The Robustness of Ecological Communities: Theory and Application.

Abstract

As ecologists, we frequently rely on mathematical models to formulate and test our hypotheses concerning ecological communities. An important problem is whether and why interacting species coexist. Once our hypothesis for why coexistence happens is translated into the form of a model, we check to see whether the proposed mechanism could indeed lead to coexistence. Usually, the golden standard for evaluating coexistence has been to check whether the model possesses an all-positive, stable stationary state (where this state may be an equilibrium point, a limit cycle, or a chaotic or otherwise aperiodic orbit). This perspective, however, ignores another important aspect of the same problem: the robustness of the stationary state against parameter changes. We may find coexistence in a model, but if that coexistence collapses after even very slight parameter perturbations, it is not actually expected to hold. The purpose of this dissertation is fourfold. First, it aims at working out the quantitative, formal mathematical machinery for evaluating the robustness of ecological communities under complex circumstances, such as ones involving population structure or nonequilibrium community dynamics. Second, it applies this machinery to various ecological problems, ranging from the theoretical to the applied, to demonstrate the kinds of uses robustness analysis has. Among the models discussed are the sensitivity of a field-parametrized model of annual plant competition to parameter changes, the analysis of coexistence in the tolerance-fecundity tradeoff model, and predicting species diversity in a model of interspecific facilitation. Third, it takes a look at some of the consequences of robustness analysis for community patterns, arguing that the elementary biological fact that species are by and large discrete, well-defined entities is a natural consequence of the basic structure of ecological interactions, not of any model details. Fourth, the dissertation synthesizes some of the general conclusions of robustness analysis to formalize the concept of the ecological niche, revealing a fundamental unity between functional, temporal, and spatial mechanisms of diversity maintenance.