Optimal Network Architectures for Spatially Structured Populations with Heterogeneous Diffusion

The motivation of this article is to derive new management guidelines to maximize the overall population size using popular management and conservation strategies, such as protected marine areas and ecological corridors. These guidelines are based on the identification of the network architectures for which the total population size is maximized. Describing the biological roles of the typical network variables in the fate of the population is a classic problem with many practical applications. This article suggests that the optimal network architecture relies heavily on the degree of mobility of the population. The recommended network architecture for populations with reduced mobility (in the absence of cost of dispersal and landscapes made up of many sources) is a graph with a patch that has routes toward any other patch with a lower growth rate. However, for highly mobile populations there are many possible network architectures for which the total population size is maximized (e.g., any cyclic graph). We have paid special attention to species with symmetric movement in heterogeneous landscapes. A striking result is that the network architecture does not have any influence on the total population size for highly mobile populations when any pair of different patches can be connected by a sequence of paths.