Measuring Resilience in Stochastic Systems

This paper develops mathematical and statistical techniques for measuring the resilience of inherently stochastic ecological systems. To correspond to the deterministic idea of resilience measured by the return time to equilibrium following perturbation, resilience in stochastic systems is defined as the variability in population densities relative to environmentally driven variability in population growth rates. Stochastic resilience defined in this way is calculated from a community matrix describing the average interaction strengths within and among species. The procedure to calculate stochastic resilience is demonstrated on simulated data sets consisting of time series of population densities. The simplicity of the procedure makes it a potential tool for application to a wide range of ecological communities.