How mechanistic models with landscape resistance, direct temperature effects on life-cycle timing, and the Allee effect explain bark beetle outbreaks

Background/Question/Methods

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 masseto 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 dispersal to new trees.   Adult beetles must colonize during a relatively narrow window of time to take advantage of warm temperatures for oviposition, but must also attack late enough to make sure that cold-hardened larvae appear during winter freeze.  Thus the beetles exist in 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.   Impacts due to MPB have been larger than fire, challenging researchers to predict risk factors and rates of population growth.  However, statistical models fit to data at a variety of scales have failed to describe MPB outbreaks in anything more than probabilistic terms.

Results/Conclusions

We have developed a mechanistic approach based on:  differential beetle motility between forested and unforested habitats (landscape resistance), phloem temperature control of MPB phenology, and the Allee effect resulting from the need to mass-attack new hosts.  The resulting partial differential model describes MPB aggregation at scales commensurate with changes in host density.   Solutions are complicated and discontinuous, but homogenization results in a surprisingly simple diffusive approach suitable for rapid integration over watersheds and regions and able to accommodate forest demographics resolved on 30m scales.   In fact, with a speed-up of over six orders of magnitude, it is feasible to calibrate the model using Markov Chain Monte Carlo (MCMC) procedures and Aerial Damage Survey (ADS) data from central Idaho.  We determine a distribution of motility and demographic parameters in a Bayesian framework, and validate the model by comparison with ADS data collected in the eastern Cascades.  This description of MPB behavior captures patterns of observed damage as well as details of demographic growth rates.