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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.
So−far developed and published Polish equations for determination of aboveground biomass of Scots pine are based on two predictors: diameter at the breast height (DBH) and tree height. The main goal of the presented study were i) to build the simplified empirical biomass equations that use exclusively DBH as the independent variable, and ii) to compare the obtained results with values from equations based on both predictors (optimal model). The empirical material consisted of biomass data for 90 Scots pines growing on typical habitats in Bory Lubuskie (western Poland). The elaborated equations have a lower accuracy than the optimal ones. The R² value for all biomass components is higher than 0.69, and reaches as much as 0.976 in the case of dry wood biomass. The root mean square error (RMSE) for such components as dry biomass of bark and alive or dead branches and branches with needles is lower for the simplified model. However, for the dry wood biomass the optimal model has lower RMSE value. Because this component has the largest share in the total aboveground tree biomass (AGB), the resulting RMSE for the AGB is lower than for the optimal model. Optimal model is also more accurate when the mean error is considered. The simplified model can be used when there are no height measurement available or there is an anxiety that the use of height−diameter models significantly increases the uncertainty of results.
The objective of the study was to determine the quantitative and valuable potential of wood resources of black locust (Robinia pseudoacacia) and Douglas fir (Pseudotsuga menziesii) in individual regional directorates of the State Forests (RDSFs) in Poland. We used data from the State Forests Information System database (values for the end of 2014) to determine the amount of the resources of the analysed species in forests under the State Forests management. The monetary value of black locust and Douglas fir resources was determined using both the indicator method and on the basis of sales prices of individual assortments. The occurrence, and hence the resources of black locust and Douglas fir in our country are characterized by considerable spatial diversity. Generally speaking, studied tree species are of minor importance in Polish forests as far as area and volume are concerned, but both species can the most often and in the large abundance be found in the western and northern Poland. The average sale price of wood of the tested species varied a lot in individual regional directorates of the State Forests (fig.). In the case of black locust the average sale price ranged from 99 PLN/m³ in RDSF Szczecinek to 151 PLN/m³ in RDSF Krakow, while for Douglas fir the values from 59 PLN/m³ in RDSF Łódź to 277 PLN/m³ in RDSF Katowice were obtained. The total value of black locust timber resources was assessed by the sale price method at PLN 262.4 million, and by the indicator method at PLN 186.4 million. In the case of Douglas fir timber, these values were much higher and amounted to PLN 375.0 and 309.2 million, respectively. The highest value of the studied species stands was noted in the RDSF with the largest amount of their resources.
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.
Paper discusses the influence of site quality on self−thinning process in silver birch stands growing on abandoned farmlands in Mazowieckie region (central Poland). Number of trees in a stand decreases with increasing age. The better the site (the higher site index value), the higher number of trees can be observed. However at the age of 10 difference between sites of various quality (site index) become insignificant. There is no need to include site index into the self−thinning models for young silver birch stands.
The paper analyses the production and allocation of biomass in young, spontaneoussilver birch afforestation occurring on post-agricultural lands in the Mazowszeregion (central Poland). We investigated 114 sample plots of age varying from 1 to 19 years. During the first 15 years after their establishment on abandoned farmland, the naturally regenerated silver birch stands produced on average approximately 75 tons of dry biomass per hectare. The major (50–70%) part of this biomass was stored in the tree stems and this share increased with age. The fractions of biomass in the foliage and roots decreased over time, while the share of biomass in the branches remained rather constant. The significant age-dependency of the allometric relationships suggested the need to use age-sensitive biomass expansion factors to estimate the biomass from the stem volume.
The main aim of the study was to compare the radial growth of Persian walnut and Schrenk spruce trees growing under the same ecological conditions in the Sary-Chelek range of the Tien-Shan Mountains, as well as to analyse the response of these species to the selected climate factors in line with the altitude gradient. Four study plots were established at the altitude of 1350, 1400, 1450 and 1500 m a.s.l. Results indicated that (1) walnut and spruce in the Sary-Chelek Biosphere Reserve have different patterns of radial increment and reaction to climate factors, despite growing in the same habitat, (2) spruce radial growth responded to low precipitation and low temperature during the April to September period of the previous year; (3) walnut radial increment patterns varied significantly with changes in altitude, whereas spruce patterns did not; and (4) walnut radial increment patterns responded positively to high temperature during contemporary growing season and to precipitation during the prior growing season. In addition, it was noted that precipitation during the contemporary growing season could negatively influence growth.
The paper presents the tables for indirect determination of the age of silver birch (Betula pendula Roth) trees basing on easy to measure dendrometric parameters. We elaborated empirical formulae that enable deter− mination of tree age using total tree height, breast height diameter and stump diameter as the predictors. Data was collected in 40 pure silver birch stands growing on former farmlands in Mazowsze region (central Poland). Sample material consisted of data from the stem analyses of 200 trees and measurements of 600 stumps. Obtained equations explain 70−86% of the age variability. The best fit was achieved for joint use of total tree height and breast height diameter as the independent variables.
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