On the Theory of Partially Inbreeding Finite Populations. I. Partial Selfing

Abstract

Some stochastic theory is developed for monoecious populations of size N in which there are probabilities β and 1 - β of reproduction by selfing and by random mating. It is assumed that β >> N^-1. Expressions are derived for the inbreeding coefficient of one random individual and the coefficient of kinship of two random separate individuals at time t. The mean and between-lines variance of the fraction of copies of a locus that are identical in two random separate individuals in an equilibrium population are obtained under the assumption that there is an infinite number of possible alleles. It is found that the theory for random mating populations holds if the effective population number is N_e = N'/(1 + F_IS), where F_IS is the inbreeding coefficient at equilibrium when N is infinite and N' is the reciprocal of the probability that two gametes contributing to random separate adults come from the same parent. When there is a binomial distribution of successful gametes emanating from each adult, N' = N. An approximation to the probability that an allele A survives if it is originally present in one AĀ heterozygote is found to be 2(N'/N)( F_ISs₁ + (1 - F_IS) s₂), where s₁ and s₂ are the selective advantages of AA and AĀ in comparison with ĀĀ. In the last section it is shown that if there is partial full sib mating and binomial offspring distributions N _e = N/(1 + 3F_IS).

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