An individual–based model of plant–herbivore interactions was developed to test the potentially interactive effects of explicit space and coevolution on population and community dynamics. Individual plants and herbivores resided in cells on a lattice and carried linked interaction genes. Interaction strength between individual plants and herbivores depended on concordance between these genes (gene–for–gene coevolution). Mating and dispersal among individuals were controlled spatially within variably sized neighbourhoods. Without evolution we observed high–frequency plant–herbivore oscillations (blue spectra) with small individual neighbourhoods, and stochastic fluctuations (white spectra) with large neighbourhoods. Evolution resulted in decreased interaction strength, decreased herbivore–induced plant mortality, increased population sizes, and longer–term fluctuations (reddened spectra). Small herbivore neighbourhoods led to herbivore extinction only with evolution. To explore the increased population size response to evolution we ran simulations without evolution while tuning plant–herbivore interaction strength from high to none. We found that herbivore populations were maximized at intermediate levels of interaction strength that coincided with the interaction strength achieved when the system tuned itself through evolution. Overall, our model shows that the small–scale details of phenotypically variable individual–level interactions, leading to evolutionary dynamics, affect large–scale population and community dynamics.