Sometimes being heterozygous for a gene confers a genetic benefit relative to being homozygous for either of the 2 alleles. As demonstrated by Fisher in 1922, when this occurs in a population with random matings a stable balanced polymorphism will be reached and maintained. The equilibrium gene frequencies will be dependent on the relative extent to which the heterozygote is fitter than either of the two homozygote states.


Example: Inheritance of sickle cell hemoglobin in West Africa, where the sickle cell trait offers survival benefit because of the prevalence of malaria.





Homozygote Allele 1

1 – s

Homozygote Allele 2

1 - t



• "s" and "t" are the relative benefit of being heterozygous vs each homozygote state. Each is a decimal fraction from 0 to 1. Both "s" and "t" must be positive numbers.

• A value for "s" or "t" of 1 indicates a lethal condition with death prior to reproduction.


frequency of allele 1 at equilibrium =

= t / (s + t)


frequency of allele 2 at equilibrium =

= s / (s + t)


Using the Hardy-Weinberg equation:


frequency of heterozygote state =

= 2 * (frequency of allele 1) * (frequency of allele 2)


frequency of homozygote allele 1 state =

= ((frequency of allele 1) ^ 2)


frequency of homozygote allele 2 state =

= ((frequency of allele 2) ^ 2)


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