Species interactions commonly coevolve as complex geographic mosaics of populations shaped by differences in local selection and gene flow. We use a haploid matching-alleles model for coevolution to evaluate how a pair of species coevolves when fitness interactions are reciprocal in some locations ("hot spots") but not in others ("cold spots"). Our analyses consider mutualistic and antagonistic interspecific interactions and a variety of gene flow patterns between hot and cold spots. We found that hot and cold spots together with gene flow influence coevolutionary dynamics in four important ways. First, hot spots need not be ubiquitous to have a global influence on evolution, although rare hot spots will not have a disproportionate impact unless selection is relatively strong there. Second, asymmetries in gene flow can influence local adaptation, sometimes creating stable equilibria at which species experience minimal fitness in hot spots and maximal fitness in cold spots, or vice versa. Third, asymmetries in gene flow are no more important than asymmetries in population regulation for determining the maintenance of local polymorphisms through coevolution. Fourth, intraspecific allele frequency differences among hot and cold spot populations evolve under some, but not all, conditions. That is, selection mosaics are indeed capable of producing spatially variable coevolutionary outcomes across the landscapes over which species interact. Altogether, our analyses indicate that coevolutionary trajectories can be strongly shaped by the geographic distribution of coevolutionary hot and cold spots, and by the pattern of gene flow among populations.
Keywords: antagonism; coevolution; geographic mosaic; hard and soft selection; hot and cold spots; mutualism.