Dynamic Base-age Invariant Site Index Models for Scotch Pine (Pinus silvestris L.) in Kastamonu Forest Regional Directorate

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1 ORAL PRESENTATION Dynamic Base-age Invariant Site Index Models for Scotch Pine (Pinus silvestris L.) in Kastamonu Forest Regional Directorate Muammer Şenyurt 1, and İlker Ercanli 2 1 Asst. Prof., Cankiri Karatekin University, Cankiri, Turkey; 2 Asst. Prof., Cankiri Karatekin University, Cankiri, Turkey. msenyurt@karatekin.edu.tr Abstract: The precise predictions of forest site quality is important for operative forest management and essential for stratifying forest areas into productive classes, e.g. site classes. The estimations of site quality are significant input variable for forest growth and yield models. Many methods have been developed for estimating site index and constructing site index curves, Clutter et al. (1983) described three general methods having special importance in forest literature; (1) the guide curve method, (2) the parameter prediction method and (3) the difference equation methods. Cieszewski and Bailey (2000) introduced the Generalized Algebraic Difference Approach (GADA), a generalization of the ADA. The generalized algebraic difference approach (GADA) can produce base-age invariant models with variable asymptotes, which are capable of describing a polymorphic family of growth curves. The dynamic site index models derived by GADA have shown better and more successful properties than the fixed baseage site index models in many studies. In this study, Data from stem analysis of 50 dominant trees were used to evaluate dynamic base-age invariant site index models derived from Bertalanffy-Richards and Hosfeld with Generalized Algebraic Difference Approach for Scotch pine (Pinus silvestris L.) stands located in Kastamonu Forest Regional Directorate. The site index model based on Bertalanffy-Richards produced the coefficient of determination with and RMSE with The site index model based on Hosfeld produced the coefficient of determination with 0.89 and RMSE with These dynamic polymorphic site index models with multiple asymptotes are more successful in fulfilling all of desirable properties of height growth pattern than either anamorphic or single polymorphic models. Therefore, the new dynamic base-age invariant site index models developed based on GADA methodology can be recommended for dominant height prediction and forest site quality evaluations in these scotch pine stands. Keywords: site index model, generalized algebraic difference approach, scotch pine, Kastamonu forest regional directorate Introduction: The accurate and effective site quality predictions for forest stands are required for sustainable forest planning (Clutter et. al., 1983), because various forestry practices and activities depend on the productivity of forest sites, similarly called as forest site quality. Also, stand growth and yield highly were affected by the forest site quality; the variables of the site quality are important input variables for forest growth and yield models (Husch et al. 1972). In virtue of this importance of site quality, a variety of methods for estimating site productivity have been developed in forest history (Clutter et al., 1983; Palahi et. al. 2004). In these alternatives, because of independence of dominant height growth over a quite wide range of stand density, site index, defined as the height of trees that have always been dominant or co-dominant and healthy at a reference age, is the most widely used method of site quality evaluation for even-aged forest stands (Álvarez-González et. al. 2005; Carmean 1972). Clutter et al. (1983) described three general methods to develop site index models; (1) the guide curve method, (2) the parameter prediction method and (3) the difference equation methods (Palahi et al. 2004). The guide curve method producesaaverage height growth including anaomorphic site index curves for forest population Clutter et al. (1983). The parameter prediction method depends on the relationships between the parameters of site index curves and site qualities (Carmean 1972). As an application of the difference equation method, Bailey and Clutter (1974) applied a technique formalizing the base-age invariance feature for dynamic site index models that is called the algebraic difference approach (ADA) in forest literature. Cieszewski and Bailey (2000) further prolonged 179 I n t e r n a t i o n a l C a u c a s i a n F o r e s t r y S y m p o s i u m

2 Dynamic Base-age Invariant Site Index Models for Scotch Pine (Pinus silvestris L.) in Kastamonu Forest Regional Directorate the algebraic difference parameter prediction approach (ADA) and introduced the Generalized Algebraic Difference Approach (GADA), a generalization of the ADA. Cieszewski and Bailey (2000) described that GADA site index model as having a general form; Y = f (t, t 0, Y 0), where Y is the function s value at t, and Y 0 is the reference variable defined as the value of the function at age t 0. In developing site index prediction systems, the GADA site index models presents some desirable characteristics of site index models including polymorphism, multiple horizontal asymptote, one-inflection point and, base-age invariance (Bailey and Cieszewski 2000). The objective of the present study is to develop a dynamic site index system based on the general algebraic difference approach (GADA) for Scotch pine (Pinus silvestris L.) stands in Kastamonu Forest Regional Directorate. Material and Methods: In this study, the poylmorpmic method were used to develop a dynamic site index system based on the general algebraic difference approach (GADA) for Scotch pine (Pinus silvestris L.) stands in Kastamonu Forest Regional Directorate. The data from stem analysis of 50 dominant trees obtained by Senyurt (2011) were used to evaluate dynamic base-age invariant site index models derived from Bertalanffy-Richards and Hosfeld with Generalized Algebraic Difference Approach for Scotch pine (Pinus silvestris L.) stands. These sample plots were randomly selected to represent the range of site qualities and ages variability throughout these stands. These sampled stands were naturally regenerated and uniformly stocked stands (60-90% tree layer cover), without any evidence of historical damage such as fire or storms. The sample plot determination was examined according to 10 neighbor trees method. The major advantage of this method is the lack of any requirement to be in geometric shapes for sample plots, providing normal closure and the determination of sample plot according to age. This method is very practical and gives information for forest yield studies made in even aged and pure stands as in geometric shaped sample plots (Senyurt 2011). In this study, one dominant and co-dominant trees were sampled for stem analysis in the sample plots. These sample trees had to be dominant or co-dominant free-growing trees with no obvious evidence of growth abnormalities or damages. These sampling trees for stem analysis were felled, and also the cross-sectional cuts were made at the first 0.3 m and the second 1.3 m of the stem and every 2 m throughout the tree stem. The number of rings was counted at each crosssectioned point, and then these values were converted to stump age, which can be considered equal to tree age. A number of statistical growth functions have been used to model the height-age relationship in forest literature (Diéguez-Aranda et al. 2006; Gadow and Hui 1999). In particular, the Bertalanffy-Richards (Richards 1959) and Hossfeld (Hossfeld 1882) growth models have been the most popular and suitable as for site index predictions systems (Elfving and Kiviste 1997; Hui and Gadow 1999; Pienaar and Turnbull 1973). Bertalanffy-Richards growth model: Hossfeld growth model: In these models, h and h 0 are dominant height (m) at age t and t 0 (years), X is the parameter relating site and a, b, c, b 1, b 2, b 3 are fitted regression parameters. These growth models were evaluated by using numeric and graphic analysis of the prediction and residuals of these models. The evaluation criteria are mean squared error (MSE), root mean squared error (RMSE) and the adjusted coefficient of determination ( criteria were: ). The model evaluation 180 I n t e r n a t i o n a l C a u c a s i a n F o r e s t r y S y m p o s i u m

3 Muammer Şenyurt, and İlker Ercanli In addition to this evaluation of models including these statistical criteria, the correspondence to desirable biological presumption for site index models were analyzed to provide efficient and accurate site index predictions, e. g. Polymorphism, sigmoid growth pattern, multiple asymptotes, passing a zero point etc. Results: The parameter predictions, including its standard error, t-value and p value, and models goodness-of-fit statistics, e.g., MSE, RMSE, for these growth models are presented in tables 1.All parameters of these models were found to be significant at the 0.05 probability level (P < 0.05).These goodness-offit statistics proposed that Bertalanffy- Richards growth model has the better predictive ability with (0.9033), MSE (5.2667), RMSE (2.2949) than Hossfeld growth model. Table 3. Parameter estimations and goodness-of-fit statistics of candidate models for Oriental beech Model MSE RMSE Parameter Estimate S. E. t-value Approx. P > t Bertalanffy- Richards Hossfeld b < b < b < b < b < The mathematical expression of the site index model based on Bertalanffy-Richards growth mode is the following: In addition to evaluating these statistical criteria, the biological desirable presumptions of site index models, e.g. polymorphism, sigmoid growth pattern and multiple asymptotes, were checked as important attributes for developing site index prediction systems. In Fig. 1., the families of site index curves with different site indices, including 10, 12, , 28 m and 30 m at 100 years, were presented. When this graph was examined, it is 181 I n t e r n a t i o n a l C a u c a s i a n F o r e s t r y S y m p o s i u m

4 Dynamic Base-age Invariant Site Index Models for Scotch Pine (Pinus silvestris L.) in Kastamonu Forest Regional Directorate concluded that the shape of these site index curves fulfilled some desirable biological presumptions for site index predictions, e.g. polymorphism and sigmoid growth pattern. Mainly, a polymorphic sigmoid growth pattern which had different shapes at each site index values was accomplished for this site index model. Also, multiple asymptotes as another desirable attribute, which have implied as the varying asymptotic values of models with site index values, can be obtained by this site index model with some simulations of height predictions for 250 ages. SI=30 m SI=10 m Fig. 1.The site index curves generated with Bertalanffy-Richards growth model Discussion: This study presented the Dynamic Base-Age Invariant Site Index Models based on Generalized Algebraic Difference Approach for Scotch pine (Pinus sylvestris L.) stands in Kastamonu Forest Regional Directorate. In modeling dominant height-age relationships, the Bertalanffy-Richards (Richards 1959) and Hossfeld (Hossfeld 1882) growth models were used. In these models, Bertalanffy-Richards growth model accounted for 90 % of the total variance in height-age relationships in dominant trees. This site index equation has important desirable attributes for modeling height-age relationships, e.g. polymorphism, multiple asymptotes and sigmoid growth pattern. Other studies about site index modeling, e.g. Cieszewski and Bailey (2000), Cieszewski (2002), Cieszewski (2003), Cieszewski (2004), Corral-Rivas et al. (2004), Diéguez-Aranda et al. (2005), Diéguez-Aranda et al. (2006), Martín-Benito et al. (2008), has been reported in these desirable model results for site index predictions. This dynamic baseage invariant site index models can be presented to give effective and superior site index predictions by using GADA methodology for these studied Scotch pine (Pinus sylvestris L.) stands. References Álvarez-González, J., Ruiz Gonzalez, A., Rodriguez Soalleiro, R., M. Barrio Anta Development of ecoregion-based site index models for even-aged stands of Pinus pinaster Ait. in Galicia (northwestern Spain). Annals of Forest Science 62: Bailey, R.L., J. L. Clutter Base-age invariant polymorphic site curves. Forest Science 20: Carmean, W. H Site index curves for upland oaks in the Central States. Forest Science 18: Cieszewski, C.J., R. L.Bailey Generalized algebraic difference approach: theory based derivation of dynamic site equations with polymorphism and variable asymptotes. Forest Science 46: Cieszewski, C. J Comparing fixed and variable-base-age site equations having single versus multiple asymptotes.forest Science48 (1): I n t e r n a t i o n a l C a u c a s i a n F o r e s t r y S y m p o s i u m

5 Muammer Şenyurt, and İlker Ercanli Cieszewski, C. J Developing a wellbehaved dynamic site equation using a modified Hossfeld IV function Y 3 = (Ax m )/ (C + X m-1 ): a simplified mixed-model and scant Subalpine fir data. Forest Science 49: Cieszewski, C. J GADA Derivation of Dynamic Site Equations with Polymorphism and Variable Asymptotes From Richards to Weibull and Other Exponential Functions. Plantation Management Research Cooperative, Athens. Clutter, J. L., Fortson, J. C., Pienaar, L. V., Brister, G. H., R. L. Bailey Timber Management: A Quantitative Approach. John Wiley & Sons, New York. Corral-Rivas J. J., Alvarez-Gonzalez, J. G., Ruız- Gonzalez, A. D., K.von Gadow Compatible height and site index models for five pine species in El Salto, Durango (Mexico). Forest Ecology andmanagemnt 2004;201: Diéguez-Aranda, U., Burkhart, H. E., R.Rodriguez-Soalleiro Modeling dominant height growth of radiata pine (Pinusradiata D. Don) plantations in northwestern Spain. Forest Ecology and Management 215: Diéguez-Aranda, U., Grandas-Arias, J. A., Álvarez-González, J. G., K. V.Gadow Site Quality Curves For Birch (Betula pubescens Ehrh.) Stands North- Western Spain. Silva Fennica 40(4): Elfving, B., A,Kiviste1997. Construction of site index equations for Pinussylvestris L. Using permanent plot data in Sweden. Forest Ecology and Management 98: Gadow, K.V., G. Y.Hui Modelling Forest Development. Kluwer Academic Publishers, Dordrect. Hossfeld, J. W Mathematik für Forstmänner, Ökonomen und Cameralisten. Gotha, 4 Bd, p 310 (in German). Husch, B., Miller, C., T. W. Beers Forest Mensuration, 2nd ed. The Ronal Press Company, New York. Martín-Benito, D., Gea-Izquierdo, G., del Río M., I Cañellas Long-term trends in dominant-height growth of Black pine using dynamic models. Forest Ecology andmanagement 256: Palahi, M., Tome, M., Pukkala, T., Trasobares, A., G. Montero Site index model for Pinussylvestris in north-east Spain. Forest Ecology and Managemnt 187: Pienaar, L.V., K. J. Turnbull The Chapman-Richards generalization of Von Bertalanffy s growth model for basal area growth and yield in even-aged stands. Forest Science 19 (1): Richards, F. J A flexible growth function for empirical use. JournalExp Botanic 10: Şenyurt, M Growth and Yield of Scotch Pine Stands located in West Blacksea Regions, PHD Thesis, Istanbul University. 183 I n t e r n a t i o n a l C a u c a s i a n F o r e s t r y S y m p o s i u m