Synchronisation Between Individuals and the Dynamics of Linked Populations

Recent research into the dynamics of linked populations, using lattices of difference equations, suggest that coupling by migration between populations often has no effect on the stability of the populations within the system. An underlying assumption of these models is that inter-population movement is segregated in time from other population processes. Here I present an individual-based model which does not require this restriction, and show that the behaviour of the model is largely unaffected by reducing the synchrony between migration events. This holds even if migration and reproduction events are completely randomly mixed. Another restriction of several previous models is that migration only occurs to nearest-neighbour sites. Again, an individual-based model is presented which allows individuals to move several times per generation and hence allow them to reproduce at a site far removed from their position at the start of the generation. This generalisation is shown to have little effect on the stability of local population. Local coupling does not appear to affect whether the equilibrium is locally stable or unstable, however, it does affect qualitative features of unstable dynamics.