Modelling diameter distributions of birch (Betula alba L.) and pedunculate oak (Quercus robur L.) stands in Northwest Spain with the beta distribution

Abstract

The diameter distribution of 125 and 172 permanent plots installed respectively in birch-dominated (Betula alba L.) and pedunculate oak-dominated (Quercus robur L.) stands in Galicia (northwest Spain) were modelled with the beta distribution. The method based on the moments of the distribution was used to fit the model to real distributions of relative frequencies of trees with the following statistics considered in the comparison of results: bias, mean absolute error (MAE), mean square error (MSE) and number of plots rejected by the Kolmogorov-Smirnov (KS) tesIn the fits of the function, the percentage of rejections by the KS test was 0.8% of the total number of cases in birch stands and 1.2% in pedunculate oak stands, at a significance level of 5%. Then, the parameters of the distribution were recovered with the parameter recovery models (PRM) from the first and the second moments of the distribution (mean diameter and variance, respectively). The extremes of the function (minimum and maximum diameters of the distributions) were modelled with simple linear models, with stand variables easily obtained from yield tables for the species in northwest Spain (quadratic mean diameter, dominant height, number of trees per hectare, age, basal area and the relative spacing index). The models recovered and calibrated in Quercus robur L. stands were most accurate in terms of MSE (with a mean value of 0.00055 in frequency of trees per one). However, the models were more accurate in Betula alba L. stands in terms of the number of rejections by the Kolmogorov- Smirnov test: 21 plots rejected in birch stands (16.8% of the total of plots) and 33 plots in pedunculate oak stands (19.2% of the total).