Rangeland Grasshopper (Orthoptera: Acrididae) Population Dynamics: Insights from Catastrophe Theory

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Abstract
Catastrophe Theory is a branch of mathematics that provides a framework for studying discontinuous phenomena. Application of the cusp catastrophe, a model with two driving or control variables, indicates that rangeland grasshopper population dynamics are catastrophic. Based on bimonthly temperature and precipitation, the cusp catastrophe modeled changes in grasshopper populations dynamics in four ecotopographic regions of Wyoming with an accuracy significantly better than chance. Although there were differences in model performance among regions, the best predictions generally occurred when the changes were large-scale outbreaks (30–45% of the total area of a region) of economic densities (≥9.6 grasshoppers/m 2 ). Because winter weather, particularly in climatically extreme years, is correlated with spring weather, it appears that the climate in December–January has predictive value with regard to population dynamics in the following spring. However, when temperature and precipitation during hatching and early development of grasshoppers (April–May) are used as the control variables, the cusp catastrophe most accurately models the observed population dynamics.

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