A model of coevolution and local adaptation between hosts and parasites in continuous space

Previous host-parasite coevolutionary theory has focused on understanding the determinants of local adaptation using spatially discrete models. However, these studies fall short of describing patterns of host-parasite local adaptation across spatial scales. In contrast, empirical work demonstrates patterns of adaptation depend on the scale at which they are measured. Here, we propose a model of host-parasite coevolution in continuous space that naturally leads to a scale-dependent definition of local adaptation and a formal definition for the spatial scale of coevolution. In agreement with empirical findings, our model implies patterns of adaptation vary across spatial scales. When measured on spatial scales shorter than the scale of coevolution, we find the farther dispersing species is locally adapted. However, when measured at longer spatial scales, the opposite pattern is observed. We discuss our results in relation to those found using spatially discrete models and to conclusions drawn from empirical studies, and provide an example of our how our results can be used to inform the design of empirical studies.