Multilevel linear mixed model for tree diameter increment in stone pine (Pinus pinea): A calibrating approach

Abstract

Diameter increment for stone pine (Pinus pinea L.) is described using a multilevel linear mixed model, where stochastic variability is broken down among period, plot, tree and within-tree components. Covariates acting at tree and stand level, as breast height diameter, density, dominant height or site index are included in the model as fixed effects in order to explain residual random variability. The effect of competition on diameter increment is expressed by including distance independent competition indices. The entrance of regional effects within the model is tested to determine whether a single model is sufficient to explain stone pine diameter increment in Spain, or if, on the contrary, regional models are needed. Diameter increment model can be calibrated by predicting random components using data from past growth measurements taken in a complementary sample of trees. Calibration is carried out by using the best linear unbiased predictor (BLUP) theory. Both the fixed effects model and the calibrated model mean a substantial improvement when compared with the classical approach, widely used in forest management, of assuming constancy in diameter increment for a short projection period.