EFFECTS OF PLEIOTROPY ON PREDICTIONS CONCERNING MUTATION-SELECTION BALANCE FOR POLYGENIC TRAITS

Michael Turelli ¹

¹ Department of Genetics, University of California, Davis, California 95616

Previous mathematical analyses of mutation-selection balance for metric traits assume that selection acts on the relevant loci only through the character(s) under study. Thus, they implicitly assume that all of the relevant mutation and selection parameters are estimable. A more realistic analysis must recognize that many of the pleiotropic effects of loci contributing variation to a given character are not known. To explore the consequences of these hidden effects, I analyze models of two pleiotropically connected polygenic traits, denoted P₁ and P₂. The actual equilibrium genetic variance for P₁, based on complete knowledge of all mutation and selection parameters for both P₁ and P₂, can be compared to a prediction based solely on observations of P₁. This extrapolation mimics empirically obtainable predictions because of the inevitability of unknown pleiotropic effects. The mutation parameters relevant to P ₁ are assumed to be known, but selection intensity is estimated from the within-generation reduction of phenotypic variance for P ₁. The extrapolated prediction is obtained by substituting these parameters into formulas based on single-character analyses. Approximate analytical and numerical results show that the level of agreement between these univariate extrapolations and the actual equilibrium variance depends critically on both the genetic model assumed and the relative magnitudes of the mutation and selection parameters. Unless per locus mutation rates are extremely high, i.e., generally greater than 10^-4, 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, i.e., within a factor of two, over a wide range of parameter values. In contrast, an alternative approximation that applies for moderate and low per locus mutation rates predicts that the extrapolation will generally overestimate the true equilibrium variance unless there is little selection associated with hidden effects. The tendency to overestimate is understandable because selection acts on all of the pleiotropic manifestations of a new mutation, but equilibrium covariances among the characters affected may not reveal all of this selection. This casts doubt on the proposal that much of the additive polygenic variance observed in natural populations can be explained by mutation-selection balance. It also indicates the difficulty of critically evaluating this hypothesis.

This article has been cited by other articles:

				X. Gu Evolutionary Framework for Protein Sequence Evolution and Gene Pleiotropy Genetics, April 1, 2007; 175(4): 1813 - 1822. [Abstract] [Full Text] [PDF]

				S. Estes, B. C. Ajie, M. Lynch, and P. C. Phillips Spontaneous Mutational Correlations for Life-History, Morphological and Behavioral Characters in Caenorhabditis elegans Genetics, June 1, 2005; 170(2): 645 - 653. [Abstract] [Full Text] [PDF]

				X.-S. Zhang, J. Wang, and W. G. Hill Redistribution of Gene Frequency and Changes of Genetic Variation Following a Bottleneck in Population Size Genetics, July 1, 2004; 167(3): 1475 - 1492. [Abstract] [Full Text] [PDF]

				M. Turelli and N. H. Barton Polygenic Variation Maintained by Balancing Selection: Pleiotropy, Sex-Dependent Allelic Effects and G x E Interactions Genetics, February 1, 2004; 166(2): 1053 - 1079. [Abstract] [Full Text] [PDF]

				N. S. Wingreen, J. Miller, and E. C. Cox Scaling of Mutational Effects in Models for Pleiotropy Genetics, July 1, 2003; 164(3): 1221 - 1228. [Abstract] [Full Text] [PDF]

				X.-S. Zhang and W. G. Hill Joint Effects of Pleiotropic Selection and Stabilizing Selection on the Maintenance of Quantitative Genetic Variation at Mutation-Selection Balance Genetics, September 1, 2002; 162(1): 459 - 471. [Abstract] [Full Text] [PDF]

				X.-S. Zhang, J. Wang, and W. G. Hill Pleiotropic Model of Maintenance of Quantitative Genetic Variation at Mutation-Selection Balance Genetics, May 1, 2002; 161(1): 419 - 433. [Abstract] [Full Text] [PDF]

				D. Waxman and J. R. Peck Pleiotropy and the Preservation of Perfection Science, February 20, 1998; 279(5354): 1210 - 1213. [Abstract] [Full Text]