Joint Effects of Pleiotropic Selection and Stabilizing Selection on the Maintenance of Quantitative Genetic Variation at Mutation-Selection Balance

Corresponding author: Xu-Sheng Zhang, Animal and Population Biology, University of Edinburgh, W. Mains Rd., Edinburgh EH9 3JT, United Kingdom., xu-sheng.zhang{at}ed.ac.uk (E-mail)

Communicating editor: J. B. WALSH

In quantitative genetics, there are two basic "conflicting" observations: abundant polygenic variation and strong stabilizing selection that should rapidly deplete that variation. This conflict, although having attracted much theoretical attention, still stands open. Two classes of model have been proposed: real stabilizing selection directly on the metric trait under study and apparent stabilizing selection caused solely by the deleterious pleiotropic side effects of mutations on fitness. Here these models are combined and the total stabilizing selection observed is assumed to derive simultaneously through these two different mechanisms. Mutations have effects on a metric trait and on fitness, and both effects vary continuously. The genetic variance (V_G) and the observed strength of total stabilizing selection (V_s,t) are analyzed with a rare-alleles model. Both kinds of selection reduce V_G but their roles in depleting it are not independent: The magnitude of pleiotropic selection depends on real stabilizing selection and such dependence is subject to the shape of the distributions of mutational effects. The genetic variation maintained thus depends on the kurtosis as well as the variance of mutational effects: All else being equal, V_G increases with increasing leptokurtosis of mutational effects on fitness, while for a given distribution of mutational effects on fitness, V_G decreases with increasing leptokurtosis of mutational effects on the trait. The V_G and V_s,t are determined primarily by real stabilizing selection while pleiotropic effects, which can be large, have only a limited impact. This finding provides some promise that a high heritability can be explained under strong total stabilizing selection for what are regarded as typical values of mutation and selection parameters.

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