مدل‌سازی توزیع طبقات قطری گونه بلوط و توده‌ جنگلی در ارسباران (ایلگنه‌چای)

Modeling diameter distribution of oak and forest stand in Arasbaran (Ilgenechay)

Document type: Research paper

Authors

Raheleh Ostadhashemi1; Reza Akhavan2; Azim Abbaslou3; Ghasem Safapour4

1Assistant Professor, Forests and Rangelands Research Department, East Azerbaijan Agriculture and Natural Resources Research and Education Center, AREEO, Tabriz, Iran.
2Associate Professor, Research Institute of Forests and Rangelands, Agricultural Research Education and Extension Organization (AREEO), Tehran, Iran.
3MSc., Forests and Rangelands Research Department, East Azerbaijan Agriculture and Natural Resources Research and Education Center, AREEO, Tabriz, Iran.
4BSc., Researcher, Forests and Rangelands Research Department, East Azerbaijan Agriculture and Natural Resources Research and Education Center, AREEO, Tabriz, Iran.

Abstract
There are various probability distribution functions that can explain the distribution of different diameter classes in forest stands, which are used for modeling bio organisms. This study aimed to compare different probability distribution functions in order to find the best distribution function of trees in different diameter classes for oak tree species as well as forest stand in Arasbaran forests. The results of this study were obtained based on data of 30 sample plots in Ilgenechay watershed of Arasbaran. That, diameter at breast height (DBH≥5) of all trees (1501 trees) including 240 oaks was measured in the sample plots. Given diameters were classified in one cm diameter classes. In order to show the distribution of different diameter classes, the functions of Gamma, Beta, Weibull, Normal and Lognormal were developed using Easy Fit and SPSS. The results showed that the Gamma model is the best distribution function for both oak and forest stand. In addition, the highest tree density was in 11 and 10 cm diameter classes for oak and forest stand respectively. Gamma function parameters obtained α=11.101 and β= 1.1508 for oak and α=7.1062 and β= 1.6329 for forest stand. These results can be used in management strategies and conducts forest stands towards sustainable development.

Introduction
The diameter distribution is a key method to describe the uniformity and growth of a stand. It provides crucial information for forest inventories on different levels of structure and dynamics of the area regarding variability of density within size classes. Furthermore Diameter distributions are crucial decision– making tools for forest management. They directly affect the choices concerning silvicultural and harvesting stages activities. For instance, timing and intensity of thinning and harvesting, as well as harvesting equipment are dependent on the diameter distributions. There are various probability distribution functions to explain the distribution of different diameter classes in the forest stand, which are used for modeling bio organisms.
Arasbaran deciduous forests are located in the northwest of Iran as a Biosphere Reserved which covers an area of 78560 hectares. The altitude varies from ca. 256 m to more than 2000 m. the importance of the area is in having a rich flora (about 97 trees and shrubs species) and unique vegetation among the vegetation of the country. According to the previous researches, Carpinus sp. and Quercus sp. are the dominant species in forests of Arasbaran respectively.
This study aimed to fit distribution functions of Beta, Gamma, Normal, Lognormal and Weibull for modelling the distribution of trees in different diameter classes in order to find the best distribution function for oak species as well as forest stand in Arasbaran forests. Regarding the importance of Arasbaran forests, this study can lead to the better recognition the stand structure in order to sustainable management of Arasbaran forests.

Methodology
The results of this study were obtained from an area of 93 ha located in research forests in Ilgenechay watershed in Arasbaran and the data collected from 30 sample plots. The diameter at breast height (DBH≥5) of all trees (1501 trees) including 240 oaks was measured in the sample plots. Given diameters were classified in one cm diameter classes. In order to determine the distribution of different diameter classes, the functions of Gamma, Beta, Weibull, Normal and Lognormal were developed using Easy Fit and SPSS.
Maximum likelihood technique was developed to estimate model parameters for diameter distribution. Likewise, The Kolmogorov–Smirnov statistic, Chi-Squared and Anderson-Darling were used to evaluate the goodness of fits.
The Results showed that the average density (number of trees), mean basal area and percentage of seedling and coppice trees were 1627.7(N ha-1), 20.6(m2 ha-1), 63.7% and 36.3% respectively in the study area.
Due to, the mode is less than the median, and they are both less than the mean, therefore the distribution is skewed to the right for both oak and forest stand. Based on The represented histogram, the diameter distribution of oak displayed approximately a bell- shaped curve. In addition, the highest tree density was in 11 and 10 cm diameter classes for oak and the forest stand respectively.
The goodness-of- fit statistics indicated that, all models displayed appropriate fits to the data for the oak distribution but the Gamma function provided the most accurate fit. Which the Gamma function parameters obtained α=11.101 and β= 1.1508. While the results revealed that the Gamma function provided the just reasonable fit for the forest stand distribution which the Gamma function parameters obtained α=7.1062 and β= 1.6329.

Conclusion
The diameter-class distribution is one of the four interrelated components, i.e., species composition, quality, volume and diameter distribution of uneven-aged forest stands. The highest diameter class of 23 cm in oak trees, the maximum DBH of 34 cm in the forest stand and non J-shaped curve of diameter distribution, all indicated young forest stand in the study area and human disturbance in the forest stands due to charcoal practices in the past decades in Arasbaran.
In order to improve the forest stand structure based on sustainable development (achieving uneven-aged forests with J-shaped curve of diameter distribution), we needs to recognize the behavior of the diameter distribution of trees and forest stands. So these results are necessary for the multi-objective and sustainable management of forests and recommended for all different tree species and parameters in different ecological conditions

Key words

Quercus petraea L; Diameter distribution; Probability distribution function; Diameter at Breast Height (DBH)
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