A Continuous Model for Oscillating Outbreaks of the Population of a Phytophagous Moth, the Tent Caterpillar, Malacosoma disstria (Lepidoptera, Lasiocampidae)

Abstract

Outbreaks of individual species populations are important phenomena in many aspects and are not alike in terms of the theory of multispecies community dynamics. Outbreaks of insect populations develop more quickly with long-lasting effects experienced by the forest industry. These events are considered as extreme unbalanced and transient processes. The mechanisms of the development and subsidence of insect outbreaks differ in different taxonomic groups of pests. The duration and occurrence of repeated outbreaks of psyllids and forest moths, which affect deciduous or coniferous forests in the same region, are different. Computational simulation is needed for understanding the dynamics of insect outbreaks. For the mathematical description of the outbreaks of forest tent caterpillar, in addition to the threshold version of the development of the insect outbreak, it is interesting to modify continuous computational models for the analysis of fluctuation dynamics. In this paper, we simulate the dynamics of spontaneously damping oscillations under a specific scenario during a population outbreak using a continuous model with delayed regulation and nonlinear counteraction by the biotic environment. The scenario described by the new phenomenological equation, which consists of a series of maxima of different sizes and final attenuation of peaks near balance, occurs for the pest tent caterpillar, Malacosoma disstria, which affects deciduous forests in North America leading to large-scale defoliation. The new scenario is qualitatively different from our model of the threshold development and subsidence of outbreaks of the psyllid Cardiaspina albitextura in Australia.