Spatial Models of Metapopulations and Benthic Communities in Patchy Environments

Book excerpt: The distribution of organisms in space has important consequences for the function and structure of ecological systems. Such distributions are often referred to as patchy, and a patch-based approach to modeling ecosystem dynamics has become a major research focus. These models have been used to explore a wide range of questions concerning population, metapopulation, community, and landscape ecology, in both terrestrial and aquatic systems. In this dissertation I develop and analyze a series of spatial models to study the dynamics of metapopulations and marine benthic communities in patchy environments. All the models have the form of a discrete-time Markov chain, and assume that the landscape is composed of discrete patches, each of which is in one of a number of possible states. The state of a patch is determined by the presence of an individual of a given species, a local population, or a group of species, depending on the spatial scale of the model. The research is organized into two main parts as follows. In the first part, I present an analysis of the effects of habitat destruction on metapopulation persistence. Theoretical studies have already shown that a metapopulation goes extinct when the fraction of suitable patches in the landscape falls below a critical threshold (the so called extinction threshold). This result has become a paradigm in conservation biology and several models have been developed to calculate extinction thresholds for endangered species. These models, however, generally do not take into account the spatial arrangement of habitat destruction, or the actual size of the landscape. To investigate how the spatial structure of habitat destruction affects persistence, I compare the behavior of two models: a spatially implicit patch-occupancy model (which recreates the extinction patterns found in other models) and a spatially explicit cellular automaton (CA) model. In the CA, I use fractal arrangements of suitable and unsuitable patches to simulate habitat destruction and show that the extinction threshold depends on the fractal dimension of the landscape. To investigate how habitat destruction affects persistence in finite landscapes, I develop and analyze a chain-binomial metapopulation (CBM) model. This model predicts the expected extinction time of a metapopulation as a function of the number of patches in the landscape and the number of those patches that are suitable for the population. The CBM model shows that the expected time to extinction decreases greater than exponentially as suitable patches are destroyed. I also describe a statistical method for estimating parameters for the CBM model in order to evaluate metapopulation viability in real landscapes. In the second part, I develop and analyze a series of Markov chain models for a rocky subtidal community in the Gulf of Maine. Data for the model comes from ten permanent quadrats (located on Ammen Rock Pinnacle at 30 meters depth) monitored over an 8-year period (1986-1994). I first parameterize a linear (homogenous) Markov chain model from the data set and analyze it using an array of novel techniques, including a compression algorithm to classify species into functional groups, a set of measures from stochastic process theory to characterize successional patterns, sensitivity analyses to predict how changes in various ecological processes effect community composition, and a method for simulating species removal to identify keystone species. I then explore the effects of time and space on successional patterns using log-linear analysis, and show that transition probabilities vary significantly across small spatial scales and over yearly time intervals. I examine the implications of these findings for predicting equilibrium species abundances and for characterizing the transient dynamics of the community. Finally, I develop a nonlinear Markov chain for the rocky subtidal community. The model is parameterized using maximum likelihood methods to estimate density-dependent transition probabilities. I analyze the best fitting models to study the effects of nonlinear species interactions on community dynamics, and to identify multiple stable states in the subtidal system.