Genetical Research

Research Article

The divergence of a polygenic system subject to stabilizing selection, mutation and drift

Nick Bartona1

a1 Department of Genetics and Biometry, University College London, 4 Stephenson Way, London NW1 2HE

Summary

Polygenic variation can be maintained by a balance between mutation and stabilizing selection. When the alleles responsible for variation are rare, many classes of equilibria may be stable. The rate at which drift causes shifts between equilibria is investigated by integrating the gene frequency distribution 2NΠ(pq)4Nμ−1. This integral can be found exactly, by numerical integration, or can be approximated by assuming that the full distribution of allele frequencies is approximately Gaussian. These methods are checked against simulations. Over a wide range of population sizes, drift will keep the population near an equilibrium which minimizes the genetic variance and the deviation from the selective optimum. Shifts between equilibria in this class occur at an appreciable rate if the product of population size and selection on each locus is small (Nsα2 < 10). The Gaussian approximation is accurate even when the underlying distribution is strongly skewed. Reproductive isolation evolves as populations shift to new combinations of alleles: however, this process is slow, approaching the neutral rate (≈ μ) in small populations.

(Received December 04 1987)

(Revised January 26 1989)

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