Stochasticity and bistability in insect outbreak dynamics

Abstract

There is a long history in ecology of using mathematical models to identify deterministic processes that may lead to dramatic population dynamic patterns like boom-and-bust outbreaks. Stochasticity is also well-known to have a significant influence on the dynamics of many ecological systems, but this aspect has received far less attention. Here, we study a stochastic version of a classic bistable insect outbreak model to reveal the role of stochasticity in generating outbreak dynamics. We find that stochasticity has strong effects on the dynamics and that the stochastic system can behave in ways that are not easily anticipated by its deterministic counterpart. Both the intensity and autocorrelation of the stochastic environment are important. Stochasticity with higher intensity (variability) generally weakens bistability, causing the dynamics to spend more time at a single state rather than jumping between alternative stable states. Which state the population tends toward depends on the noise color. High-intensity white noise causes the insect population to spend more time at low density, potentially reducing the severity or frequency of outbreaks. However, red (positively autocorrelated) noise can make the population spend more time near the high density state, intensifying outbreaks. Under neither type of noise do early warning signals reliably predict impending outbreaks or population crashes.