Population distribution and synchronized dynamics in a metapopulation model in two geographic scales

In this paper, a metapopulation model composed of patches distributed in two spatial scales is proposed in order to study the stability of synchronous dynamics. Clusters of patches connected by short-range dispersal are assumed to be formed. Long distance dispersal is responsible to link patches that are in different clusters. During each time step, we assume that there are three processes involved in the population dynamics: (a) the local dynamics, which consists of reproduction and survival; (b) short-range dispersal of individuals between the patches of each cluster; and (c) the movement between the clusters. First we present an analytic criterion for regional synchronization, where the clusters evolve with the same dynamics. We then discuss the possibility of a full synchronism, where all patches in the network follow the same time evolution. The existence of such a state is not always ensured, even considering that all patches have the same local dynamics. It depends on how the individuals are distributed among the local patches that compose a cluster after long-range dispersal takes place in the regional scale. An analytic criterion for the stability of synchronized trajectories in this case is obtained.