Adaptation versus migration in demographically unstable populations

We analyze a model of the joint population and evolutionary dynamics of a diploid "island" population that receives a recurrent influx of immigrants from a hypothetical continent population. We derive a criterion for the initial spread of a rare allele when the island population dynamics initially are chaotic. By computing a Liapunov exponent, we show that this criterion depends on a generalization of the geometric mean absolute fitness of individuals heterozygous for the rare allele. This criterion applies regardless of whether the initial population is self-sustaining or not.