Differential dispersal and the Allee effect create power-law behaviour: Distribution of spot infestations during mountain pine beetle outbreaks.

Mountain pine beetles (MPB, Dendroctonus ponderosae Hopkins) are aggressive insects attacking Pinus host trees. Pines use defensive resin to overwhelm attackers, creating an Allee effect requiring beetles to attack en masse to successfully reproduce. MPB kill hosts, leaving observable, dying trees with red needles. Landscape patterns of infestation depend on MPB dispersal, which decreases with host density. Away from contiguously impacted patches (low beetle densities), infestations are characterized by apparently random spots (of 1-10 trees). It remains unclear whether the new spots are spatially random eruptions of a locally endemic population or a mode of MPB spread, with spatial distribution determined by beetle motility and the need to overcome the Allee effect. To discriminate between the hypothesis of population spread versus independent eruption, a model of spot formation by dispersing beetles facing a local Allee effect is derived. The model gives rise to an inverse power distribution of travel times from existing outbreaks. Using landscape-level host density maps in three study areas, an independently calibrated model of landscape resistance depending on host density, and aerial detection surveys, we calculated yearly maps of travel time to previous beetle impact. Isolated beetle spots were sorted by travel time and compared with predictions. Random eruption of locally endemic populations was tested using artificially seeded spots. We also evaluated the relationship between number of new spots and length of the perimeter of previously infested areas. Spot distributions conformed strongly to predicted power-law behaviour. The spatially random eruption hypothesis was found to be highly improbable. Spot numbers grew consistently with perimeter of previously infested area, suggesting that MPB spread long distances from infestation boundaries via spots following an inverse power distribution. The Allee effect in MPB therefore accelerates, rather than limits, invasion rates, contributing to recent widespread landscape-scale mortality in western North America.