In invasion ecology, when a species arrives in an ecosystem and interacts with native organisms, boom-and-bust patterns frequently emerge. Typically, the invader enjoys temporary exponential population growth followed by similarly steep decline to intermediate abundances or extinction. Using Lotka-Volterra type differential equations, Kondoh has previously shown numerically that adaptive mismatching can result in boom-and-bust patterns. In the present study we extend this work and investigate the success of invasion in a model with spatially explicit structure.

The model describes the dynamics of an invading consumer species and two classes of native resource species that differ in their strength of interaction with the consumer but compete amongst each other. In the simplest case of a mainland-island structure, migration of naive resource from an uninfected mainland influences the insular resource's adaptation process and along with it the consumer's population dynamics.

Using both analytical and numerical methods, we investigate how migration affects boom-and-bust patterns and invasion success. The analysis also allows predicting in which part of a meta-population invasion is most likely to occur. In general, the results argue for an important role of population structure in the process of species invasion.