Résumé
This study addresses the question of how spatial heterogeneity in prey productivity and migration act to determine geographic patterns in antagonistic coevolution with a predator. We develop and analyze a quantitative coevolutionary model for a predator‐prey interaction. If the model is modified appropriately, the results could broadly apply to multispecies communities and to herbivore‐plant, parasite‐host, and parasitoid‐host associations. Model populations are distributed over a gradient in prey birth rate (as a measure of productivity). Each population, in each patch, is made up of a suite of strains. Each strain of the predator has a certain ability to successfully attack each strain of the prey. We consider scenarios of isolated patches, global migration, and stepping‐stone (i.e., local) migration over a linear string of patches. The most pervasive patterns are the following: investments in predator offense and prey defense are both maximal in the patches of highest prey productivity; when there are no constraints on maximal investment, mean predation evolves to highest levels in the most productive patches; similarly, the predator has a greater impact (measured as the percentage reduction in prey density) on the prey population in high productivity patches as compared with low productivity ones—in spite (even after evolution) of prey abundance being highest in the most productive patches; and migration has the net effect of shunting relatively offensive and defensive strains from productive patches to nonproductive ones, potentially resulting in the elimination of otherwise rare, low‐investment clones. A modification of the model to gene‐for‐gene type interactions predicts that generalist strains (in terms of the range of strains the predator can exploit or the prey can fend off) dominate in productive areas of the prey, whereas specialists prevail in marginal habitats. Assuming a wide range of productivities over the prey's geographical distribution, the greatest strain diversity should be found in habitats of intermediate productivity. We discuss the implications of our study for adaptation and conservation. Empirical studies are in broad accord with our findings.