The spatial distribution of transient alleles in a subdivided population: a simulation study

The spatial distributions of newly introducted alleles in a subdivided population are generated using a computer program to model the processes of selection, gene flow and genetic drift. Advantageous, neutral and deleterious alleles are considered, and certain aspects of the patterns generated by new alleles that are ultimately fixed and ultimately lost are examined. To characterize the spatial pattern of rare alleles, the distribution, P(i), the probability that the new allele is found in exactly i local populations before it is lost, is defined and estimated from the simulations. The shape of the P(i) distribution is surprisingly similar for selected and neutral alleles. For advantageous alleles going to fixation, the "wave of advance" is set up quickly, but stochastic effects reduce the wave speed from Fisher's (1937) value. Gene flow is much more effective in dispersing alleles in a two-dimensional array than in one dimension. Long distance gene flow has a much smaller effect in two dimensions than in one dimension.