Research Article
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Comparison of tree volume equations for brutian pine stands in Eğirdir district

Year 2019, Volume: 20 Issue: 3, 149 - 156, 30.09.2019
https://doi.org/10.18182/tjf.566019

Abstract

In this study, tree volume equations have been developed for Brutian pine (Pinus brutia Ten.). The data was obtained from the natural brutian pine stands in Eğirdir region. Totally of 405 trees are sampled and randomly separated into the two groups. Since there is no real independent dataset, two-fold evaluation scheme was applied and the prediction performance of 18 models was evaluated. For this purpose, four different criteria values were used: mean error (MD), mean absolute error (MAD), coefficient of determination (R2) and root mean square error (RMSE). The prediction performances of the models were evaluated on the basis of relative ranking. As a result of the evaluations, the most successful results were obtained with Model 4, while the most unsuccessful results were obtained with model 6. The obtained results suggested that Model 4 should be used to more reliable volume predictions for natural brutian pine stands in Eğirdir Region

Supporting Institution

Scientific Research Projects Coordination Unit of Süleyman Demirel University

Project Number

BAP-5053-YL1-17

References

  • Akindele, S.O., LeMay, V.M., 2006. Development of tree volume equations for common timber species in tropical rain forest area of Nigeria. Forest Ecology and Management, 226: 41-48.
  • Alegria, C., Tome, M., 2011. A set of models of individual tree merchantable volume prediction for Pinus pinaster Aiton in central inland of Portugal. European Journal of Forest Research, 130:871-879.
  • Alemdağ, Ş., 1962. Development, yield and management rules of Red pine (Pinus brutia Ten.) forests in Turkey. Technical Bulletin of Forestry research Institute No:11, 160s., Ankara.
  • Bailey, R.L., 1995. Upper stem volumes from stem analysis data: an overlapping bolts method. Can J. For. Res., 26(1): 170-173
  • Bi H., Hamilton, F., 1998. Stem volume equations for native tree species in southern New South Wales and Victoria. Australian Forestry 61(4): 275-286.
  • Børset, O., 1954. Volume computation of standing aspen. Commun Norweigan For Assoc, 43:397-447.
  • Bohora, S.B., Cao, Q.V., 2014. Prediction of tree diamater growth using quantile regression and mixed-effects models. Forest Ecology and Management, 319:62-66.
  • Bozkuş,H.F. ve Carus,S., 1997. Toros Göknarı (Abies cilicica Carr.) ve Sedir (Cedrus libani Link.) in Çift Girişli Gövde Hacim Tabloları ve Mevcut Tablolarla Karşılaştırılması, İstanbul Üniversitesi Orman Fakültesi Dergisi, Seri A, Cilt 47, Sayı 1, 51-70.
  • Brooks, J.R., Jiang, L., Özçelik, R., 2008. Compatible stem volume and taper equations for Brutian Pine, Cedar of Lebanon, and Cilicica Fir in Turkey. Forest Ecology and Management, 256:147-151.
  • Brooks, J.R., Wiant, H.V., 2008. Ecoregion Based Local Volume Equations for Appalachian Hardwoods. Northern Journal of Applied Forestry, 25(2): 87-92.
  • Burkhart, H.E., Tome, M., 2012. Modeling Forest Trees and Stands. Springer, Dordrecht.
  • Castedo-Dorado, F., Gómez-García, E., Diéguez-Aranda, U., Barrio-Anta, M., Crecente-Campo, F., 2012. Aboveground stand-level biomass estimation: a comparison of two methods for major forest species in northwest Spain. Annals of Forest Science, 69: 735-746.
  • Clutter, J.L., Fortson, J.C., Pienaar, L.V., Bailey, R.L., 1983. Timber Management: A Quantitative Approach. Krieger Publishing Company, Malabar, Florida.
  • Çatal, Y., 2009. Batı Akdeniz Bölgesi Kızılçam (Pinus brutia Ten.) Meşcerelerinde Artım ve Büyüme. Doktora Tezi, Süleyman Demirel Üniversitesi Fen bilimleri Enstitüsü, Isparta.
  • 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. Can. J. For. Res., 42: 1383-1394.
  • Diéguez-Aranda, U., Castedo-Dorado, F., Alvarez-Gonzalez, J.G., Rojo, A., 2006. Compatible taper function for scots pine plantations in Nortwestern Spain. Canadian Journal of Forest, 36(5): 1190-1205.
  • Eriksson, H., 1973. Volymfunktioner för stående träd av ask, asp, klibbal och contorta-tall. [Tree volume functions for ash, aspen, alder and lodgepole pine in Sweden. (Fraxinus excelsior L., Populus tremula L., Alnus glutinosa (L.) Gartn., Pinus contorta Dougl. var. latifolia Engelm.).] Skogshögskolan, Institutionen för skogsproduktion, Stockholm. Rapporter og Uppsatser nr. 26-1973. 26p.
  • Gómez-García, E., Crecente-Campo, F., Barrio-Anta, M., Diéguez-Aranda, U., 2015. A disaggregated dynamic model for predicting volume, biomass and carbon stocks in even-aged pedunculate oak stands in Galicia (NW Spain). European Journal of Forest research, 134: 569-583.
  • Hjelm, B., Johansson, T., 2012. Volume equations for poplars growing on farmland in Sweden. Scandinavian Journal of Forest Research, 27:561-566.
  • Honer, T., 1967. Standard volume tables and merchantable conversion factors for the commercial tree species of central and eastern Canada. For Manage Res and Serv Inst, Inf Rep FMR-X-5, Ottawa.
  • Kahriman, A., Sönmez, T., Şahin, A., 2017. Antalya ve Mersin yöresi kızılçam meşcereleri için ağaç hacim tabloları. Kastamonu Üniversitesi Orman Fakültesi Dergisi, 17(1): 9-22.
  • Kelly, T.F., Beltz, R.C., 1987. A Comparison of Tree Volume Estimation Models for Forest Inventory, USDA Forest Service, Southern Forest Experiment Station, Research Paper SO-233.
  • Kitikidou, K., Milios, E., Radoglou, K., 2017. Single-entry volume table for Pius brutia in panted peri-urban forest. Annals of Silvicultural Research, 41(2): 74-79.
  • Klos, R.J., Wang, G.G., Dang, Q.L., East. E.W., 2007. Taper equations for five major commercial tree species in Manitoba, Canada. West. J. Appl. For., 22: 163-170.
  • Kozak, A., Kozak, R.A., 2003. Does cross validation provide additional information in the evaluation of regression models? Canadian Journal of Forest Research, 33, 976–987.
  • Lee, D., Seo, Y., Choi, J., 2017. Estimation and validation of stem volume equations for Pinus densiflora, Pinus koraiensis, and Larix kaempferi in South Korea. Forest Science and Technology, 13:77-82.
  • Mısır, N., Mısır, M., 2004. Developing double-entry tree volume table for Ash in Turkey. Kafkas University, Artvin Faculty of Forestry 3(4):135-144.
  • Ogaya, N., 1968. Kubierungsformeln und Bestandesmassenformeln. Inaugural. Doctoral dissertation, Dissertation-. Univ., Nat.-Math. Fak, Freiburg.
  • OGM, 2018. Ormancılık İstatistikleri, Orman Genel Müdürlüğü,Ankara.
  • Özçelik, R., Çevlik, M., 2017. Batı Akdeniz Yöresi doğal sedir meşcereleri için hacim denklemleri. Turkish Journal of Forestry, 18:68-86.
  • Özçelik, R., Kalkanlı, Ş., 2018. Kaş Yöresi doğal kızılçam (Pinus brutia Ten.) meşcereleri için ağaç hacim denklemlerinin geliştirlmesi. Turkish Journal of Forestry, 19 (1): 9-19.
  • Özçelik, R., Cao, Q.V., Trincado, G., Göçer, N., 2018. Predicting tree height from diamater and dominant height using mixed-effects and quantile regression models for two species in Turkey. Forest Ecology and Management, 419-420:240-248.
  • Özkurt, A., 2000. Volume table for Eucalyptus grandis W. Hill ex. Maiden. Journal of Eastern Mediterranean Forestry Reseach Institute 6: 87-105.
  • Perez, D., 2008. Growth and volume equations developed from stem analysis for Tectora grandis in Costa Rica. Journal of Tropical Forest Science, 20: 66-75.
  • Pillsbury, N.H., McDonald, P.M., Simon, V., 1995. Reliability of Tanoak volume equations when applied to different areas. Western Journal of Applied Forestry, 10(2): 72-78.
  • Poudel, K.P., Cao, Q.V., 2013. Evaluation of methods to predict Weibull parameters for characterizing diameter distributions. For. Sci., 59(2): 243-252.
  • Rachid Casnati, C., Mason, E.G., Woollons, R., Resquin, F., 2014. Volume and taper equations for P. teada (L.) and E. grandis (Hill ex. Maiden). Agrociencia Uruguay, 18(2): 47-60.
  • Ritchie, M.W., Hann, D.W., 1984. Nonlinear equations for predicting diameter and squared diamter inside bark at breast height for Douglas-fir. Oregon State University, Forest Research Lab., Research Paper 47, 17p.
  • Rodríguez, 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: 213-223.
  • Sakıcı, O.E., Yavuz, H., 2003. Volume equations for Bormullerian Fir stands in Ilgaz Mountain. Gazi University Faculty of Forestry Journal, 3(2): 155-168.
  • Sakıcı, O.E., Sağlam, F., Seki, M., 2018. Single-and Double-entry volume equations for Crimean pine stands in Kastamonu Regional Directorate of Forestry. Turkish Jounral of Forestry, 19(19): 20-29.
  • Saraçoğlu, N., 1988. Stem volume table for Alder (Alnus glutinosa Gaertn subsp. Barbata (C.A. Mey.) Yalt.). Tr. J. Of Agriculture and Forestry, 22:215-225.
  • Schumacher, F.X., Hall, F.D.S., 1933. Logarithmic expression of timber-tree volume. J. Agric. Res., 47: 719-734.
  • Spurr, S.H., 1952. Forest Inventory. Ronald Press, New York.
  • Stolarikova, R., Salek, L., Zeahradnik, D., Dragoun, L., Jerabkova, L., Marusak, R., Merganic, J., 2014. Comparison of tree volume equations for small-leaved lime (Tilia cordota Mill.) in the Czech Republic. Scandinavian Journal of Forest Research, 29:757-763.
  • Takata, K., 1958. Construction of universal diameter-height-curves. Journal of Japanese Forest Society, 40:1.
  • Teshome, T., 2005. Analysis of individual tree volume equations for Cupressus Lusitanica in Munessa Forest, Ethiopia. Southern African Forestry Journal, 203: 27-32.
  • Yavuz, H., 1999. Volume equations and volume tables for Black pine in Taşköprü. Turkish Journal of Agriculture and Forestry, 23: 1181-1188.
  • Zianis, D., Muukkonen, P., Menuccini, M., 2005. Biomass and stem volume equations for tree species in Europe. Silva Fenn. Monogr., 4:63.

Eğirdir yöresi kızılçam meşcereleri için ağaç hacim denklemlerinin karşılaştırılması

Year 2019, Volume: 20 Issue: 3, 149 - 156, 30.09.2019
https://doi.org/10.18182/tjf.566019

Abstract

Bu çalışmada, Kızılçam (Pinus brutia Ten.) için ağaç hacim denklemleri geliştirilmiştir. Veriler, Eğirdir yöresi doğal kızılçam meşcerelerinden elde edilmiştir. 405 örnek ağaç ölçülmüş ve tesadüfi olarak iki gruba ayrılmıştır. Gerçek anlamda bağımsız veri setine sahip olunmadığı için çapraz geçerlilik testi uygulanarak, 18 modelin ortalama hata (MD), ortalama mutlak hata (MAD), belirtme katsayısı (R2) ve hata kareler ortalamasının karekökü (RMSE) değerleri hesaplanmıştır. Modellerin tahmin performansları, bu dört ölçüt değeri esas alınarak hesaplanan model nisbi sıralarına göre değerlendirilmiştir. Yapılan değerlendirmeler sonucunda, en başarılı sonuçlar Model 4 ile elde edilirken, en başarısız sonuçlar model 6 ile elde edilmiştir. Elde edilen sonuçlar, Eğirdir yöresi doğal kızılçam meşcerelerinde güvenilir hacim tahminleri için Model 4’ün kullanılmasını önermektedir.

Project Number

BAP-5053-YL1-17

References

  • Akindele, S.O., LeMay, V.M., 2006. Development of tree volume equations for common timber species in tropical rain forest area of Nigeria. Forest Ecology and Management, 226: 41-48.
  • Alegria, C., Tome, M., 2011. A set of models of individual tree merchantable volume prediction for Pinus pinaster Aiton in central inland of Portugal. European Journal of Forest Research, 130:871-879.
  • Alemdağ, Ş., 1962. Development, yield and management rules of Red pine (Pinus brutia Ten.) forests in Turkey. Technical Bulletin of Forestry research Institute No:11, 160s., Ankara.
  • Bailey, R.L., 1995. Upper stem volumes from stem analysis data: an overlapping bolts method. Can J. For. Res., 26(1): 170-173
  • Bi H., Hamilton, F., 1998. Stem volume equations for native tree species in southern New South Wales and Victoria. Australian Forestry 61(4): 275-286.
  • Børset, O., 1954. Volume computation of standing aspen. Commun Norweigan For Assoc, 43:397-447.
  • Bohora, S.B., Cao, Q.V., 2014. Prediction of tree diamater growth using quantile regression and mixed-effects models. Forest Ecology and Management, 319:62-66.
  • Bozkuş,H.F. ve Carus,S., 1997. Toros Göknarı (Abies cilicica Carr.) ve Sedir (Cedrus libani Link.) in Çift Girişli Gövde Hacim Tabloları ve Mevcut Tablolarla Karşılaştırılması, İstanbul Üniversitesi Orman Fakültesi Dergisi, Seri A, Cilt 47, Sayı 1, 51-70.
  • Brooks, J.R., Jiang, L., Özçelik, R., 2008. Compatible stem volume and taper equations for Brutian Pine, Cedar of Lebanon, and Cilicica Fir in Turkey. Forest Ecology and Management, 256:147-151.
  • Brooks, J.R., Wiant, H.V., 2008. Ecoregion Based Local Volume Equations for Appalachian Hardwoods. Northern Journal of Applied Forestry, 25(2): 87-92.
  • Burkhart, H.E., Tome, M., 2012. Modeling Forest Trees and Stands. Springer, Dordrecht.
  • Castedo-Dorado, F., Gómez-García, E., Diéguez-Aranda, U., Barrio-Anta, M., Crecente-Campo, F., 2012. Aboveground stand-level biomass estimation: a comparison of two methods for major forest species in northwest Spain. Annals of Forest Science, 69: 735-746.
  • Clutter, J.L., Fortson, J.C., Pienaar, L.V., Bailey, R.L., 1983. Timber Management: A Quantitative Approach. Krieger Publishing Company, Malabar, Florida.
  • Çatal, Y., 2009. Batı Akdeniz Bölgesi Kızılçam (Pinus brutia Ten.) Meşcerelerinde Artım ve Büyüme. Doktora Tezi, Süleyman Demirel Üniversitesi Fen bilimleri Enstitüsü, Isparta.
  • 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. Can. J. For. Res., 42: 1383-1394.
  • Diéguez-Aranda, U., Castedo-Dorado, F., Alvarez-Gonzalez, J.G., Rojo, A., 2006. Compatible taper function for scots pine plantations in Nortwestern Spain. Canadian Journal of Forest, 36(5): 1190-1205.
  • Eriksson, H., 1973. Volymfunktioner för stående träd av ask, asp, klibbal och contorta-tall. [Tree volume functions for ash, aspen, alder and lodgepole pine in Sweden. (Fraxinus excelsior L., Populus tremula L., Alnus glutinosa (L.) Gartn., Pinus contorta Dougl. var. latifolia Engelm.).] Skogshögskolan, Institutionen för skogsproduktion, Stockholm. Rapporter og Uppsatser nr. 26-1973. 26p.
  • Gómez-García, E., Crecente-Campo, F., Barrio-Anta, M., Diéguez-Aranda, U., 2015. A disaggregated dynamic model for predicting volume, biomass and carbon stocks in even-aged pedunculate oak stands in Galicia (NW Spain). European Journal of Forest research, 134: 569-583.
  • Hjelm, B., Johansson, T., 2012. Volume equations for poplars growing on farmland in Sweden. Scandinavian Journal of Forest Research, 27:561-566.
  • Honer, T., 1967. Standard volume tables and merchantable conversion factors for the commercial tree species of central and eastern Canada. For Manage Res and Serv Inst, Inf Rep FMR-X-5, Ottawa.
  • Kahriman, A., Sönmez, T., Şahin, A., 2017. Antalya ve Mersin yöresi kızılçam meşcereleri için ağaç hacim tabloları. Kastamonu Üniversitesi Orman Fakültesi Dergisi, 17(1): 9-22.
  • Kelly, T.F., Beltz, R.C., 1987. A Comparison of Tree Volume Estimation Models for Forest Inventory, USDA Forest Service, Southern Forest Experiment Station, Research Paper SO-233.
  • Kitikidou, K., Milios, E., Radoglou, K., 2017. Single-entry volume table for Pius brutia in panted peri-urban forest. Annals of Silvicultural Research, 41(2): 74-79.
  • Klos, R.J., Wang, G.G., Dang, Q.L., East. E.W., 2007. Taper equations for five major commercial tree species in Manitoba, Canada. West. J. Appl. For., 22: 163-170.
  • Kozak, A., Kozak, R.A., 2003. Does cross validation provide additional information in the evaluation of regression models? Canadian Journal of Forest Research, 33, 976–987.
  • Lee, D., Seo, Y., Choi, J., 2017. Estimation and validation of stem volume equations for Pinus densiflora, Pinus koraiensis, and Larix kaempferi in South Korea. Forest Science and Technology, 13:77-82.
  • Mısır, N., Mısır, M., 2004. Developing double-entry tree volume table for Ash in Turkey. Kafkas University, Artvin Faculty of Forestry 3(4):135-144.
  • Ogaya, N., 1968. Kubierungsformeln und Bestandesmassenformeln. Inaugural. Doctoral dissertation, Dissertation-. Univ., Nat.-Math. Fak, Freiburg.
  • OGM, 2018. Ormancılık İstatistikleri, Orman Genel Müdürlüğü,Ankara.
  • Özçelik, R., Çevlik, M., 2017. Batı Akdeniz Yöresi doğal sedir meşcereleri için hacim denklemleri. Turkish Journal of Forestry, 18:68-86.
  • Özçelik, R., Kalkanlı, Ş., 2018. Kaş Yöresi doğal kızılçam (Pinus brutia Ten.) meşcereleri için ağaç hacim denklemlerinin geliştirlmesi. Turkish Journal of Forestry, 19 (1): 9-19.
  • Özçelik, R., Cao, Q.V., Trincado, G., Göçer, N., 2018. Predicting tree height from diamater and dominant height using mixed-effects and quantile regression models for two species in Turkey. Forest Ecology and Management, 419-420:240-248.
  • Özkurt, A., 2000. Volume table for Eucalyptus grandis W. Hill ex. Maiden. Journal of Eastern Mediterranean Forestry Reseach Institute 6: 87-105.
  • Perez, D., 2008. Growth and volume equations developed from stem analysis for Tectora grandis in Costa Rica. Journal of Tropical Forest Science, 20: 66-75.
  • Pillsbury, N.H., McDonald, P.M., Simon, V., 1995. Reliability of Tanoak volume equations when applied to different areas. Western Journal of Applied Forestry, 10(2): 72-78.
  • Poudel, K.P., Cao, Q.V., 2013. Evaluation of methods to predict Weibull parameters for characterizing diameter distributions. For. Sci., 59(2): 243-252.
  • Rachid Casnati, C., Mason, E.G., Woollons, R., Resquin, F., 2014. Volume and taper equations for P. teada (L.) and E. grandis (Hill ex. Maiden). Agrociencia Uruguay, 18(2): 47-60.
  • Ritchie, M.W., Hann, D.W., 1984. Nonlinear equations for predicting diameter and squared diamter inside bark at breast height for Douglas-fir. Oregon State University, Forest Research Lab., Research Paper 47, 17p.
  • Rodríguez, 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: 213-223.
  • Sakıcı, O.E., Yavuz, H., 2003. Volume equations for Bormullerian Fir stands in Ilgaz Mountain. Gazi University Faculty of Forestry Journal, 3(2): 155-168.
  • Sakıcı, O.E., Sağlam, F., Seki, M., 2018. Single-and Double-entry volume equations for Crimean pine stands in Kastamonu Regional Directorate of Forestry. Turkish Jounral of Forestry, 19(19): 20-29.
  • Saraçoğlu, N., 1988. Stem volume table for Alder (Alnus glutinosa Gaertn subsp. Barbata (C.A. Mey.) Yalt.). Tr. J. Of Agriculture and Forestry, 22:215-225.
  • Schumacher, F.X., Hall, F.D.S., 1933. Logarithmic expression of timber-tree volume. J. Agric. Res., 47: 719-734.
  • Spurr, S.H., 1952. Forest Inventory. Ronald Press, New York.
  • Stolarikova, R., Salek, L., Zeahradnik, D., Dragoun, L., Jerabkova, L., Marusak, R., Merganic, J., 2014. Comparison of tree volume equations for small-leaved lime (Tilia cordota Mill.) in the Czech Republic. Scandinavian Journal of Forest Research, 29:757-763.
  • Takata, K., 1958. Construction of universal diameter-height-curves. Journal of Japanese Forest Society, 40:1.
  • Teshome, T., 2005. Analysis of individual tree volume equations for Cupressus Lusitanica in Munessa Forest, Ethiopia. Southern African Forestry Journal, 203: 27-32.
  • Yavuz, H., 1999. Volume equations and volume tables for Black pine in Taşköprü. Turkish Journal of Agriculture and Forestry, 23: 1181-1188.
  • Zianis, D., Muukkonen, P., Menuccini, M., 2005. Biomass and stem volume equations for tree species in Europe. Silva Fenn. Monogr., 4:63.
There are 49 citations in total.

Details

Primary Language English
Journal Section Orijinal Araştırma Makalesi
Authors

Ramazan Özçelik 0000-0003-2132-2589

Hakkı Altınkaya This is me 0000-0002-1765-1155

Project Number BAP-5053-YL1-17
Publication Date September 30, 2019
Acceptance Date June 25, 2019
Published in Issue Year 2019 Volume: 20 Issue: 3

Cite

APA Özçelik, R., & Altınkaya, H. (2019). Comparison of tree volume equations for brutian pine stands in Eğirdir district. Turkish Journal of Forestry, 20(3), 149-156. https://doi.org/10.18182/tjf.566019
AMA Özçelik R, Altınkaya H. Comparison of tree volume equations for brutian pine stands in Eğirdir district. Turkish Journal of Forestry. September 2019;20(3):149-156. doi:10.18182/tjf.566019
Chicago Özçelik, Ramazan, and Hakkı Altınkaya. “Comparison of Tree Volume Equations for Brutian Pine Stands in Eğirdir District”. Turkish Journal of Forestry 20, no. 3 (September 2019): 149-56. https://doi.org/10.18182/tjf.566019.
EndNote Özçelik R, Altınkaya H (September 1, 2019) Comparison of tree volume equations for brutian pine stands in Eğirdir district. Turkish Journal of Forestry 20 3 149–156.
IEEE R. Özçelik and H. Altınkaya, “Comparison of tree volume equations for brutian pine stands in Eğirdir district”, Turkish Journal of Forestry, vol. 20, no. 3, pp. 149–156, 2019, doi: 10.18182/tjf.566019.
ISNAD Özçelik, Ramazan - Altınkaya, Hakkı. “Comparison of Tree Volume Equations for Brutian Pine Stands in Eğirdir District”. Turkish Journal of Forestry 20/3 (September 2019), 149-156. https://doi.org/10.18182/tjf.566019.
JAMA Özçelik R, Altınkaya H. Comparison of tree volume equations for brutian pine stands in Eğirdir district. Turkish Journal of Forestry. 2019;20:149–156.
MLA Özçelik, Ramazan and Hakkı Altınkaya. “Comparison of Tree Volume Equations for Brutian Pine Stands in Eğirdir District”. Turkish Journal of Forestry, vol. 20, no. 3, 2019, pp. 149-56, doi:10.18182/tjf.566019.
Vancouver Özçelik R, Altınkaya H. Comparison of tree volume equations for brutian pine stands in Eğirdir district. Turkish Journal of Forestry. 2019;20(3):149-56.