Toros göknarında gövde çapı modelinin doğrusal olmayan karışık etkili modelleme yaklaşımı ile geliştirilmesi

Yıl 2018, , 138 - 148, 21.07.2018

Ramazan Özçelik , Emine Yiğit

https://doi.org/10.18182/tjf.395649

Cited By: 2

Öz

Bu çalışmada, doğal Toros göknarı (Abies cilicica Carr.) meşcereleri için karışık etkili modelleme tekniği ile Max ve Burkhart parçalı gövde çapı modeli kullanılarak gövde formundaki birey içi ve bireyler arası değişkenlikler ortaya konmuştur. Bu amaçla 327 örnek ağaç ölçülerek, rasgele yöntemle iki gruba ayrılmış ve 203 adet örnek ağaç (%60) model geliştirmek için, geri kalan 124 adet (%40) ağaç ise geliştirilen modelin test edilmesi amacıyla kullanılmıştır. Model ölçüt değerlerine göre, en başarılı tesadüfi etkili parametre kombinasyonu olarak β1, β3, β4 bulunmuştur. Modele tesadüfi etkilerin eklenmesi, hata korelasyonunu tamamen ortadan kaldırmamıştır. Hatalar arasındaki ağaç içi ve ağaçlar arası varyans ve otokorelasyon için modele sırasıyla bir hata varyans fonksiyonu ve otoregresif hata yapısı eklenmiştir. Bu işlem sonucunda, hata korelasyonu hemen hemen ortadan kalkmıştır. Diğer yandan, yeni bir ağaç için modelin kalibrasyonu amacıyla uygun bir Bayesian tahmincisi yardımı ile tesadüfi etkileri tahmin etmek amacıyla ekstra çap ölçümleri kullanılmıştır. Elde edilen sonuçlar test verileri ile denetlenmiştir. Ölçüt değerleri (ortalama hata, tutarlılık ve RMSE), ekstra çap ölçümleri ile tesadüfi etkilerin tahmini sonucunda, özelikle gövdenin ilk yarısındaki çap tahminlerinin oldukça başarılı olduğunu göstermiştir. Çalışmanın sonuçları, kalibrasyon için tek ve iki çap ölçümü arasında önemli farklılıkların olmadığını da ortaya koymuştur. Bu çalışmada kullanılan yöntem, doğal Toros göknarı meşcerelerinde uygulanacak farklı yönetim stratejileri ve farklı yetişme ortamlarındaki ağaçlar için gövde formundaki değişimin ortaya konması amacıyla kullanılabilir. Diğer yandan, bu çalışmanın sonuçları, karışık etkili modelleme tekniğinin, çap tahminleri için gövde çapı modellerinin etkinliğini ve esnekliğini arttırdığı yönündeki bulguları destekler niteliktedir.

Anahtar Kelimeler

Gövde çapı modeli, Tesadüfi parametre, Hata varyansı, Kalibrasyon

Developent of stem taper equation using nonlinear mixed-effects modeling approach for Taurus fir

Öz

The Max and Burkhart segmented taper equation was fitted using nonlinear mixed-effects modeling techniques to account for within- and between-individual variation in Taurus fir (Abies cilicica Carr.) stem profiles. Totally 327 sample trees measured and about 60% (203 trees) of the trees were randomly selected for model development and the reminder 40% (124 trees) of the trees used for model validation. Based on goodness-of-fit criteria, the model including three random-effects parameters β1, β3, and β4 was the best. An error variance function and a continuous auto correlation structure incorporated in model to within and between-tree residual variances and spatial autocorrelation between residuals. However, most of the residual autocorrelation was accounted for by including random effects. Upper stem diameter measurements were used to estimate random effects parameters using an approximate Bayesian estimator, which localized stem profile curves for individual trees. The procedure was tested with a validation data set. The goodness-of-fit statistics (Bias, precision, and RMSE) showed that upper stem diameter measurements and subsequent estimates of random effects improved the predictive capability of the taper equation mainly in the lower portion of the bole. Accordingly results of this research, there is no big differences between one and two additional upper stem diameter measurements for predictive capability of model. The method can localize stem curves for trees growing under different site and management conditions in natural Taurus fir stands. The results of this study support previous findings that mixed-effect modeling approach increases flexibility and efficiency of taper equations for upper stem diameter prediction.

Anahtar Kelimeler

Stem diameter model, Random parameter, Residual variance, Calibration

Kaynakça

• Arabatzis, A.A., Burkhart, H.E., 1992. An evaluation of sampling methods and model forms for estimating height-diameter relationships in loblolly pine plantations. Forest Science, 38(1): 192-198.
• Arias-Rodil, M., Diéguez-Aranda, U., Rodríguez Puerta, F., López-Sánchez, C.A., Canga Líbano, E., Cámara Obregón, A., Castedo-Dorado, F., 2015a. Modelling and localizing a stem taper function for Pinus radiata in Spain. Canadian Journal of Forest Research, 45(6): 647-658.
• Arias-Rodil, M., Castedo-Dorado, F., Cámara-Obregon, A., Diéguez-Aranda,U., 2015b. Fitting and calibrating a multilevel mixed-effects stem taper model for Maritime Pine in NW Spain. PLoS One, 10(12): e0143521.
• Arias-Rodil, M., Diéguez-Aranda, U., Burkhart, H.E., 2017. Effects of measurement error in total tree height and upper-stem diameter on stem volume prediction. Forest Science, 63(3): 250-260.
• Bates, D.M., Pinheiro, J.C., 1998. Computational Methods for Multilevel Modelling. University of Wisconsin, Madison, WI, pp. 1-29.
• Bi, H., 2000. Trigonometric varible-from taper equations for Australian Eucalyptus. Forest Science, 46(3): 397-407.
• Bueno-López, S.W., Bevilacqua, E., 2012. Nonlinear mixed model approaches to estimating merchantable bole volume for Pinus occidentalis. Biogeosciences and Forestry, 5: 247-254.
• Burkhart, H.E., Tomé, M., 2012. Modeling Forest Trees and Stands. Springer Science & Business Media. Cao, Q.V., 2009. Calibrating a segmented taper equation with two diameter measurements. Southern Journal of Applied Forestry, 33(2): 58–61.
• Clark, III A., Souter, R.A., Schlaegel, B.E., 1991. Stem profile equations for southern tree species. United States Department of Agriculture Forest Service Research Paper, SE-282.
• Davidian, M., Giltinan, D.M., 1995. Nonlinear Models for Repeated Measurement Data. New York, Chapman and Hall.
• De-Miguel, S., Mehtätalo, L., Shater, Z., Kraid, B., Pukkala, T., 2012. Evaluating marginal and conditional predictions of taper models in the absence of calibration data. Canadian Journal of Forest Research, 42: 1383-1394.
• Diéguez-Aranda, U., Dorado, F.C., González, J.G.Á., Alboreca, A.R., 2006. Dynamic growth model for Scots pine (Pinus sylvestris L.) plantations in Galicia (north-western Spain). Ecological Modelling, 191(2): 225-242.
• Fang, Z., Borders, B.E., Bailey, R.L., 2000. Compatible volume taper models for loblolly and slash pine based on system with segmented-stem form factors. Forest Science, 46: 1-12.
• Fang, Z., Bailey, R.L., 2001. Nonlinear mixed effects modeling for slash pine dominant height growth following intensive silvicultural treatments. Forest Science, 47: 287-300.
• Garber, S.M., Maguire, D.A., 2003. Modeling stem taper of three central Oregon species using nonlinear mixed effects models and autoregressive error structures. Forest Ecology and Management, 179: 507-507.
• Gómez-García, E., Crecente-Campo, F., Diéguez-Aranda, U., 2013. Selection of mixed effects parameters in a variable exponent taper equation for birch trees in northwestern Spain. Annals of Forest Science, doi: 10.1007/s13595-103-0313-9. Gómez-García, E., Diéguez-Aranda, U., Özcelik, R., Sal-Cando, M., Castedo-Dorado, F., Crecente-Campo, F., Corral-Rivas, J.J., Arias-Rodil, M., 2016. Desarrollo de una función de perfil mediante modelos mixtos para Pinus sylvestris en Turquía: selección de parámetros fijos a expandir. Bosque, 37(1): 159-167.
• Gregoire, T.G., Schabenberger, O., 1996. A non-linear mixed-effects model to predict cumulative bole volume of standing trees. Journal of Applied Statistics, 23: 257-271.
• Jiang, L., Brooks, J.R., Wang, J., 2005. Compatible taper and volume equations for yellow-poplar in West Virginia. Forest Ecology and Management, 213: 399-409.
• Kozak, A., 1988. A variable exponent taper equation. Canadian Journal of Forest Research, 18: 1363-1368.
• Kozak, A., 2004. My last words on taper equations. Forestry Chronicle, 80: 507–515.
• Lee, W.K., Seo, J.H., Son, Y.M., Lee, K.H., Von Gadow, K., 2003. Modeling stem profiles for Pinus densiflora in Korea. Forest Ecology and Management, 172:69-77.
• Leites, L., Robinson, A., 2004. Improving taper equations of loblolly pine with crown dimensions in a mixed-effects modeling framework. Forest Science, 50(2): 204-212.
• Lejeune, G., Ung, C.H., Fortin, M., Guo, X.J., Lambert, M.C., Ruel, J.C., 2009. A simple stem taper model with mixed effects for boreal black spruce. European Journal of Forest Research, 128: 505-513.
• Li, R., Weiskittel, A., Dick, A.R., Kershaw, J.A., Seymur, R.S., 2012. Regional stem taper equations for eleven conifer species in the Acadian region of North America: development and assessment. Northern Journal of Applied Forestry, 29: 5-14.
• Li, R., Weiskittel, A.R., 2010. Estimating and predicting bark thickness for seven conifer species in the Acadian Region of North America using a mixed-effects modeling approach: comparison of model forms and subsampling strategies. European Journal of Forest Research, 130: 219-233.
• Lindstrom, M.J., Bates, D.M., 1990. Nonlinear mixed effects models for repeated measures data. Biometrics, 46: 673-687.
• Max, T.A., Burkhart, H.E., 1976. Segmented polynomial regression applied to taper equations. Forest Science, 22: 283-289.
• Newnham, R.M., 1988. A Variable form Taper Function. Information Report PI-X-83. Forestry, 33p. Canada.
• Özcelik, R., Brooks, J.R., Jiang, L., 2011. Modeling stem profile of Lebanon cedar, Brutian pine and Cilicica fir in Southern Turkey using nonlinear mixed-effects models. European Journal of Forest Research, 130: 613-621.
• Özçelik, R., Yaşar, Ü., 2015. Development of stem diameter model for Bornmullerian fir (Abies nordmanniana (Stev.) subsp. bornmulleriana (Mattf.)) stands in Ayancık District using mixed effects modeling approach. Turkish Journal of Forestry, 16(2): 86-95.
• Özçelik, R., Crecente-Campo, F., 2016. Stem taper equations for estimating merchantable volume of Lebanon cedar trees in the Taurus Mountains, Southern Turkey. Forest Science, 62: 78-91.
• Özçelik, R., Cao, Q., 2017. Evaluation of fitting and adjustment methods for taper and volume prediction of black pine in Turkey. Forest Science, 63(4): 349-355.
• Parresol, B.R., Hotvedt, J. E., Cao, Q. V., 1987. A volume and taper prediction system for bald cypress. Canadian Journal of Forest Research, 17: 250-259.
• Pinheiro, J.C., Bates, D.M., 2000. Mixed Effects Models in S and S-plus. Springer, Heidelberg.
• Sabatia, C.O., Burkhart, H.E., 2014. Predicting site index of plantation loblolly pine from biophysical variables. Forest ecology and management, 326: 142-156.
• Sabatia, C.O., Burkhart, H.E., 2015. On the use of upper stem diameters to localize a segmented taper equation to new trees. Forest Science, 61(3): 411-423.
• Schabenberger, O., Pierce, F.J., 2001. Contemporary Statistical Models for the Plant and Soil Sciences. CRC press, New York.
• Scolforo, H.F., McTague, J.P., Raimundo, M.R., Weiskittel, A.R., Carrero, O., Soares Scolforo, J.R.S., 2018. Comparison of taper functions applied to eucalypts of varying genetics in Brazil: Application and evaluation of the penalized mixed spline approach. Canadian Journal of Forest Research, 48(3):(568-580).
• Sharma, M., Burkhart, H.E., 2003. Selecting a level of conditioning for the segmented polynomial taper equation. Forest Science, 49: 324-330.
• Sharma, M., Oderwald, R.G., 2001. Dimensionally compatible volume and taper equations. Canadian Journal of Forest Research, 31: 797–803.
• Sharma, M., Parton, J., 2009. Modeling Stand Density Effects on Taper for Jack pine Black spruce plantations Using Dimensional Analysis, Forest Science, 55(3): 268-282. Tang, X., Pérez-Cruzado, C., Fehrmann, L., Álvarez-González, J.G., Lu, Y., Kleinn, C., 2016. Development of a compatible taper function and stand-level merchantable volume model for Chinese fir plantations. PloS one, 11(1): e0147610.
• Trincado, G,. Burkhart, H.E., 2006. A generalized approach for modeling and localizing stem profile curve. Forest Science, 52: 670-682.
• Valentine, H.T., Gregorie, T.G., 2001. A switching model of bole taper. Canadian Journal of Forest Research, 31(8): 1400-1409.
• Vonesh, E.F., Chinchilli, V.M., 1997. Linear and Nonlinear Models for the Analysis of Repeated Measurements, Marcel Dekker, New York.
• West, P.W., Ratkowsky, D.A., Davis, A.W., 1984. Problems of Hypothesis testing of regression with multiple measurements from individual sampling units. Forest Ecology and Management, 7(3): 207-224.
• Yang, Y., Huang, S., Trincado, G., Meng, S.X., 2009a. Nonlinear mixed effects modelling of variable exponent taper equations for Lodgepole pine in Alberta, Canada. European Journal of Forest Research, 128: 415-429.
• Yang, Y., Huang, S., Meng, S.X., 2009b. Development of a tree-specific stem profile model for white spruce: a nonlinear mixed model approach with a generalized covariance structure. Forestry, 82(5): 541-555.