Landscapes are dynamic mosaics driven by disturbances and successional processes.  The importance of these dynamics for the population performance of mobile species is uncertain, despite their potential relevance to species conservation.  I present a simple model of mobile individuals in a spatially and temporally variable landscape to explore the interaction of local dispersal and spatiotemporal structure and their consequences at landscape scale.  I show the importance of site fidelity for determining whether local variation in conditions is relevant for a population and that increasing site fidelity improves population growth when local environmental variation is temporally autocorrelated.  Spatial autocorrelation of local variation also plays an important role in population performance by reducing the cost of local dispersal.  Using a spatially explicit simulation with local dispersal and density dependence linked to dynamic neutral landscape models, I further illustrate that under most conditions, population sizes are depressed in dynamic landscapes compared to static landscapes with the same quality and amount of habitat.  However, increasing spatiotemporal autocorrelation dramatically increases population size, which converges on abundance in the equivalent static landscape.  Thus, I establish the range of conditions under which the assumption of static conditions, common to many spatially explicit population models, is valid.  Finally, I show that the relation between spatiotemporal structure and population performance may often be non-linear, with a threshold degree of autocorrelation required for persistence.  This prediction appears to be qualitatively robust, though the relative sensitivity of species depends on life history.   Overall, these results have important implications for the management of dynamic landscapes, such as multiple use reserves.