Von Bertalanffy- Richard’s Function for Modelling Height- Diameter Relationship in Albizia Lebbeck L

Abstract

The tree H-D relationship is frequently used as a key input variable in growth and yield modelling and to describe stand dynamics as well. The study aimed at establishing a powerful H-D model for Albizia lebbeck L. trees using von Bertalanffy- Richard’s (vB- R’s) function. A total of 42 trees were sampled from 5 (0.025 ha) circular plots with DBH ranging from 10.25- 91.33 cm. Total tree height also varied from 10.32- 25.03 m. Two, three and four parametric vB-R’s functions were fitted to forty-two (42), H-D pairs of Albizia lebbeck L. trees to generate predictive height curves. Among the three model types, best fit model came out to be a 3- parametric model with least RSE, Mean Bias, AIC, RMSE and maximum Adj.- R2 and it appeared to be biologically realistic too. Among the models tested, four parametric was quite close to three parametric model in describing biological significance of the H-D relationship but evaluating statistics of the 3- parametric function was slightly better than that of 4- parametric function, hence the former was considered for further biological interpretation. Moreover, 3 and 4 parametric models generated sigmoid- height curves (c, d>0), while 2- parametric model generated a close to concave shape (b close to 0). The discussed model functions can be applied to similar stand conditions from where study data was collected