The spread of an advantageous allele across a barrier: the effects of random drift and selection against heterozygotes

A local barrier to gene flow will delay the spread of an advantageous allele. Exact calculations for the deterministic case show that an allele that is favorable when rare is delayed very little even by a strong barrier; its spread is allowed by a time proportional to log((B/σ)√2S)/S, where B is the barrier strength, σ the dispersal range, and fitnesses are 1:1 + S:1 + 2S. However, when there is selection against heterozytes, such that the allele cannot increase from low frequency, a barrier can cause a much greater delay. If gene flow is reduced below a critical value, spread is entirely prevented. Stochastic simulations show that with additive selection, random drift slows down the spread of the allele, below the deterministic speed of σ√2S. The delay to the advance of an advantageous allele caused by a strong barrier can be substantially increased by random drift and increases with B/(2Sρσ2) in a one-dimensional habitat of density ρ. However, with selection against heterozygotes, drift can facilitate the spread and can free an allele that would otherwise be trapped indefinitely by a strong barrier. We discuss the implications of these results for the evolution of chromosome rearrangements.