Pleiotropic Model of 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, UK., xu-sheng.zhang{at}ed.ac.uk (E-mail)

Communicating editor: R. G. SHAW

A pleiotropic model of maintenance of quantitative genetic variation at mutation-selection balance is investigated. Mutations have effects on a metric trait and deleterious effects on fitness, for which a bivariate gamma distribution is assumed. Equations for calculating the strength of apparent stabilizing selection (V_s) and the genetic variance maintained in segregating populations (V_G) were derived. A large population can hold a high genetic variance but the apparent stabilizing selection may or may not be relatively strong, depending on other properties such as the distribution of mutation effects. If the distribution of mutation effects on fitness is continuous such that there are few nearly neutral mutants, or a minimum fitness effect is assumed if most mutations are nearly neutral, V_G increases to an asymptote as the population size increases. Both V_G and V_s are strongly affected by the shape of the distribution of mutation effects. Compared with mutants of equal effect, allowing their effects on fitness to vary across loci can produce a much higher V_G but also a high V_s (V_s in phenotypic standard deviation units, which is always larger than the ratio V_P/V_m), implying weak apparent stabilizing selection. If the mutational variance V_m is 10^-3V_e (V_e, environmental variance), the model can explain typical values of heritability and also apparent stabilizing selection, provided the latter is quite weak as suggested by a recent review.

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