Metacommunity Dynamics: Integrating Local Dynamics, Stochasticity, and Connectivity

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This project will develop a novel mathematical approach for describing the dynamics of ecological communities at large spatial scales, a description of dynamics called metacommunities. From a mathematical standpoint, the project will start with relatively simple descriptions of interactions among species, such as competition and predation, at small spatial scales, coupled with descriptions of connectivity, the way species move between locations. The mathematical descriptions will then be expanded to include more detailed and realistic descriptions of interactions among species and underlying environmental changes. The models will be analyzed to determine both long-term behavior and dynamics. The mathematical models will then be used to answer important ecological questions focused on how changes in habitat quality and availability and connectivity between different habitats will affect the composition and dynamics of these metacommunities. This, in turn, will provide information about how human activities that affect habitats and connectivity will affect species composition and dynamics and can provide guidance for both conservation and restoration efforts. The mathematical models of metacommunities used will be primarily phrased in discrete time with a time step of one year, both to reflect dynamics in seasonal environments and how data is gathered. The simplest models will focus only on species presence or absence and will be difference equations, so a relatively complete analytical treatment will be possible. Equilibria and their stability can be calculated. The more complex descriptions will all be phrased as integro-difference equations where time is discrete, but the state space is continuous. The underlying dependent variables will be density functions for the abundance of the species under consideration, and the kernels in the integro-difference equations will describe the underlying ecological dynamics. Initial analyses will be numerical with the expectation that analytic treatment of conditions for persistence and coexistence will be possible, building on recent mathematical work on integro-difference equations. To treat changing conditions through time, the kernels will be modified to include explicit time dependence. The mathematical analyses will then be used to answer the underlying ecological questions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.