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Forest management in the region of Zacualtipán, Hidalgo, Mexico, has focused in the last three decades on the cultivation of pure even-aged stands of Pinus patula, the native timber species of fastest growth and high commercial value. The rapid growth of P. patula requires appropriate management of stand density to properly schedule thinnings and optimize stands' rotation. In this study, we determined the maximum line size-density relationship or self-thinning considering the stochastic frontier regression and ordinary least squares approaches for Reineke and Yoda models. In the estimation, we used data derived from 42 permanent sampling plots of 400 m2. The best estimates of the self-thinning line were obtained using the stochastic frontier models Truncated-normal and Half-normal of Reineke and Yoda. On this basis, we set diagrams for tree density management, considering the relative stand density index of Reineke (SDI) and that of Yoda (YDI). The method of stochastic frontier regression enables to directly estimate the upper limit of self-thinning without resorting to the selective use of data, where the points in which mortality from self-thinning has not yet exhibited are excluded from the analysis. For SDI and YDI, stochastic setting suggests a more conservative mortality rate compared to least squares fit. The method also allows a more efficient use of data, and incorporates information from inventory plots without remeasurements. [ABSTRACT FROM AUTHOR]

The most common method to estimate forest variables to a large or small scale is the forest inventory based on field sampling. Currently, remote sensing techniques offer a range of possibilities in forest resources estimation; this is the case of LiDAR (Light Detection And Ranging) that allows the characterization forest structure in three-dimensions. We analyzed the relationship between LiDAR and field data to estimate forest variables such as: basal area (AB), total biomass (BT), crown cover (COB) and timber volume (VOL) through four methods: 1) multiple linear regression, 2) non-linear regression, 3) ratio estimators and 4) traditional forest inventory (stratified sampling). Total estimates derived from the ratio estimator were within the 95% confidence interval calculated by traditional inventory for AB, BT and VOL; this estimator showed the closest values and precision to those obtained by traditional forest inventory. In general, estimates through non-linear models were the most optimistic compared to the traditional forest inventory. Our results indicated a good relationship (R2 > 0.50) between LiDAR metrics and field data, particularly the percentiles of height and rates of return on a defined height. From the linear models fit we generated maps for each of the forest variables analyzed. [ABSTRACT FROM AUTHOR]