Exact moment calculations for genetic models with migration, mutation, and drift

Rongwei (Rochelle) Fu, Alan E. Gelfand, Kent E. Holsinger

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

Using properties of moment stationarity we develop exact expressions for the mean and covariance of allele frequencies at a single locus for a set of populations subject to drift, mutation, and migration. Some general results can be obtained even for arbitrary mutation and migration matrices, for example: (1) Under quite general conditions, the mean vector depends only on mutation rates, not on migration rates or the number of populations. (2) Allele frequencies covary among all pairs of populations connected by migration. As a result, the drift, mutation, migration process is not ergodic when any finite number of populations is exchanging genes. In addition, we provide closed-form expressions for the mean and covariance of allele frequencies in Wright's finite-island model of migration under several simple models of mutation, and we show that the correlation in allele frequencies among populations can be very large for realistic rates of mutation unless an enormous number of populations are exchanging genes. As a result, the traditional diffusion approximation provides a poor approximation of the stationary distribution of allele frequencies among populations. Finally, we discuss some implications of our results for measures of population structure based on Wright's F-statistics.

Original languageEnglish (US)
Pages (from-to)231-243
Number of pages13
JournalTheoretical Population Biology
Volume63
Issue number3
DOIs
StatePublished - May 2003
Externally publishedYes

Fingerprint

Genetic Models
mutation
allele
gene frequency
Mutation
Gene Frequency
Population
Mutation Rate
gene
population structure
calculation
Islands
Genes
genes
statistics
matrix
loci
rate

Keywords

  • F-statistics
  • Genetic drift
  • Migration
  • Mutation
  • Population structure

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Exact moment calculations for genetic models with migration, mutation, and drift. / Fu, Rongwei (Rochelle); Gelfand, Alan E.; Holsinger, Kent E.

In: Theoretical Population Biology, Vol. 63, No. 3, 05.2003, p. 231-243.

Research output: Contribution to journalArticle

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