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 popualtion.

[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 to the homozygote classes with an equal division.