Height–diameter relationship of plantation-grown juvenile black locust trees is differentiated according to their growth rate, which is positively affected by spacing

Abstract The main objective of this study was to explore the height–diameter relationship of plantation-grown juvenile black locust trees and to clarify if the tree height can be adequately predicted at stand level from the breast-height diameter and which is the most appropriate functional form; if the predictions can be expanded to a wider region by mixed-effects modelling and which is the most relevant level for model localisation; if the random parameter components can be calibrated with stand-level variables and which of them is an appropriate predictor. We first fitted seven one-predictor models at plot level and we selected the most adequate simple function according to a set of goodness-of-fit criteria. It was then approximated over the entire data set in nine different mixed-effects model forms that were compared by Likelihood Ratio Test. Calibrations of the random parameter component of the best mixed-effects model with a height–diameter measurement of one tree at each occasion and with a function of a plantation-level variable were attempted. Our study derived a mixed-effects and a two-predictor deterministic models, based on an exponential function of the reciprocal value of the diameter, with a constant intercept of 1.3. Height–diameter relationship localisation at plot level, regardless the geographic region, was most suitable for the investigated juvenile black locust data. The specific component of the rate parameter in the mixed-effects model form differentiated the plantations according to their growth potential. A positive correlation between the height increase and the growing space was also distinguished that allowed calibration of the mixed-effects rate parameter by a linear function of spacing to develop a two-predictor deterministic function. However, the mixed-effects model showed higher predictive power than the purely deterministic relationship.