1976, pp. 949-953 (English; preview: JSTOR 2529279 ).
PM van Raden: Accounting for Inbreeding and Crossbreeding in Genetic Evaluation of Large Populations. In: Journal of Dairy Science. Volume 75, No. 11, 1992, pp. 3136-3144 ( online at journalofdairyscience.org).
Sewall Wright : Coefficients of Inbreeding and Relationship. In: The American Naturalist. Volume 56, 1922, pp. 330-338 (English; full text: JSTOR 2456273 ).

Individual evidence

↑ ^a ^b Hansjakob Müller u. a .: Medical genetics: family planning and genetics. In: Swiss Medicine Forum. Volume 5, No. 24, Swiss Academy of Medical Sciences, Basel 2005, p. 639–641, here p. 640 ( PDF: 123 kB, 3 pages on medicalforum.ch ( memento from March 29, 2018 in the Internet Archive )) ; Quote: “Genetic risks in related marriages: physical and mental disabilities (including early childhood mortality) among the offspring of related parents (basic risk in the population approx. 3%)”.

^ Andrew Read, Dian Donnai: Applied Human Genetics. De Gruyter, Berlin 2008, ISBN 978-3-11-020867-2 , p. 251 (British first published in 2007; page preview in the Google book search); Quote: “The inbreeding coefficient of a person describes the proportion of loci from which one can expect that the person concerned is homozygous due to the blood relationship of his parents [...] and also describes the probability that the person concerned will inherit two genes at any locus which are identical due to their origin. "

↑ ^a ^b ^c Jan Murken et al.: Inbreeding and kinship coefficient in different kinship relationships. In: Human Genetics. 7th, completely revised edition. Georg Thieme Verlag, 2006, ISBN 978-3-13-139297-8 , p. 252: table (there also the exact formulas; page preview in the Google book search).

^ FM Lancaster: The coefficient of inbreeding (F) and its applications. In: Genetic And Quantitative Aspects Of Genealogy. 2015, accessed on June 1, 2020 (see section The Closest Form of Inbreeding and Table 19). Compare also the Punnett square (combination square ).

^ Sewall Wright : Coefficients of Inbreeding and Relationship. In: The American Naturalist. Volume 56, 1922, pp. 330-338 (English; JSTOR 2456273 ).

^ RL Quaas: Computing the diagonal elements and inverse of a large numerator relationship matrix. In: Biometrics. Volume 32, 1976, pp. 949-953 (English; preview: JSTOR 2529279 ).

↑ . Th Meuwissen, Z. Luo: Computing Inbreeding Coefficients in Large Populations. In: Genet Sel Evol. Volume 24, 1992, pp. 305-313 (English; PMC 2711146 (free full text)).

^ PM van Raden: Accounting for Inbreeding and Crossbreeding in Genetic Evaluation of Large Populations. In: Journal of Dairy Science. Volume 75, No. 11, 1992, pp. 3136-3144 ( online at journalofdairyscience.org).

[SAMW_2005-1] Hansjakob Müller u. a .: Medical genetics: family planning and genetics. In: Swiss Medicine Forum. Volume 5, No. 24, Swiss Academy of Medical Sciences, Basel 2005, p. 639–641, here p. 640 ( PDF: 123 kB, 3 pages on medicalforum.ch ( memento from March 29, 2018 in the Internet Archive )) ; Quote: “Genetic risks in related marriages: physical and mental disabilities (including early childhood mortality) among the offspring of related parents (basic risk in the population approx. 3%)”.