Spatial-temporal generalized linear modeling of Mountain Pine Beetle outbreaks and other damage causing agents in the Rocky Mountain region

Background/Question/Methods

Tree mortality due to bark beetles, in particular the mountain pine beetle, is a growing concern in the Rocky Mountains and across the country. As this issue has become more apparent in the last few years, various spatial analysis methods have been used to analyze the spread of the outbreaks of the mountain pine beetle. Bentz et al (2010) used population models of the bark beetle and simulated climate changes to predict the potential for bark beetle outbreaks in the United States and Canada. Recent work on the Mountain Pine Beetle outbreak in British Columbia was conducted by Zhu et al (2008) where a spatial-temporal autologistic binary model was used to account for both spatial and temporal dependence on discrete time intervals. The model used logistic regression to model a response variable on explanatory variables and autoregression on responses from spatial neighborhoods. This research extends the work of autologistic binary models to generalized linear models, the multinomial model and to models for ordinal response data to assess multiple damage agents that have occurred in the Rocky Mountain Region.

Results/Conclusions

Parameters associated with mortality from the Rocky Mountain region are measured repeatedly based on spatial distance over discrete time intervals from June to August from 2005 to 2011. A spatial neighborhood structure with various distances was constructed and ordered based upon the adjacency of the initial site. The spatial-temporal autologistic regression model draws samples using Monte Carlo estimation using a Gibbs Sampler to obtain estimates of the model parameters. The model provides parameter estimation for the spatial, temporal, mortality and host tree types for various damage causing agents and the associated significance. The damage causing agents analyzed in the model for the Rocky Mountain region are Mountain Pine Beetles, Pine Engravers, the Five Needle Pine decline, and a category of all other damage causing agents in the Rocky Mountain Region. In the binary and multinomial models, the spatial parameter was found to have a significant negative impact (p < 0.001), and both the ponderosa pine and the lodgepole pine host trees showed a significant increase (p < 0.001) in damage from the Mountain Pine Beetle. Mortality also indicated a significant increase over time and the damage causing agents impacted host trees at different magnitudes with the Mountain Pine Beetle having the highest damage.