Modeling Height–Diameter Relationship Using Artificial Neural Networks for Durango Pine (Pinus durangensis Martínez) Species in Mexico

Abstract

The total tree height (h) and diameter at breast height (dbh) relationship is an essential tool in forest management and planning. Nonlinear mixed effect modeling (NLMEM) has been extensively used, and lately the artificial neural network (ANN) and the resilient backpropagation artificial neural network (RBPANN) approach has been a trending topic for modeling this relationship. The objective of this study was to evaluate and contrast the NLMEN and RBPANN approaches for modeling the h-dbh relationship for the Durango pine species (Pinus durangensis Martínez) for both training and testing datasets in a mixed-species forest in Mexico. The knowledge of this relationship is important for forest management and planning in Mexican Forestry. The total dataset considered 1000 plots (each plot 0.10 ha) (11,472 measured trees) randomly selected from 14,390 temporary forest inventory plots and the dataset was randomly divided into two parts: 50% for training and 50% for testing. An unsupervised clustering analysis was used to group the dataset into 10 cluster-groups based on the k-means clustering method. An RBPANN was performed for tangent hyperbolicus (RBPANN-tanh), softplus (RBPANN-softplus), and logistic (RBPANN-logistic) activation functions in the cross product of the covariate or neurons and the weights for the ANN analysis. Also, a different vector of hidden layers was used for training of ANNs. For both training and testing, 10 classical statistics (e.g., RMSE, AIC, BIC, and logLik) were computed for the residual values and to assess the approaches for the h-dbh relationship. For training and testing, the ANN approach outperformed the NLMEM approach, and the RBPANN-tanh had the best performance in both the training and testing of ANNs.