The balance between pleiotropic mutation and selection, when alleles have discrete effects

Waxman, David (2003) The balance between pleiotropic mutation and selection, when alleles have discrete effects. Theoretical Population Biology, 63 (2). pp. 105-114. ISSN 0040-5809

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Abstract

The theory of pleiotropic mutation and selection is investigated and developed for a large population of asexual organisms. Members of the population are subject to stabilising selection on Ω phenotypic characters, which each independently affect fitness. Pleiotropy is incorporated into the model by allowing each mutation to simultaneously affect all characters. To expose differences with continuous-allele models, the characters are taken to originate from discrete-effect alleles and thus have discrete genotypic effects. Each character can take the values n×Δ where n=0,±1,±2,…, and the splitting in character effects, Δ, is a parameter of the model. When the distribution of mutant effects is normally distributed around the parental value, and Δ is large, a “stepwise” model of mutation arises, where only adjacent trait effects are accessible from a single mutation. The present work is primarily concerned with the opposite limit, where Δ is small and many different trait effects are accessible from a single mutation.

In contrast to what has been established for continuous-effect models, discrete-effect models do not yield a singular equilibrium distribution of genotypic effects for any value of Ω. Instead, for different values of Ω, the equilibrium frequencies of trait values have very different dependencies on Δ. For Ω=1 and 2, decreasing Δ broadens the width of the frequency distribution and hence increases the equilibrium level of polymorphism. For all sufficiently large values of Ω, however, decreasing Δ decreases the width of the frequency distribution and the equilibrium level of polymorphism. The connection with continuous trait models follows when the limit Δ→0 is considered, and a singular probability density of trait values is obtained for all sufficiently large Ω.

Item Type: Article
Keywords: Pleiotropy; Mutation selection balance; Stabilising selection; Quantitative traits; Asexual population
Schools and Departments: School of Life Sciences > Biology and Environmental Science
Depositing User: David Waxman
Date Deposited: 06 Feb 2012 20:18
Last Modified: 26 Jul 2012 08:27
URI: http://sro.sussex.ac.uk/id/eprint/25259
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