Dynamic height growth model for Spanish and Tunisian cork oak (Quercus suber L.) forests
Abstract
Seven simple and advanced dynamic polymorphic functions were considered to develop a dominant height growth model for Spanish and Tunisian cork oak forests. Data from 115 stem analyses performed in two regions in each country were used to fit the equations. Parameter estimates were obtained using the Dummy variable method. Both numerical, graphical and biological consistency were used to compare alternative models. The dynamic equation finally selected was derived from the Hossfeld model by considering the shape parameter to be related to site productivity. An analysis of the dominant height growth patterns between the two countries indicated that the same dominant height growth model was valid for both countries. This dominant height growth model allows estimation of dominant height with a level of reliability of at least 83% from an age of 15 years for a prediction interval of less than 40 years.Downloads
References
Adame P., Cañellas I., Roig S., Del Río M., 2006. Modelling dominant height growth and site index curves for rebollo oak (Quercus pyrenaica Willd.) Ann For Sci 63, 929-940. http://dx.doi.org/10.1051/forest:2006076
Akaike H., 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control AC-19, 716-723. http://dx.doi.org/10.1109/TAC.1974.1100705
Álvarez-González J.G., Ruiz González A.D., Rodríguez-Soalleiro R., Barrio-Anta M., 2005. Ecoregional-based stand density management diagrams for Pinus pinaster L. in Galicia (northwest Spain). Ann For Sci 62, 115-127.
Amaro A., Reed D., Tomé M., Themido I., 1998. Modelling dominant height growth: eucalyptus plantations in Portugal. For Sci 44, 37-46.
Bailey R.L., Clutter J.L., 1974. Base-age invariant polymorphic site curves. For Sci 20, 155-159.
Bravo-Oviedo A., Del Río M., Montero G., 2007. Geographic variation and parameter assessment in generalized algebraic difference site index modelling. For Ecol Manage 247, 107-119.
Burnham K.P., Anderson D.R., 2002. Model selection and multimodel inference: a practical information-theoretic approach, 2nd ed. Springer-Verlag, New York. 488 pp.
Cañellas I., Sánchez-González M., Bovino S.M., Adame P., Herrero C., Roig S., Tomé M., Paulo J.A., Bravo F., 2008. Silviculture and carbon sequestration in Mediterranean oak forests. In: Managing forest ecosystems: the challenge of climate change (Bravo F., Jandl R., LeMay V., Von Gadow K., eds). Springer, Netherlands. pp. 317-338. http://dx.doi.org/10.1007/978-1-4020-8343-3_18
Calama R., Cañadas N., Montero G., 2003. Interregional variability in site index models for even-aged stands of stone pine (Pinus pinea L.) in Spain. Ann For Sci 60, 259-269. http://dx.doi.org/10.1051/forest:2003017
Carmean W.H., 1972. Site index curves for upland oaks in the central states. For Sci 18, 109-120.
Chaar H., Stiti B., Montero G., 2005. Production and silviculture of cork oak forest in Ain Snoussi, Tunisia. Proceedings of International Congress Cork Plantations, Factories and Traders: the Past, Present and Future of the Cork Business. Palafrugell, Gerona (Spain).
Cieszewski C.J., 2004. GADA derivation of dynamic site equations with polymorphism and variable asymptotes from Richards, Weibull, and other exponential functions. PMRC Technical Report 2004-5.
Cieszewski C.J., 2003. 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. For Sci 49, 539-554.
Cieszewski C.J., 2002. Comparing fixed and variable base-age site equations having single versus multiple asymptote. For Sci 48, 7-23.
Cieszewski C.J., 2001. Three methods of deriving advanced dynamic site equations demonstrated on inland Douglas-fir site curves. Can J For Res 31, 165-173. http://dx.doi.org/10.1139/x00-132
Cieszewski C.J., 1994. Development of a variable density height-growth-model through defining multidimensional height growth spaces. PhD thesis. U of Alberta, Edmonton, Ab, Canada. 72 pp.
Cieszewski C.J., Bailey R.L., 2000. Generalized algebraic difference approach: theory based derivation of dynamic site equations with polymorphism and variables asymptotes. For Sci 46(1), 116-126.
Cieszewski C.J., Zasada M., Strub M., 2006. Analysis of different base models and methods of site model derivation for Scots pine. For Sci 52(2), 187-197.
Cieszewski C.J., Harrison M., Martin S.W., 2000. Practical methods for estimating non-biased parameters in self-referencing growth and yield models Plantation Management Research Cooperative Technical Report 2000-7, DB Warnell School of Forest Resources University of Georgia.
Clutter J.L., Fortson J.C., Peinar L.V., Brister G.H., Bailey R.L., 1983. Timber Management – A quantitative approach. John Wiley and Sons, New York. 333 pp.
Diéguez-Aranda U., Burkhart H.E., Amateis R.L., 2006. Dynamic site model for loblolly pine (Pinus taeda L.) plantations in the United States. For Sci 52(3), 262-272.
Direction Generale Des Forets, 1986. Plan d'aménagement: 1987-2011. Forêt domaniale de Amdoun. 2eme série. Ministère de l'Agriculture.
Direction Generale Des Forets, 1983. Plan d'aménagement: 1984-2007.Forêt domaniale de Amdoun, 1er série. Ministère de l'Agriculture.
Draper N.R., Smith H., 1981. Applied regression analysis. John Wiley & Sons, New York, 709 pp.
Fabbio G., Frattegiani M., Manetti M.C., 1994. Height estimation in stem analysis using second differences. For Sci 40, 329-340.
Fang Z., Bailey R.L., 1998. Height-diameter models for tropical forests on Hainan island in southern China. For Ecol Manage 110, 315-327.
FAO, 2006. World Reference Base for Soil Resources World Soil Resources Reports 103, Rome. 145 pp.
García O., 1983. A stochastic differential equation model for the height growth of forest stands. Biometrics 39, 1059-1072. http://dx.doi.org/10.2307/2531339
Gea-Izquierdo G., Cañellas I., Montero G., 2008. Site index in agroforestry systems: age-dependent and age-independent dynamic diameter growth model for Quercus ilex in Iberian open oak woodlands. Can J For Res 38, 101-113. http://dx.doi.org/10.1139/X07-142
Gregoire T., Schanbenberger O., Barrett J.P, 1995. Linear modelling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements. Can J For Res 25, 137-156. http://dx.doi.org/10.1139/x95-017
Hossfeld J.W., 1822. Mathematik für Forstmänner, Ökonomen und Cameralisten (Gotha, 4 Bd, S 310).
Huang S., Yang Y., Wang Y., 2003. A critical look at procedures for validating growth and yield models in Modelling forest systems (Amaro A., Reed D., Soares P., eds). CAB International, Wallingford, Oxfordshire, UK. pp. 271-293.
Khatree R., Naik D.N., 1995. Applied Multivariate Statistics with SAS Software. SAS Institute Inc, Cary, NC. 588 pp.
Kiviste A., 1998. Estimation of Estonian forest growth change in 1951-1994 on the basis of forest inventory data. In: Climate Change Studies in Estonia (Lallista T.T., Kuldna P., eds). Stockholm Environment Institute, Estonian Ministry of Environment, Tallinn, Estonia. pp. 191-196.
Korf V., 1939. Príspevek k matematické definici vzrustového zákona hmot lesních porostu. Lesnicka Prace 18, 339-379.
Krumland B.E., Eng H., 2005. Site index systems for major young-growth forest and woodland species in northern California. Cal Dept Forestry and Fire Protection, Cal For Rep No 4.
Lundqvist B., 1957. On the height growth in cultivated stands of pine and spruce in Northern Sweden. Medd Fran Statens Skogfoesk Band 47, pp. 1-64.
Mcdill M.E., Amateis R.L., 1992. Measuring forest site quality using the parameters of a dimensionally compatible height growth function. For Sci 38, 409-429.
Montero G., Cañellas I., 1999. Manual de forestación del alcornoque (Quercus suber L). MAPA-INIA. 103 pp.
Myers R.H., 1990. Classical and modern regression with applications, 2nd ed. Duxbury Press, Belmont, CA. 488 pp.
Parresol B.R., 2001. Additivity of nonlinear biomass equations. Can J For Res 31, 865-878. http://dx.doi.org/10.1139/x00-202
Pereira H., 2007. Cork: biology, production and uses. Elsevier. 336 pp.
Pretzsch H., Biber P., Dursky J., Gadow K.V., Hasenauer H., Kändler G., Kenk G., Kublin E., Nagel J., Pukkala T., Skovsgaard J.P., Sodtke R., Sterba H., 2002. Recommendations for standardized documentation and further development of forest growth simulators. Forstw Cbl 121, 138-151. http://dx.doi.org/10.1046/j.1439-0337.2002.00138.x
Ratkowski D.A., 1983. Nonlinear regression modelling. A unified practical approach. Marcel Dekker, Inc, New York, Basel. 276 pp.
Richards F.J., 1959. A flexible growth function for empirical use. Journal of Experimental Botany 10, 290-300. http://dx.doi.org/10.1093/jxb/10.2.290
Ryan T.P., 1997. Modern regression methods. John Wiley and Sons, New York.
Sánchez-González M., Cañellas I., Montero G., 2008. Base-age invariant cork growth model for Spanish cork oak (Quercus suber L.) forests. Eur J Forest Res 127, 173-182. http://dx.doi.org/10.1007/s10342-007-0192-4
Sánchez-González M., Calama R., Cañellas I. And Montero G., 2007. Management oriented growth models for multifunctional Mediterranean forests: the case of the cork oak (Quercus suber L.) In: Scientific tools and research needs for multifunctional Mediterranean forest ecosystem managemen (Palahí M., Birot Y.,Rois M., eds). EFI proceedings 56, 71-84.
Sánchez-González M., Tomé M., Montero G., 2005. Modelling height and diameter growth of dominant cork oak trees in Spain. Ann For Sci 62, 633-643. http://dx.doi.org/10.1051/forest:2005065
San Miguel A., Allué M., Cañellas I., Montero G., Bengoa J., Torres E., 1992. The most important forest ecosystems and their silvopastoral treatments in Spain. IUFRO Centennial, Berlin-Eberswalde (Germany). 11 pp. PMCid:495307
SAS Institute Inc, 2004. SAS/ETS 91 user's guide. SAS Institute Inc, Cary, NC. 1028 pp.
Tomé M., Coelho M.B., Almeida A., Lopes F., 2001. O modelo SUBER. Estrutura e equações utilizadas, Relatórios técnico-científicos do GIMREF nº 2/2001, Centro de Estudos Florestais, Instituto Superior de Agronomia, Lisboa.
Vanclay J.K., Skovsgaard J.P., 1997. Evaluating forest growth models. Ecol Model 98, 1-12. http://dx.doi.org/10.1016/S0304-3800(96)01932-1
West P.W., Ratkowsky D.A., Davis A.W., 1984. Problems of hypothesis testing of regressions with multiple measurements from individual sampling units. Forest Ecology and Management 7, 207-224. http://dx.doi.org/10.1016/0378-1127(84)90068-9
Zimmerman D.L., Núñez-Antón V., 2001. Parametric modelling of growth curve data: an overview (with discussion). Test 10, 1-73. http://dx.doi.org/10.1007/BF02595823
© CSIC. Manuscripts published in both the printed and online versions of this Journal are the property of Consejo Superior de Investigaciones Científicas, and quoting this source is a requirement for any partial or full reproduction.
All contents of this electronic edition, except where otherwise noted, are distributed under a “Creative Commons Attribution 4.0 International” (CC BY 4.0) License. You may read here the basic information and the legal text of the license. The indication of the CC BY 4.0 License must be expressly stated in this way when necessary.
Self-archiving in repositories, personal webpages or similar, of any version other than the published by the Editor, is not allowed.
