A system for calculating the merchantable volume of oak trees in the northwest of the state of Chihuahua, Mexico

Abstract

The taper functions of Kozak (1988), Bi (2000) and Fang et al. (2000) were comparatively analyzed in the present paper to develop a system for calculating the merchantable volume of oaks in the northwestern region of the state of Chihuahua (Mexico). Taper data corresponding to 298 trees were collected in mixed and uneven-aged pine-oak stands located throughout the study area, and covering the existing range of ages, stand densities and sites. Results show that the compatible segmented model developed by Fang et al. (2000) best described the experimental data and is therefore recommended for estimating tree diameter at a specific height, height to a specific diameter, merchantable volume, and total volume for oaks. The equation developed in this study is a fundamental tool for use in forest surveys in the study region and is simple enough to ensure its operational implementation. The results of the statistical analysis show that the equation can be recommended for other regions, although some local adaptations may be needed.

Keywords

commercial volume / Quercus / taper function / variable inflexion point

References

[1] Bates D.M., Watts D.G.. Nonlinear Regression Analysis and Its Applications. 1988, New York: Wiley

[2] Belsey D.A.. Conditioning diagnostics, collinearity and weak data in regression. 1991, New York: John Wiley & Sons, Inc.

[3] Bi H.. Trigonometric variable-form taper equations for Australian eucalyptus. For Sci, 2000, 46: 397-409.

[4] Bi H., Hamilton F.. Stem volume equations for native tree species in southern New South Wales and Victoria. Aus For, 1998, 61: 275-286.

[5] Bi H., Long Y.. Flexible taper equation for site-specific management of Pinus radiata in New South Wales, Australia. For Ecol Manage, 2001, 148: 79-91.

[6] Bruce D.R., Curtis O., Vancoevering C.. Development of system and taper volume tables for red alder. For Sci, 1968, 14: 339-350.

[7] Cao Q.V., Burkhart H.E., Max T.A.. Evaluations of two methods for cubic-foot volume prediction of loblolly pine to any merchantable limit. For Sci, 1980, 26: 71-80.

[8] Castedo D.F.. Modelo dinámico de crecimiento para las masas de Pinus radiata D. 2003, España: Universidad de Santiago de Compostela

[9] Castedo F., Barrio M., Parresol B.R., Álvarez J.G.. A stochastic height-diameter model for maritime pine ecoregions in Galicia (northwestern Spain). Ann For Sci, 2005, 62: 455-465.

[10] Corral-Rivas J.J., Álvarez J.G., Ruíz G.A., Gadow Kv.. Compatible height and site index models for five pine species in El Salto, Durango (Mexico). For Ecol Manage, 2004, 201: 145-160.

[11] Corral-Rivas J.J., Álvarez G.J., Aguirre C.O., Hernández F.J.. The effect of competition on individual tree basal area growth in mature stands of Pinus cooperi Blanco in Durango (Mexico). Eur J Forest Res, 2005, 124: 133-142.

[12] Corral-Rivas J.J., Diéguez-Aranda U., Corral S., Castedo F.. A merchantable volume system for major pine species in El Salto, Durango (Mexico). For Ecol Manage, 2007, 238(1–3): 118-129.

[13] Diéguez-Aranda U., Castedo-Dorado F., Álvarez J.G., Rojo A.. Compatible taper function for Scots pine plantations in northwestern Spain. Can J For Res, 2006, 36(5): 1190-1205.

[14] Fang Z., Bailey R.L.. Compatible volume and taper models with coefficients for tropical species on Hainan Island in Southern China. For Sci, 1999, 45: 85-100.

[15] Fang Z., Borders B.E., Bailey R.L.. Compatible volume-taper models for loblolly and slash pine based on a system with segmented-stem form factors. For Sci, 2000, 46: 1-12.

[16] González E.M.S., González E.S.. Los encinos de Durango, México. En: J. S. Marroquín de la F. (De.). III Seminario nacional sobre utilización de encinos. Reporte Científico Número Especial 15. Fac. Cienc. Ftales. UANL. Linares, N.L. México, 1995, I: 234-237.

[17] Hilt D.E.. Development of taper functions from variable-top merchantable volume equations. For Sci, 1980, 26: 117-120.

[18] Hernández ER. 2004. Función de ahusamiento y simulador de trozado para Sequoia sempervirens (D.Don) Endl. 2004. Tesis de ingeniero forestal. Facultad de ciencias forestales. Universidad de Chile, 84 pp.

[19] Huang S., Price D., Titus S.J.. Development of ecoregion-based height-diameter models for white spruce in boreal forests. For Ecol Manage, 2000, 129: 125-141.

[20] Hussein K.A., Schmidt M., Kotzé H., Gadow Kv.. Parameter-parsimonious Taper Functions for Describing Stem Profiles. Scientia Silvae Sinicae, 2008, 44(6): 1-8.

[21] Judge G.G., Griffiths W.E., Hill R.C., Lütkephol H., Lee T.C.. Introduction to the theory and practice of econometrics. 1988, New York: John Wiley & Sons

[22] Kozak A.. A variable-exponent taper equation. Can J For Res, 1988, 18: 1363-1368.

[23] Kozak A.. Effects of multicollinearity and autocorrelation on the variable-exponent taper functions. Can J For Res, 1997, 27: 619-629.

[24] Kozak A., Kozak R.A.. Does cross validation provide additional information in the evaluation of regression models?. Can J For Res, 2003, 33: 976-987.

[25] Kozak A., Munro D., Smith J.. Taper functions and their application in forest inventory. For Chron, 1969, 45: 278-283.

[26] Larson P.R.. Stem form development of forest trees. For Sci Monogr, 1963, 5: 1-41.

[27] Lee W.K., Seo J.H., Son Y.M., Lee K.H., Gadow Kv.. Modeling stem profiles for Pinus densiflora in Korea. For Ecol Manage, 2003, 172: 69-77.

[28] LeMay V.M., Kozak A., Marshall P.L., Muhairwe C.. Literature review for development of a dynamic taper model for tree growth. 1991, Vancouver, British Columbia: Internal Report for the B.C. Science Council

[29] Max T.A., Burkhart H.E.. Segmented polynomial regression applied to taper equations. For Sci, 1976, 22(3): 283-289.

[30] Morris D.M., Forslund R.R.. The relative importance of competition, microsite, and climate in controlling the stem taper and profile shape in jack pine. Can J For Res, 1992, 22: 1999-2003.

[31] Muhairwe C.K.. Taper equations for Eucalyptus pilularis and Eucalyptus grandis for the north coast in New South Wales, Australia. For Ecol Manage, 1999, 113: 251-269.

[32] Muhairwe C.K., LeMay V.M., Kozak A.. Effects of adding tree, stand, and site variables to Kozak’s variable-exponent taper equation. Can J For Res, 1994, 24: 252-259.

[33] Myers R.H.. Classical and modern regression with applications, 1990 2 Belmont, California: Duxbury Press

[34] Návar J., Domínguez P.A.. Ajuste de modelos de volumen y funciones que describen el perfil diamétrico de cuatro especies de pino plantadas en el Nordeste de México. Invest Agrar Sist Recur For, 1997, 6(1–2): 147-163.

[35] Návar J., Domínguez P.A., Contreras J.C., Estrada M.C.. Ajuste de siete modelos de ahusamiento a los perfiles fustales de Pinus hartwegii Lindl. Del Noroeste de México. Agrociencia, 1997, 31: 73-81.

[36] Neter J., Wasserman W., Kutner M.H.. Applied linear statistical models: regression, analysis of variance and experimental designs, 1990 3 Boston: Irwin

[37] Newnham R.. A variable-form taper function. Petawawa Nt. For. Inst. Information Rep, 1988, PI-X-83: 1-33.

[38] Newnham R.. Variable-form taper functions for four Alberta tree species. Can J For Res, 1992, 22: 210-223.

[39] Ormerod D.W.. A simple bole model. For Chron, 1973, 49: 136-138.

[40] Parresol B.R., Tomas C.C.. A simultaneous density-integral system for estimating stem profile and biomass: Slash pine and Willow Oak. Can J For Res, 1996, 26: 773-781.

[41] Pérez D., Burkhart H.E., Stiff C.. A variable-form taper function for Pinus oocarpa Schiede. in Central Honduras. For Sci, 1990, 36: 186-191.

[42] Pompa G.M., Velázquez M.A., Ramírez M.H., Rodríguez F.C.. Sistema de cubicación para el género Pinus en La Ucodefo 7 “Norogachi-Guachochi Chihuahua”. Rev Cienc For, 1998, 23(83): 17-23.

[43] Rose C.E., Lynch T.B.. Estimating parameters for tree basal area growth with a system of equations and seemingly unrelated regressions. For Ecol Manage, 2001, 148: 51-61.

[44] Rojo A., Perales X., Sanchez-Rodriguez F., Álvarez J.G., Gadow Kv.. Stem taper functions for maritime pine (Pinus pinaster Ait.) in Galicia (Northwestern Spain). Eur J Forest Res, 2005, 124: 177-186.

[45] Ryan T.P.. Modern regression methods. 1997, New York: John Wiley & Sons

[46] Rzedowski J.. Vegetación de México. 1978, México: Editorial Limusa.

[47] SAS Institute Inc. SAS/ETS® 9.1 User’s Guide. 2004, Cary, NC: SAS Institute Inc

[48] SEMARNAT. 2005. Control técnico de aprovechamientos. Listado electrónico. Delegación federal de Chihuahua. Subdelegación de gestión para la protección ambiental y recursos naturales, 150 pp.

[49] Trelease W.. The American Oaks. Prc National Acad Sci (US), 1924, 20: 1-255.

[50] Wabo E., Marquina J., Bratovich R.. Modelos de perfil de fuste para clones comerciales de Populus deltoides Marsh en la zona continental de la provincia de Buenos Aires. Quebracho Rev Cienc For, 2002, 9: 83-94.

[51] Zellner A.. An efficient method of estimating seemingly unrelated regressions and test for aggregation bias. J Am Stat Assoc, 1962, 57: 348-368.

[52] Zhang L., Peng L., Huang S., Zhou X.. Development and evaluation of ecoregion-based tree height-diameter models for jack pine in Ontario. For Chron, 2002, 78: 530-538.

[53] Zimmerman D.L., Núñez-Antón V.. Parametric modelling of growth curve data: An overview (with discussion). Test, 2001, 10: 1-73.