Migration and mutation in stochastic models of gene frequency change

✍ Scribed by J. A. Sved; B. D. H. Latter

• Publisher: Springer
• Year: 1977
• Tongue: English
• Weight: 683 KB
• Volume: 5
• Category: Article
• ISSN: 0303-6812
• DOI: 10.1007/bf00275807

✦ Synopsis

Migration has in the past been introduced deterministically into stochastic gene frequency models. Migration at rate m then reduces the between-population variability by a factor of (1 - m)2 each generation. We show that with stochastic migration, whether of fixed or variable numbers of individuals, a positive term delta m is added to the variance. As a result of the delta m term, the equilibrium value of the between-population variability is increased compared to the corresponding value for deterministic migration by a factor of approximately (1 - m)-2 for small m. An equivalent result is derived for mutation, using the infinite allele model for a single population. We show in addition that these results may be derived much more simply by use of identity-by-descent probability methods, but only if a modified definition of the probability of identity-by-descent is used, involving the sampling with instead of without replacement of pairs of genes from the population.