Spatial distributions of genotypes under isolation by distance.

The spatial distributions of single-locus diploid genotypes, produced within populations of sexually reproducing individuals under isolation by distance, are measured and characterized in detail by quantifying the join-counts for simulated model populations. The models more realistically reflect spatially explicit distributions of genotypes in populations, because unlike the classical theory, they include the stochasticity inherent in the process of matings between genotypes. This stochasticity causes the formation of large areas or patches containing mostly one homozygous genotype, which is not predicted by the classical theory. A number of previously uncharacterized features of the spatial structures produced under isolation by distance are revealed. Spatial autocorrelation measures based on counts of pairs of homozygotes are highly consistent quantifications of the concentrations of homozygotes in patchy genotypic distributions for a given level of dispersal. Most strikingly, the degree of intermixing of homozygotes with heterozygotes over small spatial scales is much higher than previously thought, unless dispersal is extremely limited (e.g., Wright's neighborhood size less than approximately 5.0). Among implications for studies of spatial structure of real populations, one is that the results provide a basis for using join-counts as estimators of gene dispersal based solely on genetic data.