Modeling the Distribution of Marketable Timber Products of Private Teak (Tectona grandis L.f.) Plantations


Management of marketable products of private plantations will not be sustainable without class girth being identifiable readily. Modeling marketable products is a key to obtain good fitness between observed and theoretical girth distribution. We determine the best parameter recovery method with the Weibull function for two sylvicultural regimes (coppice and high forest). Data on stand variables were collected from 1101 sample plots. The three Weibull function parameters were estimated with three parameters recovery methods: the maximum likelihood method, the method of moments and the method of percentiles. Stepwise regression and the simultaneously re-estimated parameter using the Seemingly Unrelated Regression Estimation were applied to model each parameter. The results indicated that the three methods successfully predicted girth size distributions within the sample stands. The method of moments was the best one with lowest values of Reynolds error index and Kolmogorov-Smirnov statistic however the sylvicultural regimes. The Weibull parameter distribution model developed for each of the two sylvicultural regimes was quite reliable.

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Fonton, N. , Atindogbé, G. , Akossou, A. , Missanon, B. , Fadohan, B. & Lejeune, P. (2013). Modeling the Distribution of Marketable Timber Products of Private Teak (Tectona grandis L.f.) Plantations. Open Journal of Forestry, 3, 115-121. doi: 10.4236/ojf.2013.34019.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Anyonge, C. H., & Roshetko, J. M. (2003). Farm-level timber production: Orienting farmers towards the market. Unasylva, 54, 48-56.
[2] Aoudji, A. K. N., Adégbidi, A., Agbo, V., Atindogbé, G., Toyi, M. S. S., Yêvidé, A. S. I., Ganglo, J. C., & Lebailly, P. (2012). Functioning of farm-grown timber value chains: Lessons from the smallholderproduced teak (Tectona grandis L.f.) poles value chain in Southern Benin. Forest Policy and Economics, 15, 98-107.
[3] Atindogbé, G. (2012). Evaluation et caractérisation de la ressource en teck (Tectona grandis L.f.) dans les plantations privées du Sud-Bénin. Thèse de doctorat, Bénin: Université d’Abomey-Calavi.
[4] Bailey, R. L., & Dell, T. R. (1973). Quantifying diameter distributions with Weibull function. Forest Sciences, 19, 97-104.
[5] Borders, B. E., Souter, R. A., Bailey, R. L., & Ware, K. D. (1987). Percentile-based distributions characterize forest stand tables. Forest Sciences, 33, 570-576.
[6] Frazier, J. R. (1981). Compatible whole-stand and diameter distribution models for loblolly pine stands. Ph.D. Thesis, Blacksburg: Virginia Polytechnic Institute.
[7] Hafley, W. L., & Schreuder, H. T. (1977). Statistical distributions for fitting diameter and height data in even-aged stands. Canadian Journal of Forest Research, 7, 481-487.
[8] Harrison, S. R., Herbohn, J. L., & Niskanen, A. J. (2002). Non-industrial, smallholder, small-scale and family forestry: What’s in a name? Small-Scale Forest Economics. Management and Policy, 1, 1-11.
[9] Kilkki, P., & Paivinen, R. (1986). Weibull function in the estimation of the basal area dbh-distribution. Silva Fennica, 20, 149-156.
[10] Kilkki, P., Maltamo, M., Mykkanen, R., & Paivinen, R. (1989). Use of the Weibull function in estimating the basal area dbhdistribution. Silva Fennica, 23, 311-318.
[11] Knoebel, B. R., Burkhart, H. E., & Beck, D. E. (1986). A growth and yield model for thinned stands of yellow-poplar. Forest Sciences Monograph, 27, 64.
[12] Lafond, V., Cordonnier, T., De Coligny, F., & Courbaud, B. (2012). Reconstructing harvesting diameter distribution from aggregate data. Annals of Forest Science, 69, 235-243.
[13] Leduc, D. J., Matney, T. G., Belli, K. L., & Baldwin, V. C. (2001). Predicting diameter distributions of longleaf pine plantations: A comparison between artificial neural networks and other accepted methodologies. USDA For Serv Res Pap SRS-25.
[14] Lei, Y. (2008). Evaluation of three methods for estimating the Weibull distribution parameters of Chinese pine (Pinus tabulaeformis). Forest Sciences, 54, 566-571.
[15] Lejeune, P. (1994). Construction d’un modèle de répartition des arbres par classes de grosseur pour des plantations d’épicéa commun (Picea abies L Karst) en Ardenne belge. Annals of Forest Science, 51, 53-65.
[16] Lindsay, S. R., Wood, G. R., & Woollons, R. C. (1996). Stand table modeling through the Weibull distribution and usage of skewness information. Forest Ecology and Management, 81, 19-23.
[17] Little, S. N. (1983). Weibull diameter distributions for mixed stands of western conifers. Canadian Journal of Forest Research, 13, 85-88.
[18] Liu, C., Zhang, S. Y., Lei, Y., Newton, P. F., & Zhang, L. (2004). Evaluation of three methods predicting diameter distributions of black spruce (Picea mariana) plantations in central. Canadian Journal of Forest Research, 34, 2424-2432.
[19] Louppe, D. (2008). Tectona grandis (L. f). In D. Louppe, A. A. OtengAmoako, & M. Brink (Eds.), Ressources végétales de l’Afrique Tropicale. Bois d’oeuvre 1. [Traduction de: Plant Resources of Tropical Africa. Timbers 1. 2008]. Wageningen, Pays-Bas: Fondation PROTA; Leiden, Pays-Bas: Backhuys Publishers; Wageningen, PaysBas: CTA.
[20] Maldonado, G., & Louppe, D. (1999). Les plantations villageoises de teck en Cote d’Ivoire. Bois et Forêts des Tropiques, 262, 19-30.
[21] Mateus, A., & Tomé, M. (2011). Modelling the diameter distribution of eucalyptus plantations with Johnson’s SB probability density function: Parameters recovery from a compatible system of equations to predict stand variables. Annals of Forest Science, 68, 325-335.
[22] Murthy, P. D. N., Xie, M., & Jiang, R. (2004). Weibull models. Wiley series in probability and statistics. Hoboken.
[23] Nanang, D. M. (1998). Suitability of the normal, log-normal and Weibull distributions for fitting diameter distributions of neem plantations in Northern Ghana. Forest Ecology and Management, 103, 1-7.
[24] Nawir, A. A., Kassa, H., Sandewall, M., Dore, D., Campbell, B., Ohlsson, B., & Bekele, M. (2007). Stimulating smallholder tree planting—Lessons from Africa and Asia. Unasylva, 58, 53-59.
[25] Newton, P. F., & Amponsah, I. G. (2005). Evaluation of Weibull-based parameter prediction equation systems for black spruce and jack pine stand types within the context of developing structural stand density management diagrams. Canadian Journal of Forest Research, 35, 2996-3010.
[26] Niskanen, A. (1998). Financial and economic profitability of reforestation in Thailand. Forest Ecology and Management, 104, 57-68.
[27] Odiwe, A. F., Adewumi, R. A., Alami, A. A., & Ogunsanwo, O. (2012). Carbon stock in topsoil, standing floor litter and above ground biomass in Tectona grandis plantation 10-years after establishment in Ile-Ife, Southwestern Nigeria. International Journal of Biological and Chemical Sciences, 6, 3006-3016.
[28] Parresol, B. R., Fonseca, T. F., & Marques, C. P. (2010). Numerical details and SAS programs for parameter recovery of the SB distribution. Forest Service, Southern Research Station, General Technical Report SRS-122, United States Department of Agriculture, 31 p.
[29] Pauwels, D. (2003). Conception d’un systeme d’aide à la decision pour le choix d’un Scenario sylvicole: Application aux peuplements de mélèze en Région wallonne. Thèse de Doctorat, Gembloux: Faculté Universitaire des Sciences Agronomiques.
[30] Razali, A. M., Salih, A. A., & Mahdi, A. A. (2009). Best estimate for the parameters of the three parameter Weibull distribution. Proceedings of the 5th Asian Mathematical Conference, Malaysia, 2009.
[31] Rennolls, K., Geary, D. N., & Rollinson, T. J. D. (1985). Characterizing diameter distributions by the use of the Weibull distribution. Forestry, 58, 57-66.
[32] Reynolds, M. R., Burk, T. E., & Huang, W. C. (1988). Goodness of fit tests and model selection procedures for diameter distribution models. Forest Sciences, 34, 373-399.
[33] Rondeux, J., Laurent, C., & Thibaut, A. (1992). Construction d’une table de production pour le douglas (Pseudotsuga mensiesii Mirb. Franco) en Belgique. Bulletin des Recherches Agronomiques de Gembloux, 27, 327-347.
[34] Scherr, S. J. (2004). Building opportunities for small-farm agroforestry to supply domestic wood markets in developing countries. Agroforestry Systems, 61-62, 357-370.
[35] Torres-Rojo, J. M., Magana, O. S., & Acosta, M. (2000). Metodología para mejorar la predicción de parámetros de distribuciones diamétricas. Agrociencia, 34, 627-637.
[36] WorldClim (2005). WorldClim Global Climate Data (GIS Data).
[37] Zhang, L., Packard, K. C., & Liu, C. (2003). A comparison of estimation methods for fitting Weibull and Johnson’s SB distributions to mixed spruce-fir stands in northeastern North America. Canadian Journal of Forest Research, 33, 1340-1347.

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