The construction of diameter-height models based on nonlinear mixed effect regression equations for oriental spruce located in mixed oriental spruce-scotch pine stands at Trabzon Forest District

Öz

Because of hard-working and time-consuming measurements for tree height, heights for all tree in sample plots can't be measure in many forest applications. These unmeasured tree heights can be predicted by height-diameter models relating tree height and diameters. In modeling the relationships between tree height and diameter, autocorrelation or serially correlations can be occurred in nested sampling systems for tree data measuring forest ecosystems. In this study, it is proposed to predict Nonlinear Mixed Effect Regression Models to alleviate these autocorrelation problems for constructing stand height-diameter curves in Oriental spruce (Picea orientalis (L.) Link) trees growing admixtures with scotch pine (Pinus sylvestris L.). The Schnute (1981), Huang et al. (2009), Wykoff et. al. (1982) nonlinear mixed effect model structure were predicted and compared for model height-diameter relationships in this study. In comparing these models, The Schnute (1981)'s nonlinear mixed effect model produced the best prediction results based on accuracy statistics. The Akaike (AIC) and Bayesian (BIC) Information Criterion were calculated as 15242 and 15257 and Schnute (1981) model predicted the % 95 percent of variability for height (R2=0.95). Schnute (1981) model with significant explanatory at variability of height and without serial correlation in diameter and height data will be use reliably to obtain predictions for oriental spruce tree heights. Keyword: Relationships between height and diameter, Oriental spruce, Nonlinear mixed effect regression model

Anahtar Kelimeler

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Trabzon Orman Bölge Müdürlüğü doğu ladini-sarıçam karışık meşcereleri için karışık etkili doğrusal olmayan regresyon denklemleri ile doğu ladini çap-boy modellerinin geliştirilmesi

Öz

Tek ağaçların boy ölçümü zor ve zaman alıcı olduğundan; birçok ormancılık uygulamasında tüm ağaçların boyları ölçülememektedir. Ölçülemeyen ağaç boyları, meşceredeki ağaçların göğüs çapları ile boyları arasındaki istatistiksel ilişkileri modelleyen regresyon denklemleri ile tahmin edilmektedir. Bu çalışmada, Trabzon Orman Bölge Müdürlüğü sınırları içerisinde yer alan Doğu ladini (Picea orientalis (L.) Link)-Sarıçam (Pinus sylvestris L.) karışık meşcerelerinde gelişim gösteren doğu ladini ağaçlarının çap-boy denklemlerinin oluşturulmasında, Doğrusal Olmayan Karışık Etkili Regresyon Modelleri geliştirilmesi amaçlanmıştır. Tek ağaçların çap-boy ilişkisini modellemek üzere, Schnute (1981), Huang vd (2009), Wykoff vd. (1982)'in Karışık Etkili Model yapıları oluşturulmuş ve başarı durumlarına göre karşılaştırılmıştır. En başarılı model olarak belirlenen Schnute (1981)'ın modeline ilişkin Akaike (AIC) Bilgi Ölçütü değeri; 15242 ve Bayesian (BIC) Bilgi Ölçütü değeri ise; 15257 olarak hesaplanmış olup, Schnute (1981)'ın modeli ile tek ağaçların boy gelişimindeki değişimin %95'ni (R2=0.95) tahmin edilmektedir. Önemli derecede açıklayıcıca sahip olan ve çap-boy verilerindeki seri korelasyon problemini taşımayan Karışık Etkili Doğrusal Olmayan Schnute (1981)'ın modeli, Doğu ladini ağaçlarının boyunun tahmininde güvenilir bir şekilde kullanılabilecektir. Anahtar kelimeler: Çap-boy ilişkisi, Doğu ladini, Karışık etkili doğrusal olmayan regresyon modeli

Anahtar Kelimeler

• Çap-boy ilişkisi, Doğu ladini, Karışık etkili doğrusal olmayan regresyon modeli

Kaynakça

1. Adame, P., del Río, M., Cañellas, I., 2008. A mixed nonlinear height-diameter model for pyrenean oak (Quercus pyrenaica Willd.). For.Eco. and Man., 256, 88–98
2. Avery, T.E., Burkhart, H. E. 1983. Forest Measurements, Mcgraw- Hill Series in Forest Resources, Mcgraw-Hill Book Company, New York, 331 s.
3. Budhathoki, C.B., Lynch, T.B., Guldin, J.M., 2008. A mixed- effects model for dbh–height relationship of shortleaf pine (Pinus echinata Mill.). South.J.Appl.For. 32:5-11.
4. Calama, R., Montero, G., 2004. Interregional nonlinear height- diameter model with random coefficients for stone pine in Spain. Can.J.For.Res. 34:150-163.
5. Castedo-Dorado, F., Barrio Anta, M., Parresol, B.R., Álvarez- González, J.G., 2005. Stochastic height-diameter model for maritime pine ecoregions in Galicia (northwestern Spain). Ann.For.Sci., 62:455-465
6. Castedo-Dorado, F., Diéguez-Aranda, U., Barrio, M., Sánchez, M., von Gadow, K., 2006. A generalized height-diameter model including random components for radiata pine plantations in northeastern Spain . For.Ecol.Manage. 229:202-213.
7. Clutter, J.L., Allison, B.J., 1974. A growth and yield model for Pinus radiata in New Zealand. In: Growth Models for Tree and Stand Simulation. J.Fries (ed), Royal College of Forestry, Stockholm, Sweden. Department of Forest Yield Research Note 30: 136–160.
8. Crecente-Campo, F., Tomé, M., Soares, P., Diéguez-Aranda, U., 2010. A generalized nonlinear mixed-effects height-diameter model for Eucalyptus globulus Spain.For.Eco. and Man, 259: 943-952. L. in northwestern

9. Curtis, R.O., 1967. Height-diameter and height–diameter-age equations for second growth Douglas-Fir. For.Sci. 13:365-375.
10. Davis, S.L., Johnson, K.N., Bettinger, P.S., Howard, T.E., 2001. Forest Management, McGraw-Hill, 804 p. NewYork.
11. Doğanay, B., 2007. Uzunlamasına çalışmaların analizinde karma etki modelleri. Ankara Üniversitesi, Sağlık bilimleri Enstitüsü Yüksek Lisans Tezi, 94 s.
12. Eerikäinen, K., 2003. Predicting the height–diameter pattern of planted Pinus kesiya stands in Zambia and Zimbabwe. For. Ecol. Manage. 175:355-366.
13. Ercanlı, İ., 2010. Trabzon ve Giresun orman bölge müdürlükleri sınırları içerisinde yer alan Doğu Ladini (Picea orientalis (l.) Link)-Sarıçam (Pinus sylvestris L.) Karışık meşcerelerine ilişkin büyüme modelleri. Doktora Tezi, KTÜ Fen Bilimleri Enstitüsü, Trabzon.
14. Ercanlı, İ., Yavuz, A., Kahriman, A., 2011, ormancılıkta artım ve büyümenin modellenmesinde yeni bir regresyon analizi yaklaşımı:karışık model eşitlikleri, I. Ulusal Akdeniz Orman ve Çevre Sempozyumu, 26-28 Ekim, Kahramanmaraş.
15. Fang, Z., Bailey, R.L., 1998. Height-diameter models for tropical forests on Hainan Island in southern China. For.Ecol.Manage. 110:315-327.
16. Fekedulengn, D., Siurtain, M.P.M., Colbert, J.J., 1999. Parameter estimation of nonlinear growth models in forestry. Silv.Fenn., 33:327-336.
17. Fulton, M.R., 1999. Patterns in height-diameter relationship for selected tree species and sites in eastern Texas. Can.J.For.Res. 29:1445-1448.
18. Gadow K., Real P, Álvarez Gonzáles J.G. 2001. Modelización del Crecimiento y la Evolución de los Bosques. IUFRO World Series, Vol. 12, Vienna.
19. Gadow, K.V., Hui, G.Y., 1999. Modelling Forest Development, Kluwer Academic Publishers, 213 p., Dordrect
20. Gaffrey, D., 1988. Forstamts-und bestandesindividuelles Sortimentierungsprogramm als Mittel zur Planung, Aushaltung und Simulation. Diploma Thesis. Göttingen, Forstwissenschaftlicher Fachbereich, 86 pp.
21. Harrison,W., Burk, T., Beck, D., 1986. Individual tree basal area increment and total height equations for Appalachian mixed hardwoods after thinning. South. J.Appl.For. 10, 99-104.
22. Hökkä, H., 1997. Height-diameter curves with random intercepts and slopes for trees growing on drained peatlands. For.Ecol.Manage. 97:63-72.
23. Huang, S., Meng, S.X., Yang, Y., 2009. Using nonlinear mixed model technique to determine the optimal tree height prediction model for black spruce, Modern Applied Science, 3(4):3-18.
24. Huang, S., Price, D., Titus, S. J., 2000. Development of ecoregion- based height-diameter models for white spruce in boreal forests. For. Ecol. Manage. 129:125-141.
25. Huang, S., Titus, S. J., Wiens D. P., 1992. Comparison of nonlinear height-diameter functions for majör Alberta tree species. Canadian Journal of Forest Research, 22:1297-1304.
26. Huang, S., Titus, S.J., 1993. An index of site productivity for uneven-aged and mixed-species stands. Can.J.For.Res. 23:558- 562.
27. İyit, N., 2008. İlişkili Veri Analizinde Lineer Karma Modellerin Yapılandırılması, Selçuk Üniversitesi Fen Bilimleri Enstitüsü Doktora Tezi, 162 s., Konya.
28. İyit, N., Genç, A., Arslan, F., 2006. Analysis of repeated measures for continuoes response data using General Linear Model and Mixed Models, Proceedings of the international conference on modeling and simulation, pp:937-942, Konya, Turkey.
29. Jayaraman, K., Lappi, J., 2001. Estimation of height–diameter curves through multilevel models with special reference to evenaged teak stands. For. Ecol. Manage. 142:155-162.
30. Jayaraman, K., Zakrzewski, W.T., 2001. Practical approaches to calibrating height-diameter relationships for natural sugar maple stands in Ontario. For.Ecol.Manage. 148:169-177.
31. Kahriman, A., 2011. Karadeniz Bölgesi sınırları içerisinde yer alan Sarıçam (Pinus sylvestris L.)-Doğu Kayını (Fagus orientalis Lipsky) karışık mesçerelerine ilişkin büyüme modellerinin geliştirilmesi. Doktora Tezi, KTÜ Fen Bilimleri Enstitüsü, 250 s.
32. Kalıpsız, A., 1984. Dendrometri, İstanbul Üniversitesi Orman Fakültesi Yayınları , İstanbul.
33. Keselman, H.J., Algina, J., Kowalchuk, R.K., Wolfinger, R.D., 1998. A comparison of two approaches for selecting covariance structures in the analysis of repeated measures. Communications in Statistics-Computation and Simulation, 27(3):591-604.
34. Lappi, J., 1997. A longitudinal analysis of height–diameter curves. For.Sci. 43:555-570.
35. Lei Y., Parresol B. R., 2001). Remarks on height-diameter modeling (Res Note SRS-10), USDA For Service, Southern Research Station, Asheville, NC.
36. Littell, R. C., Miliken, G.A., Stroup, W.W., Wolfinger, R.D., 2005. SAS system for mixed models, SAS Institute Inc., Cary,, NC, USA
37. Lopez Sanchez, C.A., Varela, J.G., Dorado, F.C., Alboreca, A.R., Soalleiro, R.R., Alvarez Gonzalez, J.G., Rodriguez, F.S., 2003. A height-diameter model for Pinus radiata D.Don in Galicia (Northwest Spain). Ann. For.Sci. 60:237-245.
38. Lynch, T.B, Holley A.G., Stevenson, D.J. 2005. A random- parameter height-dbh model for cherrybark oak., South J.Appl.For.29:22-26
39. Mehtätalo, L., 2004. A longitudinal height-diameter model for Norway spruce in Finland., Can.J.For.Res. 34:131-140
40. Meng, S.X., Huang, S., Lieffers, V.J., Nunifu, T., Yang, Y., 2008. Wind speed and crown class influence the height–diameter relationship of lodgepole pine: Nonlinear mixed effects modeling, For.Eco. and Management, 256:570-577
41. Mısır, N., 2003. Karaçam Ağaçlandırmalarına İlişkin Büyüme Modelleri, Doktora Tezi, KTÜ. Fen Bilimleri Enstitüsü, 222 s., Trabzon.
42. 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.
43. Paulo, J.A., Tomé, J., Tomé, M., 2011. Nonlinear fixed and random generalized height–diameter models for Portuguese cork oak stands. Annals of Forest Science, 68: 295-309
44. Peng, C., 1999. Nonlinear height- diameter models for nine boreal forest tree species in Ontario (OFRI-Rep 155), Ministry of Natural Resources Institutes.
45. Peng, C., Zhang, L., Liu, J., 2001. Developing and validating nonlinear height-diameter models for major tree species of Ontario’s boreal forests. North.J.Appl.For. 18:87-94.
46. Robinson, A.P.,Wykoff, W.R., 2004. Imputing missing height measures using a mixed-effects modeling strategy. Can.J.For.Res. 34:2492-2500.
47. SAS Institute Inc., 2004. SAS/STAT 9.1 User's Guide: statistics, Version 9.1, SAS Institute Inc., Cary, NC., 816 s.
48. Saunders, M.R., Wagner, R.G., 2008. Long-term spatial and structural dynamics in Acadian mixedwood stands managed under various silvicultural systems. Can.J.For.Res., 38, 498- 517.
49. Schmidt, M., Kiviste, A., von Gadow, K.A., 2010. spatially explicit height-diameter model for Scots pine in Estonia, Eur. J. Forest Res., 23:1-13
50. Schnute, J., 1981. A versatile growth model with statistically stable parameters. Can. J. Fish. Aquat.Sci. 38:1128-1140.
51. Searle, S.R., Casella, G., Mc Culloch, C.E., 1992. Variance components, John Wiley and Sons Inc., USA.
52. Sharma, M., Parton, J., 2007. Height-diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach . For.Ecol.Manage. 249:187-198.
53. Sharma, M., Zhang, S.Y., 2004. Height-diameter models using stand characteristics for Pinus banksiana and Picea mariana. Scand. J.For.Res. 19:442-451.
54. Soares, P., Tomé, M., 2002. Height–diameter equation for first rotation eucalypt plantations in Portugal. For.Ecol.Manage. 166:99-109.
55. Sönmez, T., 2009. Generalized height-diameter models for Picea orientalis (L.). Journal of Environmental Biology, 30 (5), 767- 772.
56. Temesgen, H., Gadow, K.V., 2004. Generalized height-diameter models-an application for major tree species in complex stands of interior British Columbia. Eur.J.For.Res. 123:45-51.
57. Trincado, G., VanderSchaaf, C.L., Burkhart, H.E., 2007. Regional mixed-effects height-diameter models for loblolly pine (Pinus taeda L.) plantations. Eur.J.For.Res., 126:253-262 .
58. van Lear, A., Akça A., 2007. Forest mensuration:in Managing Forest Ecosystems, Dordrecht, The Netherlands: Springer. 383 s.
59. Wolfinger R., Chang, M.,1999. Comparing the SAS GLM and MIXED Procedures for repeated measures. SAS Institute, Inc., Cary, NC.
60. Wykoff, W.R., Crookston, N.L., Stage, A.R., 1982. User’s guide to the stand prognosis model. USDA For. Serv. Gen. Tech. Rep. INT-133.
61. Yang, R.C., Kozak, A., Smith, J.H.G., 1978, The potential of Weibull-type functions as a flexible growth curve. Canadian Journal of Forest Research, 8:424-431
62. Ye, S., 2005. Covariance structure selection in linear mixed models for longitudinal data, M. Sc. Thesis, department of Bioinformatics and Biostatistics, University of Lousville, Kentucky, USA.
63. Zhang, L., 1997. Cross-validation of non-linear growth functions for modelling tree height–diameter relationships. Ann. Bot. 79: 251-257.
64. Zhang, L., Peng, C., Huang, S., Zhou, X., 2002. Development and evaluation of ecoregion-based jack pine height-diameter models for Ontario. For. Chron. 78:530-538.