LINEAR AND NONLINEAR MODELS WITH USE OF COVARIATES FOR HYPSOMETRIC RELATIONSHIP OF TWO TROPICAL PINE SPECIES
DOI:
https://doi.org/10.5902/1980509820651Keywords:
h/d curves, tropical pines, height-diameter relationship, covariates.Abstract
http://dx.doi.org/10.5902/1980509820651
Traditionally, most studies use linear models to adjust the hypsometric relationship using diameter at breast height (DBH) as the only independent variable. However, it is known that the linearity does not characterizes faithfully biological growth and other variables related to forest stand, or individual trees, influence in height growth. The aim of this study was to evaluate linear and nonlinear models’ performance for hypsometric relationship of two tropical pine species, as well as the effect of covariates adding in models’ parameters estimation. The data used provided from Pinus caribaea var. hondurensis and Pinus oocarpa stands, with different ages and site index, located in the counties of Nova Ponte and Indianápolis, Minas Gerais state. Linear and nonlinear models were fitted in its original form and including the covariates age, site index and species in the estimation of each models’ parameter. The models were compared using the following statistical criteria: residual standard error (Syx), Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC) and also by graphical analysis of standardized residuals. It was found that nonlinear models show greater ability to describe height behavior, and the inclusion of covariates in models’ parameters improved its fit quality, considering the statistical accuracy criteria adopted.
Downloads
References
ASSMANN, E. Waldertragskunde. München: BLV, Verlagsgessellschaft, 1961. 435p.
BARROS, D.A. de. et al. Comportamento de modelos hipsométricos tradicionais e genéricos para plantações de Pinus oocarpa em diferentes tratamentos. Boletim de Pesquisa Florestal, Colombo,n.45, p.3-28, jul./dez. 2002.
BARTOSZECK, A. C. de P e S. et al. Modelagem da relação hipsométrica para bracatingais da região metropolitana de Curitiba – PR. Floresta, Curitiba, v.32, n.2, p. 189-204, abr./jun., 2002.
BARTOSZECK, A.C. de P e S. et al. Dinâmica da relação hipsométrica em função da idade, do sítio e da densidade inicial de povoamentos de bracatinga na região metropolitana de Curitiba – PR. Revista Árvore, Viçosa, v. 28, n. 4, p. 517-533, jul./ago. 2004.
CALAMA, R.; MONTERO, G. Interregional nonlinear height–diameter model with random coefficients for stone pine in Spain. Canadian Journal of Forest Research, Ottawa, v. 34, p. 150-163, jan.2004.
CALEGARIO,N. et al. Melhoria da qualidade de ajuste de modelos biométricos florestais pelo emprego da teoria dos modelos não-lineares generalizados.ScientiaForestalis, Piracicaba, v. 69, p. 38-50, dez., 2005.
EMBRAPA. Sistema brasileiro de classificação de solos. 2ª Ed. Rio de Janeiro: Embrapa Solos, 2006. 306p.
FANG, Z.; BAILEY, R.L. Height-diameter models for tropical forests on Hainan Island in southern China, Forest Ecology and Management, Amsterdam, v. 110, p. 315-327, out. 1998.
FERREIRA, D. F. Estatística básica. Lavras: Editora UFLA, 2ª Ed. 2009. 664p.
GUIMARÃES, M. A. M. et al. Heigth- diameter models in forestry with inclusion of covariates. Cerne, Lavras, v. 15, n. 3, p. 313-321, jul./set. 2009.
LEITE, H.G.; ANDRADE, V.C. de L.; Importância das variáveis altura dominante e altura total em equações hipsométricas e volumétricas. Revista Árvore, Viçosa, v. 27, n. 3, p. 301-310, mai./jun.2003.
MACHADO, S.A.et al. Análise do comportamento da relação hipsométrica com respeito à idade para plantações de Pinus elliottii no estado do Paraná. Cerne, Lavras, v. 1, n. 1, p. 5-12, 1994.
MCCULLAGH, P.; NELDER, J. A. Generalized linear models. London: Chapman & Hall, 1983. 261p.
NEWTON, P.F.; AMPONSAH, I.G. Comparative evaluation of five height–diameter models developed for black spruce and jack pine stand-types in terms of goodness-of-fit, lack-of-fit and predictive ability. Forest Ecology and Management, Amsterdam, v.247, p. 149-166, ago. 2007.
R DEVELOPMENT CORE TEAM.R: A language and environment for statistical computing. R Foundation for StatisticalComputing, Vienna, Austria. ISBN 3-900051-07-0. 2008. Disponível em: < (http://www.R-project.org) >. Acesso em: 25 de Janeiro de 2010.
SILVA, G. F.et al. Análise da influência de diferentes tamanhos e composições de amostras no ajuste de uma relação hipsométrica para Eucalyptusgrandis. Revista Árvore, Viçosa, v.31, n.4, p.685-694, jul./ago. 2007.
WOLFINGER, R. Covariance structure selection in general mixed models. Communications in Statistics - Simulation, Ontario, v. 22, n. 4, p. 1079-1106, 1993.
ZAHNG, L. Cross-validation of non-linear growth functions for modeling tree height-diameter relationships. Annals of Botany, London, v. 79(3), p. 251-257, mar. 1997.
