The Modeling of diameter structures with the Log-Logistic function in the natural forest of Durango, México Modeling of diameter structures with the Log-Logistic function in the natural forest of Durango, México

Abstract

Diametric distribution models are useful tools for predicting growth and yield of forest stands and planning sustainable forest management activities. The objective of this work was to analyze the fitting capacity of the Log-Logistic probability density function through a parameter estimator based on percentiles and to evaluate the precision of two modeling alternatives of diameter distributions of natural stands in the northwestern of Durango state. Six percentile estimators were evaluated and compared with the maximum likelihood approach based on the performance of the Kolmogorov-Smirnov (KS), Anderson-Darling (AD) and Cramér-Von Mises (W²) statistics. For the modeling of the diametric distribution, the graphical and numerical behavior of the prediction (PPM) and parameter recovery (PRM) methods was evaluated with the mean bias (SM) and mean absolute error (EMA). The best parameter estimator resulted from the diameter that accumulates the 25th and 79th percentiles, considering the percentage of stands where it was more accurate in terms of the KS, AD and W², as well as its performance with respect to maximum likelihood approach. The modeling of the number of trees per diameter class with the PRM and PPM approaches proved to have similar accuracy from the measurement of quadratic mean diameter, basal area per hectare, height and dominant diameter. This work contributes significantly to providing a tool for easy application in growth models developed for natural forests of the Sierra Madre Occidental in Mexico.