Spatial-temporal modeling of forest gaps generated by colonization from below- and above-ground bark beetle species

Studies of forest declines are important, because they both reduce timber production and affect successional trajectories of landscapes and ecosystems. Of particular interest is the decline of red pines, which is characterized by expanding areas of dead and chlorotic trees in plantations throughout the Great Lakes region. Here we examine the impact of two bark beetle groups, red turpentine beetles and pine engraver bark beetles, on tree mortality and the subsequent gap formation over time in a plantation in Wisconsin. We construct spatial-temporal statistical models that quantify the relations among red turpentine beetle colonization, pine engraver bark beetle colonization, and mortality of red pine trees while accounting for correlation across space and over time. We extend traditional Markov random-field models to include temporal terms and multiple-response variables aimed at developing a suitable set of statistical models for addressing the scientific questions about the forest ecosystem under study. For statistical inference, we adopt a Bayesian hierarchical modeling approach and devise Markov chain Monte Carlo algorithms for obtaining the posterior distributions of model parameters as well as posterior predictive distributions. In particular, we implement path sampling combined with perfect simulation for autologistic models while formally addressing the posterior propriety under an improper uniform prior. Our data analysis results suggest that red turpentine beetle colonization is associated with a higher likelihood of pine engraver bark beetle colonization and that pine engraver bark beetle colonization is associated with higher likelihood of red pine tree mortality, whereas there is no direct association between red turpentine beetle colonization and red pine tree mortality. There is strong evidence that red turpentine beetle colonization does not kill a red pine tree directly, but rather predisposes the tree to subsequent colonization by pine engraver bark beetles. The evidence is also strong that pine engraver bark beetles are the ultimate mortality agents of red pine trees.