## Population Genetics

Another common use of mathematical models is in population genetics. For example, basic assumptions of Mendelian inheritance and independent assortment allow modeling the genotypic distribution of a population following random mating without migration, mutation, or selection according to the Hardy-Weinberg equation:

where p and q are frequencies in the parental generation of the A and B alleles respectively, and p2, 2pq, and q are the frequencies in offspring of AA, AB, and BB genotypes, respectively.1-4'5-1

Other population genetics models have been derived that include selection, mutation, or migration rates. For example, the change in allele frequency in a mixed population due to migration from population b into population a can be estimated with:

qab = qa + (qb - qa)m where qab denotes the allele frequency in the mixed population after migration; qa and qb are the allele frequencies in populations a and b, respectively; and m is the fraction of individuals in the mixed population that are immigrants.1-4-1 Additionally, the change in allele frequency due to selection against the BB genotype can be estimated with:

where qt is the allele frequency population before selection occurs, s is the coefficient of selection against the BB genotype, and q(t+1) is the allele frequency after selection has occurred.1-4-1 If there is no selection against the BB genotype then s=0 and if the BB genotype is lethal before the age of reproduction, then s = 1. If reproduction is compromised, but not eliminated, by the BB genotype, then 0<s <1.

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