The proposed research will develop new mathematical models that incorporate both demography and coevolution into spatially structured host-parasite interactions. Because these new models will allow mathematical analysis, they represent a substantial advance over past work that has relied exclusively on numerical simulations. Analysis of these models will elucidate the role that gene flow and coevolution play in shaping the geographic distributions and range limits of parasites. In addition, the results will generate testable predictions for how changes in rates of gene flow alter the equilibrium sizes of parasite geographic ranges. These predictions become increasingly important as natural patterns of gene flow become disrupted through habitat fragmentation, potentially leading to range expansions of parasites and infectious diseases.