SITE INDEX MODEL FOR NATURAL STANDS OF REBOLLO OAK (<i>Quercus pyrenaica</i> Willd.) IN GALICIA, NW IBERIAN PENINSULA

Díaz-Maroto, Ignacio Javier; Fernández-Parajes, José; Vila-Lameiro, Pablo; Barcala-Pérez, Eva

doi:10.5902/198050981761

ABSTRACT

Data from stem analysis of 56 dominant trees of Quercus pyrenaica Willd., in natural stands in Galicia (NW Iberian Peninsula), were used to evaluate four dynamic site equations derived with the Generalized Algebraic Difference Approach (GADA). All the equations are base-age invariant and directly estimate height and site index from any height and age. The fittings were made using a data structure involving all possible growth intervals. The GADA formulation derived on the basis of the Bertalanffy-Richards model by considering the asymptote and the initial pattern parameters as related to site productivity. It is therefore recommended for height growth prediction and site classification for natural stands of rebollo oak in Galicia. The autocorrelation was analyzed with a test of residuals using Durbin’s t-test without reaching a manifest result of autocorrelation between managed data.

Keywords:
Quercus pyrenaica; site index model; height growth; Generalized Algebraic Difference Approach

RESUMO

Dados da análise de tronco de 56 árvores dominantes de Quercus pyrenaica Willd. de florestas naturais da Galicia (NW Península Ibérica) foram utilizados para avaliar quatro equações dinamicas de índice de sitio obtidas com a Abordagem Generalizada de Diferença Algébrica (GADA). Todas as equações são baseadas na idade invariante e diretamente estimam a altura e o índice de sitio. Os ajustes foram feitos utilizando uma estrutura de dados que incluiam todos os possíveis intervalos de crescimento. A formulação GADA teve base no modelo Bertalanffy-Richards, considerando a assíntota e do padrão inicial como parâmetros relacionados à produtividade do sitio. Assim, recomenda-se o modelo na previsão do crescimento em altura e classificação de sitios para povoamentos naturais de carvalho negro na Galicia. A autocorrelação foi analisada com um teste de resíduos utilizando Durbin’s t-teste, sem chegar a um resultado significativo de autocorrelação entre os dados.

Palavras-chave:
Quercus pyrenaica; modelo de índice de sitio; crescimento em altura; Abordagem das Diferenças Algébricas Generalizadas

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REFERENCES

ADAME, P. et al Modelling dominant height growth and site index curves for rebollo oak (Quercus pyrenaica Willd.). Annals of Forest Science, Nancy, v. 63, p. 929-940, 2006.
BAILEY, R. L.; CIESZEWSKI, C. J. Development of a well-behaved site-index equation: jack pine in north- central Ontario: comment. Canadian Journal of Forest Research, Ottawa, v. 30, p. 1667-1668, 2000a.
BAILEY, R. L.; CIESZEWSKI, C. J. Generalized Algebraic Difference Approach: Theory based derivation of dynamic site equations with polymorphism and variable asymptotes. Forest Science, Bethesda, v. 46, p. 116-126, 2000b.
BAILEY, R. L.; CLUTTER, J. L. Base-age invariant polymorphic site curves. Forest Science , Bethesda, v. 20, p. 155-159, 1974.
BARRIO, M.; DIÉGUEZ-ARANDA, U. Site quality of pedunculate oak (Quercus robur L.) stands in Galicia (northwest of Spain). European Journal of Forest Research, New York, v. 124, p. 19-28, 2005.
BERTALANFFY, L. V. Problems of organic growth. Nature, London, v. 163, p. 156-158, 1949.
BERTALANFFY, L. V. Quantitative laws in metabolism and growth. The Quarterly Review of Biology, Chicago, v. 32, p. 217-231, 1957.
BIGING, G.S. Improved estimates of site index curves using a varying-parameter model. Forest Science , Bethesda, v. 31, p. 248-259, 1985.
CARMEAN, W. H. Site index curves for upland oaks in the Central States. Forest Science , Bethesda, v. 18, p. 109-120, 1972.
CARVALHO, J. P. et al O Carvalho Negral. Vila Real, Portugal: UTAD-CEGE, 2005. 206 p.
CARVALHO, J. P.; PARRESOL, B. R. A site model for Pyrenean oak (Quercus pyrenaica) stands using a dynamic algebraic difference equation. Canadian Journal of Forest Research , Ottawa, v. 35, p. 93-99, 2005.
CIESZEWSKI, C. J. Comparing fixed and variable-base- age site equations having single versus multiple asymptotes. Forest Science , Bethesda, v. 48, p. 7-23, 2002.
CIESZEWSKI, C. J. Developing a well-behaved dynamic site equation using a modified Hossfeld IV function Y3 = (axm)/(c + xm-1), a simplified mixed-model and scant subalpine fir data. Forest Science , Bethesda, v. 49, p. 539-554, 2003
CIESZEWSKI, C. J. GADA derivation of dynamic site equations with polymorphism and variable asymptotes from Richards, Weibull, and other exponential functions. Georgia: University of Georgia PMRC-TR, 2004. 16p
CIESZEWSKI, C. J.; STRUB, M.; ZASADA, M. New dynamic site equation that fits best the Schwappach data for Scots pine (Pinus sylvestris L.) in Central Europe. Forest Ecology and Management, Amsterdam, v. 243, p. 83-93, 2007.
CLUTTER, J. L. et al Timber management: a quantitative approach. New York: Wiley & Sons, 1983. 333 p.
DAVIS, L.S. et al Forest management: to sustain ecological, economic, and social values. New York, EEUU: McGraw-Hill, 2001. 886 p.
DGCONA. Tercer Inventario Forestal Nacional, Galicia (A Coruña, Lugo, Ourense y Pontevedra). Madrid, España: Ministerio de Medio Ambiente, 2001. 122 p.
DÍAZ-MAROTO, I. J.; VILA-LAMEIRO, P.; SILVA-PANDO, F. J. Autoecology of oaks (Quercus robur L.) in Galicia (Spain). Annals of Forest Science , Nancy, v. 62, p. 737-749, 2005.
DÍAZ-MAROTO, I. J.; FERNÁNDEZ-PARAJES, J.; VILA-LAMEIRO, P. Autecology of rebollo oak (Quercus pyrenaica Willd.) in Galicia (Spain). Annals of Forest Science , Nancy, v. 63, p. 157-167, 2006.
DÍAZ-MAROTO, I. J. et al A comparison of the autecology of Quercus robur L. and Q. pyrenaica Willd.: present habitat in Galicia, NW Spain. Forestry , Edinburgh, v. 80, p. 223-239, 2007.
DIÉGUEZ-ARANDA, U. et al Site quality equations for Pinus sylvestris L. plantations in Galicia (northwestern Spain). Annals of Forest Science , Nancy, v. 62, p. 143-152, 2005a.
DIÉGUEZ-ARANDA, U.; BURKHART, H. E.; RODRÍGUEZ-SOALLEIRO, R. Modelling dominant height growth of radiata pine (Pinus radiata D. Don) plantations in north-western Spain. Forest Ecology Management, Amsterdam, v. 215, p. 271-284, 2005b.
DIÉGUEZ-ARANDA, U. et al Site quality curves for birch stands in north-western Spain. Silva Fennica, Vantaa, v. 40, p. 631-644, 2006.
DURBIN, J. Testing for serial correlation in least-square regression when some of the regressors are lagged dependent variables. Econometrica, New York, v. 50, p. 410-421, 1970.
DYER, M. E.; BAILEY, R. L. A test of six methods for estimating true heights from stem analysis data. Forest Science , Bethesda, v. 33, p. 3-13, 1987.
GARCÍA, O. A stochastic differential equation model for the height growth of forest stands. Biometrics, New York, v. 39, p. 1059-1072,1983.
GOELZ, J. C. G.; BURK, T. E. Development of a well- behaved site index equation: jack pine in north central Ontario. Canadian Journal of Forest Research , Ottawa, v. 22, p. 776-784, 1992.
GOELZ, J. C. G.; BURK, T. E. Measurement error causes bias in site index equations. Canadian Journal of Forest Research , Ottawa, v. 26, p. 1586-1593, 1996.
GREGOIRE, T.G.; SCHABENBERGER, O.; BARRETT, J. P. Linear modelling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements. Canadian Journal of Forest Research , Ottawa, v. 25, p. 137-156, 1995.
HUANG, S. Development of compatible height and site index models for young and mature stands within an ecosystem-based management framework. In: AMARO, A.; TOMÉ, M. (Eds.) Empirical and process-based models for forest tree and stand growth simulation. Lisboa, Portugal: Edições Salamandra-Novas Tecnologias, 1999, p. 61-98.
HUANG, S.; YANG, Y.; WANG, Y. A critical look at procedures for validating growth and yield models. In: AMARO, A.; REED, D.; SOARES, P. (Eds.) Modelling forest systems. Wallingford, EEUU: CAB International, 2003, p. 271-293.
HUMMEL, F. C. et al Code of sample plot procedure. London:, HMSO, 1959. 113 p. (Forestry Commission Bulletin 31).
KOZAK, A.; KOZAK, R. Does cross validation provide additional information in the evaluation of regression models? Canadian Journal of Forest Research , Ottawa, v. 33, p. 976-987, 2003.
KURINOBU, S. et al A provisional growth model with a size-density relationship for a plantation of Paraserianthes falcataria derived from measurements taken over 2 years in Pare, Indonesia. Journal of Forest Research, Tokyo, v. 12, p. 230-236, 2007.
McDILL, M. E.; AMATEIS, R. L. Measuring forest site quality using the parameters of a dimensionally compatible height growth function. Forest Science , Bethesda, v. 38, p. 409-429, 1992.
MESON, M. Aspectos autoecológicos de Quercus pyrenaica Willd.: distribución y climatología. Boletín Estación Central Ecología, Madrid, v. 12, p. 24-33, 1983.
MONSERUD, R. A. Height growth and site index curves for inland Douglas-fir based on stem analysis data and forest habitat type. Forest Science , Bethesda, v. 30, p. 943-965, 1984.
MYERS, R. H. Classical and modern regression with applications. 2 nd ed. Belmont: Duxbury Press, 1990. 488 p.
NETER, J.; WASSERMAN, W.; KUTNER, M. H. Applied linear statistical models: regression, analysis of variance and experimental designs. 3th ed. Boston: Irwin, 1990. 842 p.
NEWBERRY, J. D. A note on Carmean’s estimate of height from stem analysis data. Forest Science , Bethesda, v. 37, p. 368-369, 1991.
NIGH, G. D. Compatibility improvements and bias reduction in height-age models. British Columbia: Forestry Division Services Branch, Ministry of Forest, Victoria, 1995. 10p.
NORD-LARSEN, T. Developing dynamic site index curves for European beech (Fagus sylvatica L.) in Denmark. Forest Science , Bethesda, v. 52, p. 173-181, 2006.
RICHARDS, F. J. A flexible growth function for empirical use. Journal of Experimental Botany, Oxford, v. 10, p. 290-300, 1959.
RYAN, T. P. Modern regression methods. John Wiley & Sons, New York. 1996. 515 p.

Publication Dates

Publication in this collection
Jan-Mar 2010

This is an open-access article distributed under the terms of the Creative Commons Attribution License

[1] ADAME, P. et al Modelling dominant height growth and site index curves for rebollo oak (Quercus pyrenaica Willd.). Annals of Forest Science, Nancy, v. 63, p. 929-940, 2006.

[2] BAILEY, R. L.; CIESZEWSKI, C. J. Development of a well-behaved site-index equation: jack pine in north- central Ontario: comment. Canadian Journal of Forest Research, Ottawa, v. 30, p. 1667-1668, 2000a.

[3] BAILEY, R. L.; CIESZEWSKI, C. J. Generalized Algebraic Difference Approach: Theory based derivation of dynamic site equations with polymorphism and variable asymptotes. Forest Science, Bethesda, v. 46, p. 116-126, 2000b.

[4] BAILEY, R. L.; CLUTTER, J. L. Base-age invariant polymorphic site curves. Forest Science , Bethesda, v. 20, p. 155-159, 1974.

[5] BARRIO, M.; DIÉGUEZ-ARANDA, U. Site quality of pedunculate oak (Quercus robur L.) stands in Galicia (northwest of Spain). European Journal of Forest Research, New York, v. 124, p. 19-28, 2005.

[6] BERTALANFFY, L. V. Problems of organic growth. Nature, London, v. 163, p. 156-158, 1949.

[7] BERTALANFFY, L. V. Quantitative laws in metabolism and growth. The Quarterly Review of Biology, Chicago, v. 32, p. 217-231, 1957.

[8] BIGING, G.S. Improved estimates of site index curves using a varying-parameter model. Forest Science , Bethesda, v. 31, p. 248-259, 1985.

[9] CARMEAN, W. H. Site index curves for upland oaks in the Central States. Forest Science , Bethesda, v. 18, p. 109-120, 1972.

[10] CARVALHO, J. P. et al O Carvalho Negral. Vila Real, Portugal: UTAD-CEGE, 2005. 206 p.

[11] CARVALHO, J. P.; PARRESOL, B. R. A site model for Pyrenean oak (Quercus pyrenaica) stands using a dynamic algebraic difference equation. Canadian Journal of Forest Research , Ottawa, v. 35, p. 93-99, 2005.

[12] CIESZEWSKI, C. J. Comparing fixed and variable-base- age site equations having single versus multiple asymptotes. Forest Science , Bethesda, v. 48, p. 7-23, 2002.

[13] CIESZEWSKI, C. J. Developing a well-behaved dynamic site equation using a modified Hossfeld IV function Y3 = (axm)/(c + xm-1), a simplified mixed-model and scant subalpine fir data. Forest Science , Bethesda, v. 49, p. 539-554, 2003

[14] CIESZEWSKI, C. J. GADA derivation of dynamic site equations with polymorphism and variable asymptotes from Richards, Weibull, and other exponential functions. Georgia: University of Georgia PMRC-TR, 2004. 16p

[15] CIESZEWSKI, C. J.; STRUB, M.; ZASADA, M. New dynamic site equation that fits best the Schwappach data for Scots pine (Pinus sylvestris L.) in Central Europe. Forest Ecology and Management, Amsterdam, v. 243, p. 83-93, 2007.

[16] CLUTTER, J. L. et al Timber management: a quantitative approach. New York: Wiley & Sons, 1983. 333 p.

[17] DAVIS, L.S. et al Forest management: to sustain ecological, economic, and social values. New York, EEUU: McGraw-Hill, 2001. 886 p.

[18] DGCONA. Tercer Inventario Forestal Nacional, Galicia (A Coruña, Lugo, Ourense y Pontevedra). Madrid, España: Ministerio de Medio Ambiente, 2001. 122 p.

[19] DÍAZ-MAROTO, I. J.; VILA-LAMEIRO, P.; SILVA-PANDO, F. J. Autoecology of oaks (Quercus robur L.) in Galicia (Spain). Annals of Forest Science , Nancy, v. 62, p. 737-749, 2005.

[20] DÍAZ-MAROTO, I. J.; FERNÁNDEZ-PARAJES, J.; VILA-LAMEIRO, P. Autecology of rebollo oak (Quercus pyrenaica Willd.) in Galicia (Spain). Annals of Forest Science , Nancy, v. 63, p. 157-167, 2006.

[21] DÍAZ-MAROTO, I. J. et al A comparison of the autecology of Quercus robur L. and Q. pyrenaica Willd.: present habitat in Galicia, NW Spain. Forestry , Edinburgh, v. 80, p. 223-239, 2007.

[22] DIÉGUEZ-ARANDA, U. et al Site quality equations for Pinus sylvestris L. plantations in Galicia (northwestern Spain). Annals of Forest Science , Nancy, v. 62, p. 143-152, 2005a.

[23] DIÉGUEZ-ARANDA, U.; BURKHART, H. E.; RODRÍGUEZ-SOALLEIRO, R. Modelling dominant height growth of radiata pine (Pinus radiata D. Don) plantations in north-western Spain. Forest Ecology Management, Amsterdam, v. 215, p. 271-284, 2005b.

[24] DIÉGUEZ-ARANDA, U. et al Site quality curves for birch stands in north-western Spain. Silva Fennica, Vantaa, v. 40, p. 631-644, 2006.

[25] DURBIN, J. Testing for serial correlation in least-square regression when some of the regressors are lagged dependent variables. Econometrica, New York, v. 50, p. 410-421, 1970.

[26] DYER, M. E.; BAILEY, R. L. A test of six methods for estimating true heights from stem analysis data. Forest Science , Bethesda, v. 33, p. 3-13, 1987.

[27] GARCÍA, O. A stochastic differential equation model for the height growth of forest stands. Biometrics, New York, v. 39, p. 1059-1072,1983.

[28] GOELZ, J. C. G.; BURK, T. E. Development of a well- behaved site index equation: jack pine in north central Ontario. Canadian Journal of Forest Research , Ottawa, v. 22, p. 776-784, 1992.

[29] GOELZ, J. C. G.; BURK, T. E. Measurement error causes bias in site index equations. Canadian Journal of Forest Research , Ottawa, v. 26, p. 1586-1593, 1996.

[30] GREGOIRE, T.G.; SCHABENBERGER, O.; BARRETT, J. P. Linear modelling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements. Canadian Journal of Forest Research , Ottawa, v. 25, p. 137-156, 1995.

[31] HUANG, S. Development of compatible height and site index models for young and mature stands within an ecosystem-based management framework. In: AMARO, A.; TOMÉ, M. (Eds.) Empirical and process-based models for forest tree and stand growth simulation. Lisboa, Portugal: Edições Salamandra-Novas Tecnologias, 1999, p. 61-98.

[32] HUANG, S.; YANG, Y.; WANG, Y. A critical look at procedures for validating growth and yield models. In: AMARO, A.; REED, D.; SOARES, P. (Eds.) Modelling forest systems. Wallingford, EEUU: CAB International, 2003, p. 271-293.

[33] HUMMEL, F. C. et al Code of sample plot procedure. London:, HMSO, 1959. 113 p. (Forestry Commission Bulletin 31).

[34] KOZAK, A.; KOZAK, R. Does cross validation provide additional information in the evaluation of regression models? Canadian Journal of Forest Research , Ottawa, v. 33, p. 976-987, 2003.

[35] KURINOBU, S. et al A provisional growth model with a size-density relationship for a plantation of Paraserianthes falcataria derived from measurements taken over 2 years in Pare, Indonesia. Journal of Forest Research, Tokyo, v. 12, p. 230-236, 2007.

[36] McDILL, M. E.; AMATEIS, R. L. Measuring forest site quality using the parameters of a dimensionally compatible height growth function. Forest Science , Bethesda, v. 38, p. 409-429, 1992.

[37] MESON, M. Aspectos autoecológicos de Quercus pyrenaica Willd.: distribución y climatología. Boletín Estación Central Ecología, Madrid, v. 12, p. 24-33, 1983.

[38] MONSERUD, R. A. Height growth and site index curves for inland Douglas-fir based on stem analysis data and forest habitat type. Forest Science , Bethesda, v. 30, p. 943-965, 1984.

[39] MYERS, R. H. Classical and modern regression with applications. 2 nd ed. Belmont: Duxbury Press, 1990. 488 p.

[40] NETER, J.; WASSERMAN, W.; KUTNER, M. H. Applied linear statistical models: regression, analysis of variance and experimental designs. 3th ed. Boston: Irwin, 1990. 842 p.

[41] NEWBERRY, J. D. A note on Carmean’s estimate of height from stem analysis data. Forest Science , Bethesda, v. 37, p. 368-369, 1991.

[42] NIGH, G. D. Compatibility improvements and bias reduction in height-age models. British Columbia: Forestry Division Services Branch, Ministry of Forest, Victoria, 1995. 10p.

[43] NORD-LARSEN, T. Developing dynamic site index curves for European beech (Fagus sylvatica L.) in Denmark. Forest Science , Bethesda, v. 52, p. 173-181, 2006.

[44] RICHARDS, F. J. A flexible growth function for empirical use. Journal of Experimental Botany, Oxford, v. 10, p. 290-300, 1959.

[45] RYAN, T. P. Modern regression methods. John Wiley & Sons, New York. 1996. 515 p.

Brasil

Brasil

SITE INDEX MODEL FOR NATURAL STANDS OF REBOLLO OAK (Quercus pyrenaica Willd.) IN GALICIA, NW IBERIAN PENINSULA

MODELO DE ÍNDICE DE SITIO EM POVOAMENTOS NATURAIS DE CARVALHO NEGRO (Quercus pyrenaica Willd.) DA GALICIA, NW DA PENÍNSULA IBÉRICA

ABSTRACT

RESUMO

REFERENCES

Publication Dates