Résumé
There has been a renewed controversy on the processes that determine evolution in spatially structured populations. Recent theoretical and empirical studies have suggested that parasites should be expected to be more ''prudent'' (less harmful and slower transmitting) when infection occurs locally. Using a novel approach based on spatial moment equations, we show that the evolution of parasites in spatially structured host populations is determined by the interplay of genetic and demographic spatial structuring, which in turn depends on the details of the ecological dynamics. This allows a detailed understanding of the roles of epidemiology, demography and network topology. Demographic turnover is needed for local interactions to select for prudence in the susceptible-infected models that have been the focus of previous studies. In diseases with little demographic turnover (as typical of many human diseases), we show that only parasites causing diseases with long-lived immunity are likely to be prudent in space. We further demonstrate why, at intermediate parasite dispersal, virulence can evolve to higher levels than predicted by non-spatial theory.