Abstract

Theoretical Notions of Ecological Stability and Their Relation to Temporal Variability

Student: Chace Covington (Francis Marion University
Faculty Mentor: Craig Jackson (OWU Department of Mathematics and Computer Science)

Ecological stability describes how an ecosystem, such as a freshwater plankton community, behaves after an environmental change. Measures of stability can be made using experimental data or by using theoretical community matrices that describe how individual species are related in the ecosystem. If there is a link between empirical and theoretical measures of stability, understanding that link will allow ecologists to better understand how outside forces, such as human actions, affect the long-term health of ecosystems. In our study we use computer simulations to determine mathematical relationships between several different measurements of ecological stability.

Ecological stability describes how populations of species in an ecosystem behave after a disturbance and can be measured by empirically and theoretically. Our experiment uses a firstorder multivariate autoregressive model framework to explore the possible relationships between empirical and theoretical measures of ecological stability and the possible relationships between different theoretical measures of ecological stability. The empirical measures of stability included in this study are the average population coefficient of variation, the weighted average population coefficient of variation, and the community coefficient of variation. All theoretical measures of stability included are derived from a theoretical community matrix and include asymptotic resilience, initial resilience and reactivity, and intrinsic stochastic invariability. We find no evidence for any relationship between empirical and theoretical measures of ecological stability. This result is in agreement with previous experimental research by Downing, Jackson, and Plunket. However, we do observe clear relationships between different theoretical measures of ecological stability. We formalize these relationships with inequalities similar to those derived by Arnoldi et al. for continuous models.