Bayesian approach for modeling diameter distributions of patula pine (Pinus patula Schiede ex Schltdl. & Cham.) stands in Southern Mexico

Abstract

Characterization of the diameter distribution of forest stands managed for timber production provides accurate estimates of existing wood volume by diameter class and area unit. It provides the basis for determining the stand's ecological and economic value, its structure, the potential for ecosystem services, and appropriate management practices. Patula pine is one of the most important conifers in southern Mexico and requires biometric tools to improve management strategies. This study aimed to use the Bayesian approach to estimate the parameters of Johnson's SB (JSB) and Weibull (W) probability density functions (pdf) and to model the diameter distribution of patula pine stands in southern Mexico. We used data from 462 diameter distributions derived from 66 permanent 400 m2 sampling plots. The results indicated that the Bayesian approach was appropriate for estimating the JSB and W pdf parameters. Due to the similarity between the nonparametric tests and the goodness-of-fit statistics of the functions, the graphical analysis helped to select the W function as the better option to adequately model the diameter distribution of the analyzed stands. The equations developed for parameter prediction of the W function with stand variables allowed us to characterize and project the theoretical distribution of diameter classes in a simple accurate way with variables easily obtained from forest inventories. The Bayesian approach proved to be an effective method for estimating the pdf parameters used. This allowed for the correct characterization of the observed diameter distribution, and its implementation was easy for executing the procedure. Diameter distribution models are a powerful tool for forest inventory and management of patula pine stands analyzed in southern Mexico.