Density dependent dispersal: A direct explanation for the complexities of insect outbreaks

Insect outbreaks have potentially serious economic and social impacts throughout the world. Rangeland grasshoppers in the Western United States experience very large changes in densities in patches that also range across many scales. Approaches that have looked for explanations by nonspatial feedbacks and environmental drivers have yielded no major success in describing, much less predicting, these outbreaks.

A simple model based on a cellular automata framework shows dynamics that mimic the empirical results of fifty years of sampling. The results demonstrate both a temporal signal and a spatial signal that correspond to the observed outbreaks. Instead of simple density dependent mortality, as has been described in field experiments, a form of density dependent dispersal is applied. If the density of individuals in any cell is greater than a nominal carrying capacity, the individuals disperse. This dispersal acts in a manner that gives rise to a power law distribution in outbreak sizes and a fractal spatial pattern for outbreak distributions.

Since the grasshopper populations are a mixture of species with differing dispersal distances, the model accounts for differential dispersal behavior and accounts for potentially long distance dispersal as occurs in several rangeland species.

The model framework allows for exploration of various pest management strategies and their efficacy with respect to outbreaks. The model shows that standard methods of pest management do not eliminate outbreaks over time and that scale invariance is not altered.