Modeling stem profile of caucasian fir and oriental spruce mixed stands in ardanuç, Turkey using nonlinear mixed-effects models

The objective of this study is to develop segmented polynomial taper equations which enable detailed volume estimations using the nonlinear mixed-effects modeling approach for Caucasian fir - Oriental spruce mixed stands in Artvin-Ardanuç region of Turkey. For this purpose, the data obtained from 213 felled sample trees in total, which are 107 Caucasian fir and 106 Oriental spruce, were used. The Jiang et al.'s stem profile model produced the best prediction results for both tree species. The adjusted coefficient of determination ((Radj^2), Standart Error of Estimate (SEE), Bias (E), and Mean Absolute Error (|E|) values of the model were found as 98.7 % and 98.3%, 1.700 and 1.814 cm, 0.143 and 0.167 cm, 1.179 and 1.269 cm for Caucasian fir and Oriental spruce trees, respectively. Based on AIC, BIC and -2LnL criteria, the model including random-effects in two parameters (b3 ve b4) were the best for both tree species. This mixed-effects model with two random parameters showed homogeneous residual variance and autocorrelation was almost removed. In addition, among 12 different calibration choices, the best results were obtained with the choice involving the measurement of five diameters that divide the sample tree measurements into two equal parts for Caucasian fir and of four diameters that are the lowest the base of the sample tree for Oriental spruce. It is also proposed to construct both single and double entry tree volume equations for the both tree species.These selected models accounted for 98.2 and 98.8% – 98.1 and 99.2% of the total variance in single and double entry tree volume equations for Caucasian fir and Oriental spruce, respectively. Tree volume equations were tested with independent data set for both tree species within the border of Ardanuç Forest District Directorates, and concluded that these equations can be used for these stands at the 0.05 significant level.