Forest insect populations: Modeling of critical events as first- and second-order phase transitions

Abstract

In this article, methods are examined for modeling of critical events in forest insect populations by describing the processes of development of a population outbreak as analogs of first- and second-order phase transitions in physical systems. Measurable parameters characterizing the phase transition processes are proposed. For several forest insect species, first-order phase transition models were analyzed, which allowed to characterize risks of insect outbreaks. Second-order phase transitions were used to describe a spatial distribution of insects among trees (food items) on sample plots. These transitions characterize critical frequency of individuals per victim unit (tree); after attaining this frequency, insects colonize and start consuming all food items. It was also shown that a second-order phase transition model can describe the interaction of a baculovirus with spongy moth caterpillars. This model helped to estimate the latent period of the baculovirus's impact on the insect population and the time required for absolute mortality of caterpillars at different doses of the baculovirus. The proposed approach requires minimal data on the state of an ecosystem.