In this study, statistical nonlinear mixed effect models were used to model taper of individual trees in Pinus nigra stands distributed within the Çankiri Forests. The data from 210 trees that were felled from Pinus nigra stands were used in this study. Three tree taper equations were fitted and evaluated based on the sum square error (SSE), mean square error (MSE), root mean square error (RMSE) and the adjusted coefficient of determination (R²adj). The Jiang et al.'s equation was found to produce the most satisfactory fits with the SSE (4125.7), MSE (2.1771), RMSE (1.4755) and (0.976). The stem taper equation of Jiang et al. was used within the scope of mixed-effect model structures that involved both random and constant effect parameters. The nonlinear mixed-effect modeling approach for the stem taper equation of Jiang et al. with SSE (3254.8), MSE (1.71759), RMSE (1.3119) provided much better fitting and precise predictions than those produced by the nonlinear fixed effect model structures for this model. Within various sampling scenarios including different numbers of the sub-sample trees based on some sampling strategies from the validation data set, the sampling scheme with three top diameter sub-sample in a tree produced the best predictive results (SSE = 313.5321, MSE = 0.8637 and RMSE = 0.9345) in relation to the fixed effect predictions.

En este estudio se utilizaron modelos estadísticos no lineales de efectos mixtos para modelar el ahusamiento de árboles individuales en rodales de Pinus nigra distribuidos en bosques de Çankırı. Se utilizaron datos de 210 árboles que fueron talados. Se ajustaron y evaluaron tres ecuaciones de ahusamiento de árbol, basadas en la suma del error cuadrático (SSE), el error cuadrático medio (MSE), la raíz del error cuadrático medio (RMSE) y el coeficiente de determinación ajustado (R²adj). La ecuación de Jiang et al. produjo los ajustes más satisfactorios según SSE (4125,7), MSE (2,1771), RMSE (1,4755) y Radj²(0,976). Esta ecuación de ahusamiento del fuste se utilizó en el ámbito de un modelo de efecto mixto que involucra parámetros del azar y del efecto constante. El modelo no lineal de efectos mixtos para la ecuación de ahusamiento del fuste de Jiang et al. con SSE (3.254,8), MSE (1,71759) y RMSE (1,3119), proporcionó predicciones más ajustadas y precisas que los modelos no lineales de efectos fijos. Dentro de varios escenarios de muestreo, incluyendo diferentes números de los árboles de submuestra, basados en algunas estrategias de muestreo del conjunto de datos de validación, el esquema de muestreo con tres submuestra de diámetro superior en un árbol produjo los mejores resultados predictivos (SSE = 313,5321, MSE = 0,8637 y RMSE = 0,9345) en relación con las predicciones de efecto fijo.

Statistical nonlinear mixed effect models were used to predict relationships between the total height and diameter at breast height of individual trees in Oriental beech (Fagus orientalis Lipsky) stands in Kestel, Bursa, Northwestern Turkey. 124 sample plots were selected to represent various stand conditions such as site quality, age, and stand density. Nine generalized nonlinear height-diameter models were fitted and evaluated based on Akaike's information criterion, Schwarz's Bayesian Information Criterion (BIC), Root Mean Square Error (RMSE), Absolute Bias and Adjusted Coefficient of Determination (R²adj). The nonlinear Schnute's model was selected as the best predictive model. The height-diameter model based on the nonlinear mixed effect modeling approach accounted for 90.6 % of the total variance in height-diameter relationships and root mean square error (RMSE) values of 1.48 m. Various sampling scenarios that differed in sampling design and size of the selected sub-sample trees from the validation data set revealed that four randomly selected sub- sample trees in a given plot produced the best predictive results (43.3 % reduction of the sum of square errors, 98.4 % reduction of absolute bias, and 36.9 % reduction of the RMSE) in relation to the fixed effect predictions.

Modelos estadísticos no lineales de efectos mixtos se utilizaron para predecir las relaciones entre la altura total y el diámetro a la altura del pecho (DAP) en rodales de árboles de haya oriental (Fagus orientalis Lipsky) en Kestel, Bursa, al noroeste de Turquía. Un total de 124 parcelas de muestreo se seleccionaron para representar la calidad de sitio, edad y densidad de rodal. Nueve modelos no lineales generalizados de altura-diámetro se ajustaron y evaluaron con base en el criterio de información de Akaike, el criterio de información bayesiana de Schwarz, la raíz del cuadrado medio del error (RMSE por sus siglas en inglés), el sesgo absoluto y el coeficiente de determinación ajustado (R²adj). El modelo no lineal de Schnute se seleccionó como el mejor modelo predictivo. El modelo de altura-diámetro basado en el enfoque del modelo no lineal de efectos mixtos representó 90.6 % de la varianza total en las relaciones de altura-diámetro y los valores de RMSE de 1.48 m. Varios escenarios que difieren en el diseño de muestreo y el tamaño de los árboles submuestra, seleccionados del conjunto de datos de validación, revelaron que cuatro árboles submuestra seleccionados al azar produjeron los mejores resultados predictivos (reducción de 43.3 % de la suma de errores cuadrados, 98.4 % del sesgo absoluto y 36.9 % de la RMSE) en relación con las predicciones de los efectos fijos.

Diameter at breast height (DBH) is the simplest, most common and most important tree dimension in forest inventory and is closely correlated with wood volume, height and biomass. In this study, a number of linear and nonlinear models predicting diameter at breast height from stump diameter were developed and evaluated for Oriental beech (Fagus orientalisLipsky) stands located in the forest region of Ayancık, in the northeast of Turkey. A set of 1,501 pairs of diameter at breast height-stump measurements, originating from 70 sample plots of even-aged Oriental beech stands, were used in this study. About 80 % of the otal data (1,160 trees in 55 sample plots) was used to fit a number of linear and nonlinear model parameters; the remaining 341 trees in 15 sample plots were randomly reserved for model validation and calibration response. The power model data set was found to produce the most satisfactory fits with the Adjusted Coefficient of Determination, R2adj (0.990), Root Mean Square Error, RMSE (1.25), Akaike’s Information Criterion, AIC (3820.5), Schwarz’s Bayesian Information Criterion, BIC (3837.2), and Absolute Bias (1.25). The nonlinear mixed-effect modeling approach for power model with R2adj(0.993), AIC (3598), BIC (3610.1), Absolute Bias (0.73) and RMSE (1.04) provided much better fitting and precise predictions for DBH from stump diameter than the conventional nonlinear fixed effect model structures for this model. The calibration response including tree DBH and stump diameter measurements of the four largest trees in a calibrated sample plot in calibration produced the highest Bias, -5.31 %, and RMSE, -6.30 %, the greatest reduction percentage.