Stochasticity-induced persistence in coupled social-ecological systems

Abstract

Stochasticity is often associated with negative consequences for population dynamics since a population may die out due to random chance during periods when population size is very low (stochastic fade-out). Here we develop a coupled social-ecological model based on stochastic differential equations that includes natural expansion and harvesting of a forest ecosystem, and dynamics of conservation opinions, social norms and social learning in a human population. Our objective was to identify mechanisms that influence long-term persistence of the forest ecosystem in the presence of noise. We found that most of the model parameters had a significant influence on the time to extinction of the forest ecosystem. Increasing the social learning rate and the net benefits of conservation significantly increased the time to extinction, for instance. Most interestingly, we found a parameter regime where an increase in the amount of system stochasticity caused an increase in the mean time to extinction, instead of causing stochastic fade-out. This effect occurs for a subset of realizations, but the effect is large enough to increase the mean time to extinction across all realizations. Such "stochasticity-induced persistence" occurs when stochastic dynamics in the social system generates benefits in the forest system at crucial points in its temporal dynamics. We conclude that studying relatively simple social-ecological models has the benefit of facilitating characterization of dynamical states and thereby enabling us to formulate new hypothesis about mechanisms that could be operating in empirical social-ecological systems.

Keywords: Endangered species; Extinction; Human-and-natural system; Human-environment system; Social-ecological system; Stochastic fade-out; Stochastic model.