A Gaussian multi-component model for the tree diameter distribution in old-growth forests

Abstract

The old-growth forests are characterized by multi-aged structures for which the De Liocourt model with the Meyer negative exponential function is the most common descriptor of tree diameter distributions. In this study, we put forward a mixture of Gaussian functions model for describing the diameter at breast height distribution in uneven-aged mixed forest stands. For this purpose, a permanent plot of one hectare was installed in the natural silver fir-beech mixed old-growth forest Şinca Veche (Făgăras Mountains, Romania). The sample with 396 trees was split into homogeneous age groups using k-means clustering analysis and by limiting the coefficient of variation to 30%, both for the diameter and for the maximum cambial age at breast height. The proposed cumulative distribution function is generated by summing the Gaussian probability density functions obtained for each age group. For verifying the efficacy of the parameter estimation procedure and to assess the goodness-of-fit, suitable statistical criteria were used: Shapiro–Wilk normality test and the root mean square error (RMSE). The developed mixture distribution and the negative exponential distribution were both compared to the empirical diameter distribution. The comparison of the observed RMSE values (3.12 < 5.93) shows the suitability of the proposed method, with a better degree of accuracy than that achieved by applying the negative exponential model. The results of this study confirm the applicability of Gaussian multi-component models for describing tree diameter distributions in natural silver fir-beech mixed stands.