A resource-depletion model of forest insect outbreaks.

Detailed analyses of thresholded ecological interactions can improve our understanding of the transition from aperiodic to periodic dynamics. We develop a threshold model of the population dynamics of outbreaking bark beetle populations that alternate between non-epidemic and epidemic behavior. The model involves accumulation of resources during low-density periods and depletion during outbreaks. The transition between the two regimes is caused by disturbance events in the form of major tree felling by wind. The model is analyzed with particular reference to the population dynamics of the spruce bark beetle (Ips typographus) in Scandinavia for which a comprehensive literature allows full parameterization. The fairly constant outbreak lengths and the highly variable waiting time between outbreaks that are seen in the historical records of this species agree well with the predictions of the model. The thresholded resource-depletion dynamics result in substantial variation in the degree of periodicity between stochastic realizations. The completely aperiodic tree colonizations are partly predictable when the timing of the irregular windfall events are known. However, the predictability of inter-outbreak periods is low due to the large variation of cases falling most frequently in the middle between the extremes of purely nonperiodic (erratic) and periodic (cyclic) fluctuations.