Inbreeding (population sense)

An assumption of Hardy–Weinberg genotype proportions is alleles are paired independently of each other. This can be referred to as random mating in a population. Inbreeding can cause a deviation from this so that the inheritance of alleles are no longer independent. Self pollination in plants is an extreme form of this.

The deviation from Hardy–Weinberg genotype proportions due to inbreeding is quantified by [math]F_{IS}[/math].

[math]F_{IS} = \frac{H_S - H_I}{H_S}[/math]

where

[math]H_I[/math] is the observed frequency of heterozygous genotypes in a popualtion. ([math]I[/math] refers to Individual.)

[math]H_S = 2 p (1 - p) [/math] is the expected frequency of heterozygous genotypes in a popualtion. In this example it is given for the case where there are only two alleles. ([math]S[/math] refers to Subpopulation.)

[math]F_{IS}[/math] can be incorporated into expectations of genotype frequencies by adjusting Hardy–Weinberg proportions.

[math]f_{AA} = p^2 + p (1-p) F_{IS}[/math]

[math]f_{Aa} = 2 p (1-p) - 2 p (1-p) F_{IS}[/math]

[math]f_{aa} = (1-p)^2 + p (1-p) F_{IS}[/math]

This reduces the frequency of heterozygotes by a factor of [math]F_{IS}[/math] and contributes them equally to each homozygote class.