Application of Catastrophe Theory to Population Dynamics of Rangeland Grasshoppers

Catastrophe theory is a form of non-linear mathematics which allows predictions of discontinuities within systems that are governed by a relatively small number of control variables and are derivable from smooth potentials. Grasshopper population dynamics appear to possess properties which can be described by a cusp catastrophe. Previous work has shown that weather conditions at the time of hatching and early development appear to mediate outbreaks and crashes of grasshopper populations. Using several measures of temperature and precipitation and various expressions of grasshopper infestations in Wyoming, we developed a series of models using Catastrophe Theory. The cusp catastrophe based on outbreak levels of infestation (> 9.6 grasshoppers per m2) and monthly (April and May) weather data generally provided the most appropriate descriptions of grasshopper population dynamics; the best models were up to 76% accurate based on a priori criteria. Catastrophic changes in grasshopper populations occur on a very large scale (state-wide), and it appears that different weather parameters affect high and low density outbreaks.