Investigation on the response of Fagus orientalis Lipsky to some environmental variables using beta function and its comparison with Gaussian function (Case study: Kheyrud forest research station(

The current study was done in Patom, Namkhaneh, Gorazbon, Chelir and Baharbon districts in Kheyrud forest. A stratified sampling method based on landform was used to locate 190 0.1 ha circular sample plots in beech dominated forests. The number of Fagus orientalis Lipsky trees with DBH ≥ 7.5 cm within each plot was recorded along with elevation and slope of the ground. Also, at the center of plot, soil samples from first layer were taken for analyzing soil texture, bulk density and saturation moisture. In order to study the shape of response curve and extract the ecological optimum and amplitude in relation to the mentioned variables, beta function was used in the context of generalized linear model (GLM) with poison distribution and logarithmic link function. Gaussian Function were also applied to the data and its performance was compared to Beta Function using Deviance Test and the shape of response whether it is unimodal and symmetric or skewed. Beta function showed the response of beech to altitude is left-skewed, meaning it avoids lower elevations. This species has 1420 and 300-2150 m a.s.l for its optimum and ecological amplitude, respectively. Beech tree can distribute from gentle to steep slopes in the study area. The behavior of beech to slope is symmetric and unimodal attaining its optimum at 40% slope. Using beta function indicated that Fagus have amplitude of 0 to 80% regarding to slope percentage. In light of sand, clay and silt, Beech tree has 25, 43 and 35 % for optimum and 1-48 % for sand, 20-58% for clay and 17-55 % for silt for ecological amplitude, respectively. Using beta function showed the response of Fagus to sand and silt is unimodal and symmetric, but for clay it shows left-skewed shape. It implies that Fagus avoids soils containing low clay contents. The optimum and tolerance of saturation moisture for Fagus have been determined 50 and 17-55%, respectively. Fagus showed right-skewed response to bulk density. It gets its optimum at 1.6 g/cm³ and it can distribute from 1.3 to 2.7 g/cm³. Gaussian function always gives symmetric and bell-shaped species responses whereas the beta function has the advantage of describing either very skewed unimodal responses, or symmetric responses. It can also detect some types of bimodal. The results of this study showed although there is not much difference between Gaussian and beta functions based on deviance explained, but beta function could detect skewed response curve well, compared to Gaussian function. Beech tree has not always showed symmetric responses to the selected variables and the hypothesis implying Beech tree has unimodal and symmetric response to environmental variables can be rejected.