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Taper models are used to determine the diameter along the trunk and allow to determine the tree trunk volume or volume of any part of it. The paper presents the method of determining the thickness of bark along the trunk using compatible taper models. Four taper models with different levels of complexity were analyzed based on data from 13 sample plots and 39 sample trees measured in black locust (Robinia pseudoacacia L.) stands from west Poland. For modelling the over and under bark diameter and bark thickness along the trunk seemingly unrelated regression of independent equations was applied. During the analyzes, the logical assumption that the thickness of the bark at any place on the trunk is determined in a difference of over and under bark diameter was applied. It was found that selected models fit the shape of the trunk with different accuracy. The worst results were obtained with the use of a polynomial model. The best fit for modelling bark thickness along the trunk was characterized by variable−form taper models. However, regardless of the complexity and quality of fit to the trunk shape, all analyzed models allowed determining the bark thickness along the trunk without systematic error and with practically acceptable accuracy.
Regression analysis is one of the most popular statistical modeling tools, which can define linear or nonlinear relationships between individual trees and stands parameters. Mixed−effects models are one of the contemporary trends of those regression methods. These models can be applied to describe such features as: height, biomass, taper, site index or volume both at the level of a single tree and whole forest ecosystems. The aim of this work is to present the characteristics of the mixed−effects model, the applicability of linear and nonlinear mixed−effects models in forest studies, and the example of a linear mixed−effects model defining the relationship between bark thickness and diameter at breast height for Scots pine (Pinus sylvestris L.) in comparison to the linear fixed−effect model. Goodness−of−fit for the obtained linear mixed−effect model indicate its better fit to the pine bark thickness than in the case of the mixed−effects model. Moreover, most of the published research results indicate the predominance of both linear and nonlinear mixed−effects models according to fixed−effect ones. These studies indicate the wide possibilities of using mixed−effect models in forestry. However, there are also results pointing to the disadvantages of these models and put into question the legitimacy of their use in forest research. This fact to some extent confirms the results (residuals behavior) obtained in this study. Therefore, it seems necessary to conduct further research, which on the one hand will allow the potential of this solution to be used, and on the other hand will help to clarify emerging doubts.
W pracy stwierdzono istotny wpływ pochodzenia sosny na wysokość drzew oraz grubość odkładanej kory. Badania nie wykazały natomiast istotnego wpływu pochodzenia na wielkość pierśnicy i miąższość strzał bez kory w badanej populacji sosen.
This paper presents the results of investigation into the variability of selected features of morphological structure of Douglas fir trees in Poland. The research was carried out in 28 Douglas fir stands, which were at least 80 years old. The mean values of studied features amounted: diameter at breast height — 54.8 cm, height — 32.4 m, bark thickness — 3.9 cm, crown length — 13.6 m, relative crown length — 41.6% and crown width — 5.4 m. The significant variability of studied features was stated, especially large diversity bark thickness and crown width was revealed. Four regions were distinguished in Poland. These regions were characterized by some distinction of the studied features.
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