Process-based size-class distribution model of trees within forest plantations: A hierarchical modeling approach

• We model size distribution of trees in plantations.
• The model works across a range of species, sites and silvicultural treatments.
• The effect of seedling quality and site variability can be included in model parameterization.
• A hierarchical-modeling approach retains the robustness of stand scale models.

Prediction of stand structure, and how it varies with climate, disturbance and silviculture, can assist the design of adaptation options to climate change, aid silviculture response to storm damage or pest attack, and help stand managers meet product delivery schedules and maximize wood value. Making these predictions with process-based models typically requires detailed data on the existing tree population structure from which to initiate projection, or alternatively highly complex, and difficult to parameterize, models of inter-tree competition. This paper introduces a hierarchical modeling approach to address this problem. In this approach, the stand-level outputs of a process-based model, CABALA, are disaggregated among individual trees within a stand according to simple rules to provide individual tree sizes and growth trajectories. The model, designed for single-species, evenly-spaced stands, is based on a number of assumptions including: stand level allometrics can be scaled to individual trees; above-ground competition for space and resources can be used as a guide to overall inter-tree competition; trees within a stand start with a distribution of sizes as well as variation in intrinsic productive potential.The output of the model was tested across a wide range of site types for two species, Pinus radiata and Eucalyptus globulus, over a range of thinning and fertilization treatments, and for stands of ages between 2 and 27 years. Across these conditions, predicted and observed distributions were statistically similar (p = 0.05) in 38% of the 280 E. globulus height distribution, in 47% of the 280 E. globulus diameter distribution and in 85% of the 53 P. radiata diameter distribution comparisons. Overall, predictions were better for P. radiata than E. globulus, and for both species were better for older stands than young. Spatial patterns were similar: neither predicted nor observed spatial distributions exhibited spatial auto-correlation.