Effects of pleiotropy on predictions concerning mutation-selection balance for polygenic traits
Turelli, M.
Genetics 111(1): 165-195
1985
ISSN/ISBN: 0016-6731 PMID: 4029610 Document Number: 243375
To explore the consequences of the fact that many of the pleiotropic effects of loci contributing to variation in a given character are not known, models of 2 pleiotropically connected polygenic traits, P1 and P2, are analysed. The actual equilibrium genetic variance for P1, based on complete knowledge of all mutation and selection parameters for both P1 and P2, is compared to a prediction based solely on observations of P1. The mutation parameters relevant to P1 are assumed to be known, but selection intensity is estimated from the within-generation reduction in phenotypic variance for P1. The extrapolated prediction is obtained by substituting these parameters into formulas based on single-character analyses. Approximate analytical and numerical results show that unless mutation rates are high (generally >10-4 per locus), the widely used Gaussian approximation for genetic effects at individual loci is not applicable. Nevertheless, the Gaussian approximations predict that the true and extrapolated equilibria are in reasonable agreement (within a factor of 2) over a wide range of values of mutation rate and selection intensity. In contrast, an alternative approximation that applies for moderate and low mutation rates predicts that extrapolation will greatly overestimate the true equilibrium variance unless there is little selection associated with hidden effects. These conclusions cast doubt on the proposal that much of the additive polygenic variance observed in natural populations can be explained by a balance between mutation and selection, and also indicate the difficulty of critically evaluating this hypothesis.