Transient dynamics of predator-prey metapopulations: Effects of spatial structure, heterogeneity, and stochasticit

Understanding the mechanisms that allow coexistence or lead to extinction of predators and prey in natural systems has remained a major goal of both theoretical and empirical ecology ever since the problem was first identified. A great deal of progress has been made by studying the asymptotic dynamics of well-mixed models of local populations, as well as considering spatial subdivision of regional populations into patchily distributed subpopulations. However, complex systems such as spatially extended sets of ecological populations can display very complex dynamics that are not accounted for in most of the traditional asymptotic analyses.;This dissertation focuses on the dynamics of predator-prey metapopulations in transient and asymptotic regimes, with attention to dynamics that result simply from the existence of spatial subdivision (Chapter 2), heterogeneity in dispersal patterns (Chapter 3) and stochasticity (Chapter 4).;Chapter 2 shows that even when asymptotic dynamics suggest coexistence of a predator and its prey species, transient dynamics can lead to rapid extinction, depending on dispersal rates, initial conditions, and system size.;Chapter 3 shows that in a regime of strong coupling among a small to moderate number of local patches, the structure of the dispersal network can have a very strong impact on the dynamics of the system, with implications for persistence on ecological time scales. In particular, irregular dispersal networks lead to much longer transient dynamics of lower amplitude than the asymptotic dynamics more often observed in systems with regular lattice dispersal networks. Since dispersal patterns in nature are almost certainly irregular in space, this result has important implications for modeling predator-prey coexistence in natural systems.;Chapter 4 addresses the dynamics of a Markov chain model with demographic stochasticity, in terms of the frequency content of simulated time series, the number of clusters of patches with similar dynamics through time, and the probability and time to extinction. The former two analyses provide indirect but valuable information about the dynamics of the stochastic model relative to the deterministic model it is based on, with some implications for coexistence. Consistent with the results from Chapter 3, the stochastic model is sometimes less extinction prone than we would predict from a deterministic analysis.