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 ef fi cient and biologically relevant. Aims . To determine whether selected allometric equations can meet established criteria for both ef fi ciency and relevance. Methods . Nine equations were compared to de fi ne 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 ( H a ). 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 H a increased from understorey to canopy species. Conclusions . Species within understorey, subdominant, and canopy structural groups shared similar ranges of parameter values within groups that re fl ect both intrinsic architectural and developmental patterns, and environmental limitations to H a . 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.