Recurrent and synchronous insect pest outbreaks in forests

A minimal model for the interactions of trees, insects, and their enemies suggests a simple formula for splitting all forests where insect outbreaks can occur into two categories: where outbreaks are periodic and endogenously generated and where outbreaks are triggered by exogenous factors and are, in general, recurrent but aperiodic. The formula is in full agreement with all field studies in which various phenomena triggering insect outbreaks have been identified. The observed consequences of introductions and removals of insects are also well predicted by the minimal model. But, even more surprisingly, the model allows a simple and explicit condition for the synchronization of outbreaks in spatially extended forests to be derived analytically. This condition is, in general, satisfied when the insect is a so-called pest, that is, when the outbreaks are extreme. The model also predicts the possibility of traveling waves of insect outbreaks.