The biodiversity of forest stands should be analysed from the point of view of not only compositional elements but also structural diversity. The main objective of this study was to compare tree diameter structural diversity of the mixed managed and unmanaged stands with Abies alba and Fagus sylvatica . There were 62 study plots established in the Carpathians (Southern Poland) and in the Świętokrzyskie Mountains (Central Poland) in managed and unmanaged stands. The comparison of the studied stands involved the identification and modelling of size structures, the use of the Gini coefficient and the relative distribution method (including entropy and polarisation). Six structural types were distinguished: three unimodals of a different width of diameter at breast height (DBH) range (mainly for the managed stands), reverse‐J, rotated‐sigmoid and bimodal (for unmanaged stands). Modelling of the distinguished structural types by means of theoretical distributions has shown that the best results of approximation for unimodal skewed and reverse‐J DBH distributions were obtained with the single Weibull and gamma distribution, while in the case of rotated‐sigmoid and bimodal DBH distributions the best results were obtained with mixture models. The comparisons have shown that tree diameter structural diversity was more complex in unmanaged forests compared to managed stands. For managed stands the Gini coefficient assumed values from 0.31 to 0.48, while in the case of the unmanaged forests, from 0.33 to 0.73. One should aim to increase tree diameter structural diversity in managed forests, adopting the close‐to‐nature silviculture concept which consists of imitating natural processes.

Tree structural diversity is assessed by modelling stand diameter at breast height (DBH) distribution. The aim of this study was to verify the suitability of a mixture of two- and three-component Weibull and gamma models for describing irregular and multimodal DBH distributions. Investigations were carried out in natural Abies alba Mill. and Fagus sylvatica L. stands, representing the growing-up stage, in the Świętokrzyski National Park (Central Poland) and in the Pieniny National Park (Southern Poland). Sample plots (0.25–0.5 ha in area) were selected from a database used for forest dynamics analysis. The parameters of the mixture model were estimated using maximum likelihood estimation (MLE) and a combination of an expectation–maximisation (EM) algorithm with a Newton-type (NT) method. The multistart method (MM) of choosing initial values was used. The DBH distributions in mixed Abies–Fagus forests of complex structure were accurately approximated by two- and three-component mixture models. The root mean square error (RMSE) values varied from 3.4515 to 7.6682 for the Weibull mixture and from 3.6457 to 7.1419 for the gamma mixture. The results indicated that the mixture Weibull and gamma models were, in general, equally suitable for modelling irregular and multimodal DBH distributions. Finite mixture models may be used to characterise tree structural diversity, especially in uneven-aged stands of complex structure.

•Key message: New types of distribution functions are needed to model the dynamics of stands where important age classes are represented by few trees. In this study the gamma shape mixture model and two simulation methods were used for generating tree diameter data.•Context: To analyse forest dynamics, it is necessary to know distribution of the characteristics (mainly tree diameters) of trees forming particular developmental phases. In many forest inventories, the measurement of large diameter at breast height (DBH) samples is practically impossible. In this case, DBH distributions can be generated using theoretical models.•Aims: The aim of this study was to assess the precision of the approximation of empirical DBH data using the gamma shape mixture (GSM) model and kernel density estimation. The strengths and weaknesses of the two simulation methods were presented and discussed.•Methods: The GSM model was adopted to approximate empirical DBH data collected in 20 near-natural stands. Two simulation methods were used: (a) the procedure based on a multimodal distribution and gamma random numbers (MDGR procedure) and (b) MCMC techniques with Metropolis–Hastings sampling (MH method).•Results: The GSM model precisely fitted the investigated DBH distributions. The MDGR procedure was slightly more precise than the MH method, especially in the case of the samples of 250 DBHs. The level of homogeneity within the drawn DBH sets was similar for all samples.•Conclusion: The GSM model is very flexible. The DBH random variates, generated with the use of analysed procedures, represented all tree generations being significant from a biological point of view.