Coefficient of Inbreeding

The inbreeding coefficient (abbreviated IC) calculates the probability that the same ( random ) genetic information found in the offspring of already closely biologically related parents as in the last common ancestor of the two parents. The coefficient corresponding to each other about half of the kinship coefficient of the parents because they inherit only an estimated 50 percent of her heritage. Full compliance of the genetic material in comparison to their parents is in the offspring of identical twins and clones artificially produced, because that was already genetically identical individuals are - consequently, they also have an inbreeding coefficient of 1.0 (100 percent). In contrast is the statistical probability that any non- closely related two individuals have the same genetic information and selected randomly inherit them together to their offspring, about 3 percent.

Expressed Genetically meets the inbreeding coefficient of a mathematical prediction of the extent to which a descendant has inherited at any location on a chromosome ( locus) both state forms of a gene ( alleles) of a single ancestor ( homozygosity: homozygosity ). Was developed to calculate in the 1920s by the U.S. American Geneticist Sewall Wright ( see below).

The probability of genetic conformity rises on closer consanguinity of the parents, and it sinks, the more generations the last common ancestor back is:

Since an increased inbreeding coefficient leads to a higher homozygosity of the offspring and most genetic diseases are inherited receding ( recessive), it can at regionally or socially circumscribed populations or populations that mate only or mainly with each other, come to a genetic disorder in endogamous populations ( see also hereditary diseases in human inbreeding, genetic counseling ).

Estimation method

For groups or populations, the formation of a mean value is possible via all their relatives. In order to calculate their inbreeding coefficients, the degree of consanguinity of their ancestors must be known. This assessment is possible only in a specific temporal depth, because with increasing generations, all calculations are occupied by missing ancestor ( or ancestral loss ) to estimates with more or less large statistical errors.

To estimate inbreeding coefficient for individuals, social groups or populations coarse, the family name frequency of their ancestors can be evaluated: Had two parents before their marriage the same name ( isonymy ), it is concluded that a higher inbreeding coefficient.

Application in breeding

In animal breeding data exist for many species and breeds that demonstrate an adverse relationship between coefficient of inbreeding and loss of power, for example in terms of milk production, fertility or prizes; This is called inbreeding depression (reduced fitness). In such cases, it goes into the breeding aim is to keep the inbreeding coefficient as low as possible.

On the other hand, inbreeding to an ancestor with a particularly good performance also lead to an increase of power in his offspring, that outweighs the adverse influence of inbreeding depression. In such cases, it comes to a balance between the inbreeding -related increase in performance and inbreeding depression occurring.

In populations that are subject to full recovery inbreeding ( purging ), there is no longer any relationship between coefficient of inbreeding and inbreeding depression.

Calculation

Exact method by Wright

Inbreeding coefficients can be calculated in several ways. The exact ( expensive ) computation gives the formula of the geneticist Sewall Wright U.S., which he developed in the 1920s:

  • = Number of generations from father to common ancestor
  • = Number of generations from mother to common ancestor
  • = Inbreeding coefficient of the common ancestor

Calculation on Isonomiekoeffizienten

Since the formula according to Wright, the inbreeding coefficient of the individual ancestors involves with, depending on the number of generations quickly a very high computation power is required for the calculation according to Wright. For a less laborious calculation therefore exists the following approximate formula:

  • = Isonomiekoeffizient ( approximation of the inbreeding coefficient )
  • = Generations between father and common ancestor
  • = Generations between mother and common ancestor

Is calculated for each ancestor occur more than once and then summed. Here ancestors are only several times in the calculation if they feed on other ancestors; the parents of a multiple ancestors are therefore not included as they are already received with the ancestors. The inbreeding coefficient of the individual ancestors is not considered, so the approximate value obtained is rather low.

Other methods

Other calculation methods, especially suitable for very large populations ( over 100,000 individuals ), the inbreeding calculation by Quaas (1976 ), by Meuwissen (1992 ) and by van Raden (1992). Their advantage over the method by Wright is the much faster calculation of good approximations of the inbreeding coefficient, even at very large amount of data.

415751
de