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 boomand-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 warningsignals reliably predict impending outbreaks or population
crashes
