A model for coupling fire and insect outbreak in forests

Predictive models of insect outbreak exist for some processes for few species, but an additional and rarely explored complication is the potential interaction between insect outbreak and wildfire disturbances in forests. The association between insect and fire dynamics is complex, particularly when evaluated over time and at large scale, and no consensus exists in the published literature about its consequences. Thus, more insights on the issue would be useful to scientists, resource managers, and the public when making decisions on, to name a few, firefighting, operations and treatments to reduce wildfire/insect impacts. In this article we propose mathematical models incorporating the effect of insect outbreaks either as a single disturbance in the forest population dynamics or coupled with wildfire disturbances. For the beetle-tree system model analytical and numerical characterization of its temporal dynamics shows that the system exhibits the well known beetle-tree interaction described by the dual equilibrium theory. For the extended model that includes fire, numerical simulations demonstrate the potential for existence of positive feedback between wildfire and insect outbreak disturbances in certain region of fire strength. This result agrees with one of the current theories in the field.