One spot, two spot, red spot grew spots: How differential dispersal, phenology and the Allee effect predict pattern formation in mountain pine beetle impact
The mountain pine beetle (MPB, Dendroctonus ponderosae Hopkins), is an aggressive insect which attacks living host trees (of genus Pinus). Pines have significant defensive mechanisms, requiring the beetles to attack en masse to overcome an Allee effect and successfully colonize. Temperatures directly but nonlinearly influence the rates at which insects complete development in their various life stages and therefore the timing (phenology) of their emergence. Since the beetle larvae consume the phloem underneath the bark each year they exhaust their host, requiring density-dependent dispersal to overcome the attack threshold of new trees. The Allee effect creates a precarious niche depending on carefully synchronized timing and dispersal. Changing temperatures have broadened that niche across vastly larger regions, leading to tree mortality across more than thirty million hectares of western North America and impacts greater than fire. Predicting spatial behavior of impacts has proven difficult at almost any scale, and observed patterns run the gamut from apparently random spots to growing patches and aggregating spots to large-scale mortality in susceptible age classes.
We have developed a mechanistic model for spatial pattern development based on: differential beetle motility between forested and unforested habitats, the effects of phloem temperature on MPB phenology, and the Allee effect resulting from host defensive response. The model recovers over 80% of pattern variability observed in aerial damage surveys at landscape scales. Fitted dispersal parameters indicate that beetle motility decreases exponentially with host density, resulting in MPB aggregation in highly stocked patches. At lower levels of emergence we show that the interaction between differential motility and the Allee effect generates a power-law distribution of spot formation. Depending on phenology and population level, spots spread an aggregate, generating the spectrum of observed spatial impacts, from random spots to broad scale impact. The power-law hypothesis is tested against data from MPB outbreaks in Idaho, Colorado and Washington state.