An Exact Algebraic Theory of Genetic Drift in Finite Diploid Populations with Random Mating

We study random mating in a finite diploid monoecious population with two alleles at one locus. We take into account selection and a constant probability of self-mating. The generations are assumed discrete (non-overlapping). An exact algebraic theory of genetic drift is developed by the technique of transition probability matrices. The theory works on the genotype level (Hedrick, 1970), but also allows the population size to vary from generation to generation. Thus, it gives an exact statistical description of bottleneck processes, as an inhomogeneous Markov chain. Numerical Monte Carlo simulations are performed and give full agreement with the present algebraic theory. The decay rates for heterozygosity agree with the asymptotic theory by Wright (1931).