Coupled metapopulation dynamics with patch modification and memory

Abstract

All organisms alter their abiotic environment, and these modifications impact other members of the biotic community. By shaping, for example, the physical structure, resource availability, or pathogen prevalence in its local habitat, an individual of one species might enhance or diminish the future success of others. What will be the dynamics and outcomes when these environmentally-mediated interactions play out across a landscape? We introduce a simple yet flexible model to capture the dynamics of ecological communities where the state of a local patch is determined by its last occupant, and the ability of species to colonize a patch is determined by the patch state. Based in the metapopulation framework, our model can be used to describe and analyze a wide range of ecological scenarios, from the coexistence of tropical trees to immune-mediated pathogen interactions. We show that this model can exhibit diverse behaviors, including the robust coexistence of many ‘ecosystem engineers’, and present general conditions for coexistence to occur. For a simplified version of our model, stable coexistence of species is possible if and only if each species modifies patches to disfavor recolonization by conspecifics. For arbitrary symmetric patch memory effects (i.e. when the colonization rate of species i in patches last occupied by species j is equal to the colonization rate of species j in patches last occupied by species i), stable coexistence requires the matrix of memory effects to have exactly one positive eigenvalue. We show that this new stability criterion generalizes intuitive notions about inter- and intra-specific effects. Furthermore, stability in this model implies a very general relationship between diversity and robustness, which cannot be predicted by modes that omit patch memory. We will also present preliminary conclusions for systems with nonsymmetric patch memory effects, using a combination of informative special cases and numerical simulations.