title: Mutation and selection in a large population.
abstract: In this paper we study a large, but finite population, in which mutation and selection occur at a single genetic locus in a diploid organism. We provide theoretical results for the equilibrium allele frequencies, their variances and covariances and their equilibrium distribution, when the population size is larger than the reciprocal of the mean allelic mutation rate. We are also able to infer that the equilibrium distribution of allele frequencies takes the form of a constrained multivariate Gaussian distribution. Our results provide a rapid way of obtaining useful information in the case of complex mutation and selection schemes when the population size is large. We present numerical simulations to test the applicability of our theoretical formulations. The results of these simulations are in very reasonable agreement with the theoretical predictions.
authors.affiliation: Centre for the Study of Evolution, School of Life Sciences, University of East Sussex, Brighton BN1 9QG, East Sussex, UK. J.R.Peck@sussex.ac.uk
authors.forename: J R
authors.initials: JR
authors.lastname: Peck
authors.forename: D
authors.initials: D
authors.lastname: Waxman
authors.forename: A
authors.initials: A
authors.lastname: Cruikshank
mesh_terms: D000483:Alleles; D000818:Animals; D005075:Biological Evolution; D003198:Computer Simulation; D014644:Genetic Variation / Q000235:genetics*; D005828:Genetics, Population / Q000379:methods*; D006801:Humans; D008957:Models, Genetic; D015233:Models, Statistical; D009154:Mutation / Q000235:genetics*; D010641:Phenotype; D011157:Population Dynamics; D012641:Selection, Genetic