Stability under Environmental Stress: Resistance, Resilience, Persistence, and Variability

Abstract

Four main contributions are made toward understanding stability and clarifying the ambiguity that has surrounded the term stability in the past. Four different aspects of the response of populations to environmental stress.sbd.resistance, resilience, persistence, and variability.sbd.are given mathematical formulations. Methods are given to analyze a differential equation model of population growth for resistance and persistence, while resilience corresponds to the traditional Lyapunov asymptotic stability. The relation of resistance and resilience to each other depends on the underlying characteristics of negative feedback to population changes and sensitivity of the growth rate to the environment. Strong feedback mechanisms independent of the environmental factor causing the stress increase both resilience and resistance, but if the feedback mechanism makes the population growth rate sensitive to an environmental factor, the amount of resilience and resistance under changes in that factor will be inversely related. Increased diversity of resources causes increased resistance to changes in those resources but no significant change in resilience, pointing toward a possible resolution of the stability-diversity question.