Genetic variability and effective population size when local extinction and recolonization of subpopulations are frequent

Abstract

If a population (species) consists of n haploid lines (subpopulations) which reproduce asexually and each of which is subject to random extinction and subsequent replacement, it is shown that, at equilibrium in which mutational production of new alleles and their random extinction balance each other, the genetic diversity (1 minus the sum of squares of allelic frequencies) is given by 2N(e)v/(1 + 2N(e)v), where [Formula: see text] in which N is the harmonic mean of the population size per line, n is the number of lines (assumed to be large), lambda is the rate of line extinction, and v is the mutation rate (assuming the infinite neutral allele model). In a diploid population (species) consisting of n colonies, if migration takes place between colonies at the rate m (the island model) in addition to extinction and recolonization of colonies, it is shown that effective population size is [Formula: see text] If the rate of colony extinction (lambda) is much larger than the migration rate of individuals, the effective population size is greatly reduced compared with the case in which no colony extinctions occur (in which case N(e) = nN). The stepping-stone type of recolonization scheme is also considered. Bearing of these results on the interpretation of the level of genetic variability at the enzyme level observed in natural populations is discussed from the standpoint of the neutral mutation-random drift hypothesis.