N

is often cited as sufficient to prevent substantial genetic differentiation at a diploid locus in the infinite island model

As seen by examining this equation, when m is between zero and one, the effect of gene flow is to reduce the expected value of the fixation index by reducing the probability of identity both in the present (time t) and in the past (time t - 1). This makes intuitive sense: if gene flow introduces an allele copy into a subpopulation, it has not been present for sampling events between time t - 1 and time t. Therefore an allele copy introduced by gene flow has not yet had the opportunity to become identical by descent at time t and it cannot contribute to the frequency of autozygous genotypes gauged by the fixation index.

Equation 4.52 is really an expression for the balance of gene flow and genetic drift among multiple subpopulations so F is identical to FST. We can make this equation more general by using it to get an expected value of the fixation index among populations (Fst) in the infinite island model when allele frequency differentiation among subpopulations by genetic drift and allele frequency homogenization among subpopulations by gene flow, reach a net balance. With the assumption that the migration rate is small and much, much less than the effective population size (see Math box 4.1), an approximation for the expected amount of fixation among subpopulations at equilibrium in an infinite island population is:

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