Functional evaluation of height-diameter relationships and tree development in an Australian subtropical rainforest

Abstract

Context: Allometric equations describing the relationships between tree height (H) and breast height diameter (D) should be both statistically efficient and biologically relevant. Aims: To determine whether selected allometric equations can meet established criteria for both efficiency and relevance. Methods: Nine equations were compared to define the H-D relationships of 1122 individuals and 18 species from an Australian subtropical rainforest. Key results: Three-parameter asymptotic equations described initial slope (a), curvature (b), and asymptotic height (Ha). Each equation was evaluated for precision (root mean square error, RMSE) and bias in H estimates, and ease of interpretation of function parameters. For both individual species and all stems, a non-rectangular hyperbola (NRH) provided almost equally high precision and low bias as did the statistically most parsimonious generalised Michaelis-Menten function, plus linear parameter values easily relatable to tree structural and functional attributes. The value of NRH a increased linearly with wood density for canopy species, but not for understorey and subdominant species, whereas the value of NRH b decreased as Ha increased from understorey to canopy species. Conclusions: Species within understorey, subdominant, and canopy structural groups shared similar ranges of parameter values within groups that reflect both intrinsic architectural and developmental patterns, and environmental limitations to Ha. Implications: The NRH can be used to visualise both early and later tree development stages and differences among the growth patterns of species occupying different positions within a forest.