Modelling Spatial Patterns of Trees Attacked by Bark-Beetles

Many species of bark-beetles kill trees in clusters. One of the most destructive forest insect pests with this colonization pattern is the mountain pine-beetle. Heavy losses caused by this beetle are of primary concern to national forest managers in western North America. An understanding of the process of tree selection by the beetles is useful for prescribing measures that might minimize beetle damage. Here, an autologistic model is used to study the spatial patterns of lodgepole pine trees attacked by the beetles. The model is used to describe the conditional probability that a tree of a given size, age and vigour is attacked given the status of all other trees in the stand. The spatial correlation between trees is modelled by constructing a covariate that is a measure of the angles from attacked trees to other trees in the stand. Some surprising difficulties in modelling conditional probabilities are discussed. Parameter estimates are obtained by maximizing a pseudolikelihood function, and estimates of standard errors are obtained from iteratively simulated samples.