Phase transition from environmental to dynamic determinism in mountain pine beetle attack

Mountain pine beetle outbreaks are responsible for widespread tree mortality in pine forests throughout western North America. Intensive outbreaks result in significant economic loss to the timber industry and massive changes to the forest habitat. Because of the time and space scales involved in a beetle outbreak, mathematical models are needed to study the evolution of an outbreak. In this paper we present a partial differential equation model of the flight phase of the mountain pine beetle which includes chemotactic responses and tree defense. We present a numerical method for integrating this model and use this method to investigate the relationship between emergence rate, forest demographic and patterns of beetle attack. In particular we look at how emergence rate affects the beetles' ability to successfully attack strong trees, which may be an indicator of an epidemic outbreak.