Forest modelling: the gamma shape mixture model and simulation of tree diameter distributions

Rafał Podlaski

doi:10.1007/s13595-017-0629-y

Abstract

• Key messageNew 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.• ContextTo 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.• AimsThe 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.• MethodsThe 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).• ResultsThe 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.• ConclusionThe 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.

Highlights

Disturbances occurring in forest ecosystems are one of the most important determinants of spatio-temporal development in stands (Gratzer et al 2004)
The aim of this study was to assess the precision of the approximation of empirical diameter at breast height (DBH) data using the gamma shape mixture (GSM) model and kernel density estimation
This study has revealed that the GSM model is flexible and accurate when modelling the highly skewed and heavy-tailed DBH distributions of two-generation stands

Summary

Introduction

Disturbances occurring in forest ecosystems are one of the most important determinants of spatio-temporal development in stands (Gratzer et al 2004). Due to disturbances of different spatial scales, gaps of varying sizes are formed. These processes have a significant effect on the structure of forests. The specific vertical structure is closely related to the shape of the diameter at breast height (DBH) distribution (Lawton and Putz 1988; Denslow et al 1998). Many tree stands in various geographic regions contain cohorts of old trees, which are represented by only few individuals, but play a great role in stand structure and in ecosystem functioning. It is difficult to find distribution functions to represent these few large trees. During the approximation of these highly skewed and heavy-tailed DBH distributions, there is often the smoothing problem, which in turn requires the use of methods that are able to fit a tail probability well

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