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Mutation-selection balance and continuum-of-alleles models

Authors
Journal
Mathematical Biosciences
0025-5564
Publisher
Elsevier
Publication Date
Volume
91
Issue
1
Identifiers
DOI: 10.1016/0025-5564(88)90024-7

Abstract

Abstract A discrete-time model for the evolution of type densities in a haploid population that is governed by mutation and selection is analysed. Important special cases are the classical one-locus multiallele model, models like the stepwise-mutation model, and models with a continuum of possible allelic effects on a quantitative trait. Using methods from functional analysis, it is proved that for very general mutation and selection regimes a uniquely determined positive equilibrium density exists that is globally stable. Moreover, an upper bound for the equilibrium variance that can be maintained by a balance between mutation and Gaussian stabilizing selection is derived.

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