Modeling Tree Diameter Distributions in Natural Forests: An Evaluation of 10 Statistical Models

In forestry, the description of tree sizes is commonly performed by fitting statistical models to diameter distributions. However, there is little agreement on which models are more flexible to this end, especially in tropical forests. Here we provide the simultaneous evaluation at species and subplot levels of 10 models using large data sets from four representative forest types in Brazil. We aimed to detect which models provide best fits and under which sample properties (size, median, variance, skewness, and kurtosis). We show that the combination of the logit-logistic, odd Weibull, Weibull, and Johnson’s special bounded models provided reasonable descriptions for nearly all species (94.8%) and subplots (99.6%). However, there was little overlap between these four models, meaning that single models were rarely appropriate to describe the majority of cases. This complementarity was evident between the odd Weibull (better performance for more symmetrical, bimodal, or rotated-sigmoid patterns) and logit-logistic models (typical right-skewed and heavy-tailed patterns). The performance of all models was significantly related to forest type or sample properties. Models with more than three parameters had more problems related to optimization convergence, confidence interval estimation, and unrealistic fits. Finally, we discuss some theoretical issues related to the choice of appropriate models.