Predicting Tree Mortality for European Beech in Southern Germany Using Spatially Explicit Competition Indices

Individual tree mortality prediction is a key component of single tree-based stand simulators. However, accurate modeling of long-term research plot data is hampered by rare events, variable lengths of observation, and multiple sources of heterogeneity. This study makes use of a result from medicine that demonstrates the equivalence of logistic and Cox proportional hazards regression for modeling survival data in the case of large sample sizes, rare events, and variable interval periods of observation. Pooled logistic regression models are used to model tree mortality across multiple observation periods with random effects to account for heterogeneity due to plots and calendar year. The models are applied to data from 21,051 observation periods (each approximately 5 years) from 9,292 beech trees in a Bavarian long-term forest research plot network. Among the observation periods studied, 604 (2.9%) resulted in a mortality. Indices measuring competition from light, trees of the same species, conifer trees, and shading are significantly associated with mortality, whereas other variables, including dbh, fail to add additional predictive value. Analytic equations for predicting mortality in new trees are provided and yield an area underneath the receiver operating characteristic curve of 91.5%.