Modelling diameter distributions of Quercus suber L. stands in “Los Alcornocales” Natural Park (Cádiz-Málaga, Spain) by using the two-parameter Weibull function

A. Calzado, E. Torres

Abstract


Aim of study: The aim of this work was to model diameter distributions of Quercus suber stands. The ultimate goal was to construct models enabling the development of more affordable forest inventory methods. This is the first study of this type on cork oak forests in the area.

Area of study: The area of study is “Los Alcornocales” Natural Park (Cádiz-Málaga, Spain).

Material and methods: The diameter distributions of 100 permanent plots were modelled with the two-parameter Weibull function. Distribution parameters were fitted with the non-linear regression, maximum likelihood, moment and percentile-based methods. Goodness of fit with the different methods was compared in terms of number of plots rejected by the Kolmogorov-Smirnov test, bias, mean square error and mean absolute error. The scale and shape parameters in the Weibull function were related to the stand variables by using the parameter prediction model.

Main results: The best fitting was obtained with the non-linear regression approach, using as initial values those obtained by maximum likelihood method, the percentage of rejections by the Kolmogorov-Smirnov test was 2% of the total number of cases. The scale parameter (b) was successfully modelled in terms of the quadratic mean diameter under cork (R2 adj = 0.99). The shape parameter (c) was modelled by using maximum diameter, minimum diameter and plot elevation (R2 adj = 0.40).

Research highlights: The proposed model diameter distribution can be a highly useful tool for the inventorying and management of cork oak forests.

Key words: maximum likelihood method; moment method; non linear regression approach; parameter prediction model; percentile method; scale parameter; shape parameter.


Full Text:

PDF

References


Allué JL, 1990. Atlas Fitoclimático de Espa-a. Taxonomías. INIA, Ministerio de Agricultura Pesca y Alimentación. Madrid, Spain. 221 pp. PMid:2121804

Álvarez González JG, 1997. Análisis y caracterización de las distribuciones diamétricas de Pinus pinaster Ait. en Galicia. PhD Thesis. ETSIM-UPM. Spain.

Álvarez González JG, Ruiz González AD, 1998. Análisis y modelización de las distribuciones diamétricas de Pinus pinaster Ait. en Galicia. Invest Agr: Sist Recur For 7(1-2): 123-137.

Assmann E, 1970. The principles of forest yield study. Pergamon Press. New York. 506 pp.

Bailey RL, Dell TR, 1973. Quantifying diameter distributions with the Weibull function. For Sci 19(2): 97-104.

Bitterlich W, 1984. The relascope idea. Commonwealth Agricultural Bureaux. England. 242 pp.

Bullock BP, Burkhart HE, 2005. Juvenile diameter distributions of loblolly pine characterized by the two-parameter Weibull function. New For 29: 233-244. http://dx.doi.org/10.1007/s11056-005-5651-5

Cao QV, 2004. Predicting parameters of a Weibull function for modeling diameter distribution. For Sci 50(5): 682-685.

Dagnelie P, 2006. Statistique théorique et appliquée. De Boeck & Larcier. Brussels, Belgium. 511 pp. PMCid:1522015

De Benito N, 2008. Evolución histórica del pensamiento dasocrático en ordenación de alcornocales. El caso de los montes de Cortes de la Frontera (Málaga). En: Cuadernos de la Sociedad Espa-ola de Ciencias Forestales nº 27, SECF. Madrid, Spain. pp: 73-78.

Dubey SD, 1967. Some percentile estimators for Weibull parameters. Technometrics 9: 119-129. http://dx.doi.org/10.1080/00401706.1967.10490445

García Güemes C, Ca-adas N, Montero G, 2002. Modelización de la distribución diamétrica de las masas de Pinus pinea L. de Valladolid (Espa-a) mediante la función Weibull. Invest Agr: Sist Recur For 11(2): 263-282.

Gorgoso JJ, Álvarez González JG, Rojo A, Grandas-Arias JA, 2007. Modelling diameter distributions of Betula alba L. stands in northwest Spain with the two-parameter Weibull function. Invest Agr: Sist Recur For 16(2): 113-123.

Gove JH, 2003. Moment and maximum likelihood estimators for Weibull distributions under length and area-biased sampling. Environ Ecol Stat 10: 455-467. http://dx.doi.org/10.1023/A:1026000505636

Junta de Andalucía, 2004. Plan de ordenación de los recursos naturales del Parque Natural de los Alcornocales. Junta de Andalucía. Sevilla, Spain. 92 pp.

Kilkki P, Maltamo M, Mykkänen R, Päivinen R, 1989. Use of the Weibull function in estimating the basal area dbhdistribution. Silva Fenn 23(4): 311-318.

Lejeune P, 1994. Construction d'un modèle de répartition des arbres par classes de grosseur pour des plantations d'épicéa commum (Picea abies L Karst) en Ardenne belge. Ann Sci For 51: 53-65. http://dx.doi.org/10.1051/forest:19940104

Lindsay SR, Wood GR, Woollons RC, 1996. Stand table modelling through the Weibull distribution and usage of skewness information. For Ecol Manag 81(1-3): 19-23.

Liu Ch, Zhang L, Davis CJ, Solomon DS, Gove JH, 2002. A finite mixture model for characterizing the diameter distributions of mixed-species forest stands. For Sci 48(4): 653-661.

Maltamo M, 1997. Comparing basal area diameter distributions estimated by tree species and for the entire growing stock in a mixed stand. Silva Fenn 31(1); 53-65.

Maltamo M, Puumalainen J, Päivinen R, 1995. Comparison of Beta and Weibull functions for modelling basal area diameter distribution in stands of Pinus sylvestris and Picea abies. Scan J For Res 10: 284-295. http://dx.doi.org/10.1080/02827589509382895

Maltamo M, Kangas A, Uuttera J, Torniainen T, Saramäki J, 2000. Comparison of percentile based prediction methods and the Weibull distribution in describing the diameter distribution of heterogeneous Scots pine stands. For Ecol Manag 133(3): 263-274.

Marquardt DW, 1963. An algorithm for least squares estimation of nonlinear parameters. Journal of the Society for Industrial and Applied Mathematics 2: 431-441. http://dx.doi.org/10.1137/0111030

Merganic J, Sterba H, 2006. Characterisation of diameter distribution using the Weibull function: method of moments. Eur J Forest Res 125: 427-439. http://dx.doi.org/10.1007/s10342-006-0138-2

Montero G, Torres E, Ca-ellas I, Ortega C, 1996. Modelos para la estimación de la producción de corcho en alcornocales. Invest Agr: Sist Recur For 5(1): 97-127.

Montero G, Cañellas I, 1999. Manual de reforestación y cultivo de alcornoque (Quercus suber L.). Instituto Nacional de Investigación y Tecnología Agraria y Alimentaria (INIA). Ministerio de Agricultura, Pesca y Alimentación. Madrid, Spain. 103 pp.

Montero G, López E, 2008. Selvicultura de Quercus suber L. En: Compendio de Selvicultura Aplicada en Espa-a, Fundación Conde del Valle de Salazar. Madrid, Spain. pp: 779-829.

Nanang DM, 1998. Suitability of the Normal, Log-normal and Weibull distributions for fitting diameter distributions of neem plantations in Northern Ghana. For Ecol Manag 103(1): 1-7.

Nanos N, Montero G, 2002. Spatial prediction of diameter distributions models. For Ecol Manag 161(1-3): 147-158.

Newton PF, Lei Y, Zhang SY, 2005. Stand-level diameter distribution yield model for black spruce plantations. For Ecol Manag 209(3): 181-192.

Palahí M, Pukkala T, Trasobares A, 2006a. Calibrating predicted tree diameter distributions in Catalonia, Spain. Silva Fenn 40(3): 487-500.

Palahí M, Pukkala T, Trasobares A, 2006b. Modelling the diameter distribution of Pinus sylvestris, Pinus nigra and Pinus halepensis forest stands in Catalonia using the truncated Weibull function. Forestry 79(5): 553-562. http://dx.doi.org/10.1093/forestry/cpl037

Pereira H, 2007. The cork oak. In: Cork. Elsevier Science BV. Amsterdam, Netherlands. pp: 103-125. http://dx.doi.org/10.1016/B978-044452967-1/50006-6

Rennols K, Geary DN, Rollinson TJ, 1985. Characterizing diameter distributions by the use of the Weibull distribution. Forestry 58(1): 57-66. http://dx.doi.org/10.1093/forestry/58.1.57

Ribeiro F, Tome M, 2002. Cork weight prediction at tree level. For Ecol Manag 171(3), 231-241.

Río M, Montero G, 2001. Modelo de simulación de claras en masas de Pinus sylvestris L. Monografías INIA: Forestal no. 3. Ministerio de Ciencia y Tecnología. Madrid, Spain. 113 pp.

Rubin BD, Manion PD, Faber-langendoen D, 2006. Diameter distributions and structural sustainability in forests. For Ecol Manag 222(1-3): 427-438.

Sánchez-González M, Del Río M, Ca-ellas I, Montero G, 2006. Distance independent tree diameter growth model for cork oak stands. For Ecol Manag 225(1-3): 262-270.

Shifley S, Lentz E, 1985. Quick estimation of the three-parameter Weibull to describe tree size distributions. For Ecol Manag 13: 195-203.

Shiver BD, 1988. Sample sizes and estimation methods for the Weibull distribution for unthinned slash pine plantation diameter distributions. For Sci 34(3): 809-814.

Torres Rojo JM, Magaña Torres OS, Acosta Mireles M, 2000. Methodology to improve the prediction for diameter distribution parameters. Agrociencia 34: 627-637.

Torres E, 1995. Estudio de los principales problemas selvícolas de los alcornocales del Macizo del Aljibe (Cádiz y Málaga). PhD Thesis. ETSIM-UPM, Spain.

Torres E, Montero G, 2000. Los alcornocales del macizo del Algibe y sierras del Campo del Gibraltar: clasificación ecológica y caracterización selvícola y productiva. Ministerio de Agricultura, Pesca y Alimentación. Madrid, Spain. 228 pp.

Vázquez Piqué J, Pereira H, 2008. ¿Qué hay que tener en cuenta para elaborar modelos de producción de corcho? Invest Agr: Sist Recur For 17(3): 199-215.

White J, Harper JL, 1970. Correlated changes in plant size and number in plant populations. J Ecol 58: 467-485. http://dx.doi.org/10.2307/2258284

Zarnoch SJ, Dell TR, 1985. An evaluation of percentile and maximum likelihood estimators of Weibull parameters. For Sci 31(1): 260-268.

Zhang L, Packard KC, Liu CH, 2003. A comparison of estimation methods for fitting Weibull and Johnson's SB distributions to mixed spruce-fir stands in northeastern North America. Can J For Res 33(7): 1340-1347. http://dx.doi.org/10.1139/x03-054




DOI: 10.5424/fs/2013221-02142

Webpage: www.inia.es/Forestsystems