Abstract
The study was conducted to develop height-diameter at breast height (HT-DBH) models for Alnus japonica in La Trinidad, Benguet, Philippines and evaluate their predictive capability. The six widely used nonlinear growth models that were selected in this study were the Chapman-Richards, Schnute, Modified logistic, Korf/Lundqvist, Weibull and Exponential. A total of 208 Alnus japonica trees were measured using standard diameter tape for DBH (1.3 m above the ground) and Vertex and transponder was used for the total height measurement. The performance of the developed models were evaluated using the fit statistics including coefficient of determination (R2), root mean square error (RMSE), mean bias (Ē), absolute mean difference (AMD), and Akaike Information Criterion (AIC). The lack-of-fit statistics was also performed for further evaluation of the performance of the models. Based on the evaluation criteria, all six models were able to determine the DBH-height relationships and fitted the data well. Using the rank analysis, the Weibull HT-DBH model had the best performance among the six commonly used nonlinear growth models. The results of this study will help forest managers especially in La Trinidad, Benguet to easily predict the total height using the Weibull model for Alnus japonica utilizing the DBH as the predicting variable.
Similar content being viewed by others
References
Akaike H (1974) A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6): 716–723. https://doi.org/10.1109/TAC.1974.1100705
Ahmadi K, Alavi SJ, Kouchaksaraei MT, et al. (2013) Non-linear height-diameter models for oriental beech (Fagus orientalis Lipsky) in the Hyrcanian forests, Iran. Biotechnologie, Agronomie, Société et Environment 17(3): 431–440.
Arno S, Ramona H (2007) Northwest Trees: Identifying and Understanding the Region’s Native Trees. Seattle, WA: Mountaineers Books. p165.
Chapman DG (1961) Statistical problems in dynamics of exploited fisheries populations. Proc. 4th Berkeley Symp. on Mathematical Statistics and Probability. Vol. 4 Berkeley, CA. pp 153–168.
Coral-Rivas JJC, González JGA, González ADR, et al. (2004) Compatible height and site index models for five pine species in El Salto, Durango (Mexico). Forest Ecology and Management 201(2): 145–160. https://doi.org/10.1016/j.foreco.2004.05.060
Dorado FC, Diéguez-Aranda U, Anta MB, et al. (2006) A generalized height-diameter model including random components for radiata pine plantations in northwestern Spain. Forest Ecology and Management 229(1): 202–213. https://doi.org/10.1016/j.foreco.2006.04.028
Doyog ND, Lee YJ, Lee S (2017) Stem taper equation analysis for Larix kaempferi species in the Central Region of South Korea. Journal of Sustainable Forestry 36(8): 747–763. https://doi.org/10.1080/10549811.2017.1356737
Fang Z & Bailey RL (1998) Height-diameter models for tropical forests on Hainan Island in southern China. Forest Ecology and Management 110(1): 315–327. https://doi.org/10.1016/S0378-1127(98)00297-7
Huang S, Titus SJ, Wiens DP (1992) Comparison of nonlinear height-diameter functions for major Alberta tree species. Canadian Journal of Forest Research 22(9): 1297–1304. https://doi.org/10.1139/x92-172
Huang S, Price D, Titus SJ (2000) Development of ecological region-based height diameter models for white spruce in boreal forests. Forest Ecology and Management 129: 125–141. https://doi.org/10.1016/S0378-1127(99)00151-6
Huang S, Yang Y, Wang Y (2003) A critical look at procedures for validation growth and yield models. Wallingford, Oxfordshire, UK: CAB International. pp 271, 293. https://doi.org/10.1079/9780851996936.0271
Ige PO, Akinyemi GO, Smith AS (2013) Nonlinear growth functions for modeling tree height-diameter relationship for Gmelina arborea (Roxb.) in south-west Nigeria. Forest Science and Technology 9(1): 20–24. https://doi.org/10.1080/21580103.2013.773662
Kozak A, Kozak R (2003) Does cross validation provide additional information in the evaluation of regression models? Canadian Journal of Forest Research 33: 976–987. https://doi.org/10.1139/x03-022
Kozak A, Smith JHG (1993) Standards for evaluating taper estimating systems. The Forestry Chronicle 69(4): 438–444. https://doi.org/10.5558/tfc69438-4
Lee S, Doyog ND, Lee YJ (2017) Comparative Analysis of Simple Volume Models for Japanese Larch (Larix kaempferi) Species in the Central Region of South Korea. Journal of Agriculture & Life Sciences 51(4): 55–64.
Lumbres RIC, Lee YJ, Calora Jr FG, et al. (2013) Model fitting and validation of six height-DBH equations for Pinus kesiya Royle ex Gordon in Benguet Province, Philippines. Forest Science and Technology 9(1): 45–50. https://doi.org/10.1080/21580103.2013.772542
Lumbres RIC, Lee YJ, Yun CW, et al. (2015) DBH-height modeling and validation for Acacia mangium and Eucalyptus pellita in Korintiga Hutani Plantation, Kalimantan, Indonesia. Forest Science and Technology 11(3): 119–125. https://doi.org/10.1080/21580103.2014.957356
MacFarlane DW (2004) Ecologically stratified height-diameter models for hardwood species in northwestern lower Michigan. General Technical Report. NE-316 pp 87–93.
Peng C, Zhang L, Liu J (2001) Developing and validating nonlinear height-diameter models for major tree species of Ontario’s boreal forests. Northern Journal of Applied Forestry 18(3): 87–94. https://doi.org/10.1093/njaf/18.3.87
Peng C, Zhang L, Zhou X, et al. (2004) Developing and evaluating tree height-diameter models at three geographic scales for black spruce in Ontario. Northern Journal of Applied Forestry 21(2): 83–92. https://doi.org/10.1093/njaf/21.2.83
Poudel KP, Cao QV (2013) Evaluation of methods to predict Weibull parameters for characterizing diameter distributions. Forest Science 59(2): 243–252. https://doi.org/10.5849/forsci.12-00
Ratkowsky DA, Reedy TJ (1986) Choosing near-linear parameters in the four-parameter logistic model for radioligand and related assays. Biometrics 42: 575–582. https://doi.org/10.2307/2531207
Ratkwosky DA (1990) Handbook of nonlinear regression models (No. 04; QA278. 2, R3.). Marcel Dekker, New York, USA.
Richards FJ (1959) A flexible growth function for empirical use. Journal of Experimental Botany 10(2): 290–301. https://doi.org/10.1093/jxb/10.2.290
Rimondo JM (1995) Height-diameter relationship for plantation grown Eucalyptus in Kenya. Journal of Tropical Forest Science 8(2):178–184.
Saud P, Lynch TB, Anup KC, et al. (2016) Using quadratic mean diameter and relative spacing index to enhance height-diameter and crown ratio models fitted to longitudinal data. Forestry: An International Journal of Forest Research 89: 215–229. https://doi.org/10.1093/forestry/cpw004
SAS Institute Inc. (2004) SAS/STAT 9.1 User’s Guide. SAS Institute Inc., Cary. NC, USA.
Schnute J (1981) A versatile growth model with statistically stable parameters. Canadian Journal of Fisheries and Aquatic Sciences 38(9): 1128–1140. https://doi.org/10.1139/f81-153
Sharma M, Parton J (2007) Height-diameter equation-s for boreal tree species in Ontario using a mixed-effects modeling approach. Forest Ecology and Management 249(3): 187–198. https://doi.org/10.1016/j.foreco.2007.05.006
Stage AR (1963) A mathematical approach to polymorphic site index curves for grand fir. Forest Science 9(2): 167–180. https://doi.org/10.1093/forestscience/9.2.167
Yang RC, Kozak A, Smith JHG (1978) The potential of Weibulltype functions as flexible growth curves. Canadian Journal of Forest Research 8(4): 424–431. https://doi.org/10.1139/x78-062
Zeide B (1989) Accuracy of equations describing diameter growth. Canadian Journal of Forest Research 19(10): 1283–1286. https://doi.org/10.1139/x89-195
Zhang L (1997) Cross-validation of non-linear growth functions for modelling tree height-diameter relationships. Annals of Botany 79(3): 251–257. https://doi.org/10.1006/anbo.1996.0334
Zhang L, Peng C, Huang S, et al. (2002) Development and evaluation of ecoregion-based jack pine height-diameter models for Ontario. The Forestry Chronicle 78(4): 530–538. https://doi.org/10.5558/tfc78530-4
Acknowledgements
This study was carried out with the support of the Forest Science and Technology Projects [Project Nos. 2013069D10-1819-AA03 and 2014068E10-1819-AA03] provided by the Korea Forest Service.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Anacioco, K.P., Gorio, J.A.L., Padsico, M.R.S. et al. Fitting and evaluation of height-diameter models for Alnus japonica in La Trinidad, Benguet, Philippines. J. Mt. Sci. 15, 2422–2432 (2018). https://doi.org/10.1007/s11629-018-4866-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11629-018-4866-9