Development of stem diameter model for Bornmullerian fir (Abies nordmanniana (Stev.) subsp. bornmulleriana (Mattf.)) stands in Ayancık District using mixed effects modeling approach

Öz

A nonlinear mixed-effect modeling approach was used to model for Turkish fir [Abies nordmanniana (Stev.) subsp. bornmülleriana (Mattf.)] stands in Sinop-Ayancık District of Turkey. About 87% of the trees were randomly selected for model development and the reminder used for model validation. Based on goodness-of-fit criteria, the model including random-effects in all parameters was the best. The selected mixed-effects model showed homogeneous residual variance and autocorrelation was reduced with the inclusion of random-effects. Measures of bias and precision indicated that estimates of random-effects improved significantly the predictive capability of the taper equation when predicting upper stem diameters. Mixed models allow calibration of the model for new locations, by predicting random coefficients if additional stem form measurements are available. Diameter measurements from various stem locations were evaluated for tree-specific calibrations by predicting random-effects parameters using an approximate Bayesian estimator. It was found that an upper stem diameter at 8.3 m above ground was best suited for calibrating tree-specific predictions of diameter outside bark. The results of this study support previous findings indicating that the use of mixed-effects modeling approach increases flexibility and efficiency of taper equations for upper stem diameter prediction. Keywords:Stem diameter, Mixed-effects model, Bornmullerian fir, Model calibration

Anahtar Kelimeler

• Stem diameter, Mixed-effects model, Bornmullerian fir, Model calibration

Sinop Yöresi Uludağ Göknarı (Abies nordmanniana (Stev.) subsp. bornmülleriana (Mattf.)) meşcereleri için gövde çapı modelinin karışık etkili modelleme tekniği ile geliştirilmesi

Öz

Sinop-Ayancık Yöresi Uludağ göknarı [Abies nordmanniana (Stev.) subsp. bornmülleriana (Mattf.)] meşcereleri için doğrusal olmayan karışık etkili modelleme kullanılarak gövde profili modeli geliştirilmiştir. Bu amaçla ölçümü yapılan ağaçların %87’si model geliştirmek, geri kalan %13’lük kısmı ise geliştirilen modeli test etmek amacıyla kullanılmıştır. Ölçüt değerleri temel alındığında, en uygun model yapısının modelin bütün parametrelerinin tesadüfi değişken içermesi durumunda ortaya çıktığı görülmüştür. Model, homojen bir varyans yapısı göstermiş ve veriler arası otokorelasyonu azaltmıştır. Tesadüfi değişken eklenen model, ağaç gövdesi üzerinde değişik noktalardaki çap tahminlerinde önemli iyileşmeler sağlamıştır. Karışık etkili modeller, eğer ekstra çap ölçümleri mevcut ise, tesadüfi değişkenler yardımı ile yeni bir yer ya da birey için modelin kalibrasyonuna imkân sağlamaktadır. Bu amaçla ağaç gövdesi üzerindeki farklı yerlerdeki çap ölçümleri ve uygun Bayesian yaklaşımı kullanılarak kalibrasyon alternatifleri değerlendirilmiştir. Çap tahminleri için en uygun kalibrasyon seçeneğinin 8.3 m’de ölçülen çap değeri olduğu görülmüştür. Bu çalışmanın sonuçları, çap tahminleri amacıyla gövde çapı modelinin etkinliğini ve esnekliğini arttırmak amacıyla karışık etkili modelleme yaklaşımının kullanımını desteklemektedir. Anahtar kelimeler: Gövde çapı, Karışık-etkili model, Uludağ göknarı, Model kalibrasyonu

Anahtar Kelimeler

• Gövde çapı, Karışık-etkili model, Uludağ göknarı, Model kalibrasyonu

Kaynakça

1. Akaike, H., 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(2):716-723.
2. Arabatzis, A.A., Burkhart, H.E., 1992. An Evaluation of Sampling Methods and Model Forms for Estimating Height-Diameter Plantations. Forest Science, 38(1):192-198. in Loblolly-Pine
3. Brooks, J.R., Jiang, L., Ozcelik, R., 2008. Compatible stem volume and taper equations for Brutian pine, Cedar of Lebanon, and Cilicica fir in Turkey. Forest Ecology and Management, 256(1-2):147-151.
4. Burkhart, H.E., Tomé, M., 2012. Modeling forest trees and stands. Springer Science & Business Media.
5. Calama, R., Montero, G., 2005. Multilevel linear mixed model for tree diameter increment in stone pine (Pinus pinea): a calibrating approach. Silva Fenn, 39(1): 37-54.
6. Calama, R., Montero, G., 2006. Stand and tree-level variability on stem form and tree volume in Pinus pinea L.: a multilevel random components approach. Forest Systems, 15(1):24-41.
7. Cao, Q.V., Wang, J., 2011. Calibrating fixed-and mixed- effects taper equations. Forest ecology and management, 262(4):671-673.
8. Clark, A., Souter, R.A., Schlaegel, B.E., 1991. Stem Profile Equations for Southern Tree Species. Usda Forest Service Forest Research Paper(Se-282):1-113. Experiment Station

9. Davidian, M., Giltinan, D.M., 1995. Nonlinear models for repeated measurement data. (c. 62). CRC Press.
10. De-Miguel, S., Mehtatalo, 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-Revue Canadienne De Recherche Forestiere, 42(7): 1383-1394.
11. Ercanli, İ., 2015. Nonlinear Mixed Effect Models For Predicting Relationships Between Total Height And Diameter Of Oriental Beech Trees In Kestel, Turkey.
12. Fang, Z.X., Bailey, R.L., 2001. Nonlinear mixed effects modeling for slash pine dominant height growth following intensive silvicultural treatments. Forest Science, 47(3): 287-300.
13. Fang, Z.X., Borders, B.E., Bailey, R.L., 2000. Compatible volume-taper models for loblolly and slash pine based on a system with segmented-stem form factors. Forest Science, 46(1): 1-12.
14. Figueiredo-Filho, A., Borders, B.E., Hitch, K.L., 1996. Taper equations for Pinus taeda plantations in Southern Brazil. Forest Ecology and Management, 83(1): 39-46.
15. 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(1-3): 507-522.
16. Gomez-Garcia, E., Crecente-Campo, F., Dieguez-Aranda, U., 2013. Selection of mixed-effects parameters in a variable-exponent taper equation for birch trees in northwestern Spain. Annals of Forest Science, 70(7): 707-715.
17. 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(2-3): 257-271.
18. Jiang, L., 2004. Compatible taper and volume equations for yellow-poplar in West Virginia., West Virginia University, Morgantown, WV.
19. Jiang, L., Brooks, J.R., Hobbs, G.R., 2007. Using crown ratio in yellow-poplar compatible taper and volume equations. Northern Journal of Applied Forestry, 24(4): 271-275.
20. Jiang, L., Brooks, J.R., Wang, J., 2005. Compatible taper and volume equations for yellow-poplar in West Virginia. Forest ecology and management, 213(1): 399- 409.
21. Kozak, A., 1988. A Variable-Exponent Taper Equation. Canadian Journal of Forest Research-Revue Canadienne De Recherche Forestiere, 18(11): 1363-1368.
22. Kozak, A., 1998. Effects of upper stem measurements on the predictive ability of a variable-exponent taper equation. Canadian journal of forest research, 28(7): 1078-1083.
23. Kozak, A., 2004. My last words on taper equations. The Forestry Chronicle, 80(4): 507-515.
24. 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(1): 69-77.
25. 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(5): 505-513.
26. Li, R., Weiskittel, A., Dick, A.R., Kershaw, J.A., Seymour, 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(1): 5-14.
27. 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(2): 219-233.
28. Lindstrom, M.J., Bates, D.M., 1990. Nonlinear mixed effects models for repeated measures data. Biometrics: 673-687.
29. Martin, A.J., 1981. Taper and volume equations for selected Appalachian hardwood species. (c. 490). US Department of Agriculture, Forest Service.
30. Max, T.A., Burkhart, H.E., 1976. Segmented polynomial regression applied to taper equations. Forest Science, 22(3): 283-289.
31. Meydan-Aktürk, G., 2006. Doğu Ladini (Picea orientalis (L.) Link) için Trigonometrik Gövde Çapı Denkleminin Oluşturulması.Yüksek Lisans Tezi, Karadeniz Teknik Üniversitesi, Fen Bilimleri Enstitüsü,Trabzon.
32. Newnham, R.M., 1988. A Variable form Taper Function. Information Report PI-X-83. Forestry, 33p. Canada.
33. Ozcelik, R., Bal, C., 2013. Effects of adding crown variables in stem taper and volume predictions for black pine. Turkish Journal of Agriculture and Forestry, 37(2): 231-242.
34. Ozcelik, R., Brooks, J.R., 2012. Compatible volume and taper models for economically important tree species of Turkey. Annals of Forest Science, 69(1): 105-118.
35. Ozcelik, R., Brooks, J.R., Jiang, L.C., 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(4): 613-621.
36. Parresol, B.R., Hotvedt, J.E., Cao, Q.V., 1987. A Volume and Taper Prediction System for Bald Cypress. Canadian Journal of Forest Research-Revue Canadienne De Recherche Forestiere, 17(3): 250-259.
37. Perez, D.N., Burkhart, H.E., Stiff, C.T., 1990. A Variable- Form Taper Function for Pinus-Oocarpa Schiede in Central Honduras. Forest Science, 36(1): 186-191.
38. Pinheiro, J.C., Bates, D.M., 2000. Mixed effects models in S and S-plus. Springer, Heidelberg, 528p. report. United Nations Economic Commission for Europe, Convention on International Co-operative Programme on Assessment and Monitoring of Air Pollution Effects on Forests (International Co-operative Programme Forests), 23p.
39. Rodriguez, F., Lizarralde, I., Fernandez-Landa, A., Condes, S., 2014. Non-destructive measurement techniques for taper equation development: a study case in the Spanish Northern Iberian Range. European Journal of Forest Research, 133(2): 213-223.
40. Sakıcı, O.E., 2002. Kastamonu Yöresi Uludağ Göknarı Meşcerelerinde Gövde Profili, Hacim, Hacim Oran Sistemlerinin Geliştirilmesi. Yüksek Lisans Tezi, Karadeniz Enstitüsü,Trabzon. Fen Bilimleri
41. Sakici, O.E., Misir, N., Yavuz, H., Misir, M., 2008. Stem taper functions for Abies nordmanniana subsp bornmulleriana in Turkey. Scandinavian Journal of Forest Research, 23(6): 522-533.
42. Şenyurt, M., Ercanlı, İ., Saraçoğlu, Ö., 2014. Batı Karadeniz Yöresi Sarıçam meşcereleri için uyumlu Gövde çapı ve Gövde hacim denklemlerinin karışık etkili modelleme ile Geliştirilmesi. II. Ulusal Akdeniz Orman ve Çevre Sempozyumu, Antalya, s. 601-607.
43. Sharma, M., Burkhart, H.E., 2003. Selecting a level of conditioning for the segmented polynomial taper equation. Forest science, 49(2): 324-330.
44. Sharma, M., Oderwald, R.G., 2001. Dimensionally compatible volume and taper equations. Canadian Journal of Forest Research, 31(5): 797-803.
45. Sharma, M., Parton, J., 2009. Modeling stand density effects on taper for jack pine and black spruce plantations using dimensional analysis. Forest Science, 55(3): 268-282.
46. Sharma, M., Zhang, S., 2004. Variable-exponent taper equations for jack pine, black spruce, and balsam fir in eastern Canada. Forest ecology and management, 198(1): 39-53.
47. Tasissa, G., Burkhart, H.E., 1998. An application of mixed effects analysis to modeling thinning effects on stem profile of loblolly pine. Forest ecology and management, 103(1): 87-101.
48. Trincado, G., Burkhart, H.E., 2006. A generalized approach for modeling and localizing stem profile curves. Forest Science, 52(6): 670-682.
49. Vonesh, E., Chinchilli, V.M., 1997. Linear and nonlinear models for the analysis of repeated measurements. Dekker Inc., New York. 560 p.
50. West, P.W., Patkowsky, D.A., Davis, A.W., 1984. Problems of hypothesis testing of regressions with multiple measurements from individual sampling units. Forest Ecology and Management, 7:207-224.
51. Yang, Y., Huang, S., Meng, S.X., 2009a. 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.
52. Yang, Y., Huang, S., Trincado, G., Meng, S.X., 2009b. Nonlinear mixed-effects modeling of variable-exponent taper equations for lodgepole pine in Alberta, Canada. European Journal of Forest Research, 128(4): 415-429.
53. Yavuz, H., 1995. Taşköprü Orman İşletmesinde Sarıçam ve Karaçam İçin Uyumlu Gövde Çapı. Gövde Hacmi ve Hacim Oran Denklem Sistemlerinin Geliştirilmesi. Basılmamış Doçentlik Tezi. KTU Orman Mühendisliği Bölümü. Orman Amenajmanı Anabilim Dalı, Trabzon.
54. Yavuz, H., Saraçoğlu, N., 1999. Compatible and non- compatible stem taper equations for Alder. Turkish Journal of Agriculture and Forestry, 23: 1275-1282.
55. Zakrzewski, W., 1999. A mathematically tractable stem profile model for jack pine in Ontario. Northern Journal of Applied Forestry, 16(3): 138-143.