Ocena zgodności rozkładów empirycznych pierśnic drzewostanów bukowych różnych klas wieku z wybranymi rozkładami teoretycznymi

Modelling is one of the basic activities in the field of biological sciences. The main purpose of modelling is to illustrate relationships and phenomena of biological objects (and traits describing them) and present reality as close as it is possible with expected range of error. In the paper we presented results of approximation of the selected theoretical distributions, i.e. singular (normal, log−normal, gamma, two− and three−parameter Weibull, Johnsons SB) and finite mixture (normal, log−normal, gamma and Weibull) to tree diameter distributions in beech stands (Fagus sylvatica L.). The main aim of the study was to evaluate goodness of fit of selected distributions, prove legitimacy of using mixture distributions in even−aged, single−species beech stands and find the best distribution of model diameter distribution in a whole production cycle of this kind of stands. The study was conducted in 32 sample plots located in north−western Poland in stands at the age between 9 and 140. For the evaluation χ² test, a modified error index (e) and a root mean square error (RMSE) were used. We found that the RMSE and e are related in most cases with stand density. Mean values of used indicators show that finite mixture distributions are better in comparison to singular distributions. The best fitted distributions were Johnsons SB and mixture of gamma ones. Range of error index expressed with number of trees per hectare ranges 16.5−32.8% and 7.7−27.0% for this distributions, respectively. Conversely the worst results were obtained by fitting two−parameter Weibull distribution both in singular and mixture. Future diameter distribution model based on the probability distribution should be based on Johnson SB or 3−parameter Weibull distribution from singular ones or gamma from finite mixture. In case of age class apportionment unequivocal the best result were obtained with Johnson SB and partially with mixture gamma distributions.