Journal of Environment and Sociobiology

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Modelling Tree Diameter Distribution With a Case Study from Garhbeta Sal Coppice Forest, Paschim Medinipur District, West Bengal


Affiliations
1 Birla Institute of Technology and Science, Pilani, Jhunjhunu, Rajasthan, India
2 Social Environmental and Biological Association, Kolkata, India
     

   Subscribe/Renew Journal


In forestry, statistical modelling has long been an effective tool in quantitative assessment of tree sizes using probability distributions on tree diameters at breast height (dbh). It is however still unclear that which family of probability distributions, viz., symmetric, skewed, or heavy-tailed models are more flexible to this end, especially in forests within a small area like Garhbeta sal (Shorea robusta) coppice forest of Paschim Medinipur district, West Bengal. Thus, a comprehensive analysis of several descriptive and inferential statistics is provided here to identify the best-fit probability distribution in tree diameter estimation. The sample dataset comprises tree diameters (22 cm-44 cm) of 80 randomly selected sal trees, aged between 40-50 years. Twelve candidate probability distributions are evaluated in this study. The Maximum Likelihood Estimation (MLE) method is used for parameter estimation. Results from two goodness-of-fit criteria reveal that (i) the exponentiated exponential distribution provides the best fit, (ii) the Frechet (inverse Weibull), gamma, Gaussian, inverse Gaussian, lognormal and Weibull distributions provide the intermediate fit, and (iii) the rest, namely, exponential, Levy, Maxwell, Pareto and Rayleigh distributions fit poorly to the observed tree diameters in the study area. Finally, some theoretical issues related to the selection of appropriate models are discussed. However, further studies encompassing multi-variable tree diameter data are recommended to strengthen the modelling results towards commercial timber production assessment in forests.

Keywords

Garhbeta Forest, Probability Distributions, Diameter Modelling, Model Selection.
Subscription Login to verify subscription
User
Notifications
Font Size


  • Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D. and Cochran, J. J. 2014. Statistics for Business and Economics, 12 edn., Cengage Learning India Pvt. Ltd., pp. 1088.

  • Bailey, R. I. and Dell, T. R. 1973. Quantifying diameter distributions with the Weibull functions. Forest Sci., 19: 97-104.

  • Bliss, C. I. and Reinker, K. A. 1964. A lognormal approach to diameter distributions in even-aged stands. Forest Sci., 10: 350-360.

  • Coomes, D. A. and Allen, R. B. 2007. Mortality and tree-size distributions in natural mixed-age forests. J. Ecol. 95: 27-40.

  • Hafley, W. I. and Schreuder, H. T. 1977. Statistical distributions for diameter and height data in even-aged stands. Can. J. For. Res. 7: 481-487.

  • Hogg, R. V., Mckean, J. W. and Craig, A. T. 2015. Introduction to mathematical statistics. 6th edn, PRC Press: 718.

  • Johnson, N. L., Kotz, S. and Balakrishnan, N. 1995. Continuous univariate distributions. Vol. 2, 2nd edn., Wiley-Interscience : 752.

  • Lai, C. D., Xie. M. and Murthy, D. N. P. 2003. A modified Weibull distribution. IEEE Trans. Rel. 52: 33-37.

  • Leiva, V., Barros, M. and Paula, G. A. 2009. Generalized Birnbaum-Saunders models using R. Brazilian Statistical Association, Sao Paulo, Brazil : 329.

  • Lima, R. A. F., Batista, J. L. F. and Prado, P. I. 2015. Modeling tree diameter distributions in natural forests: an evaluation of 10 statistical models. Forest Sci., 61(2): 320-327.

  • Muller-Landau, H. C. et al. 2006. Coparing tropical forest tree size distributions with the predictions of metabolic ecology and equilibrium models. Ecol. Lett. 9: 589-602.

  • Pasari, S. 2015. Understanding Himalayan Tectonics from Geodetic and Stochastic Modeling. PhD Thesis, Indian Institute of Technology Kanpur, India.

  • Pasari, S. and Dikshit, O. 2014. Impact of three-parameter Weibull models in probabilistic assessment of earthquake hazards. Pure Appl. Geophys. 171(7): 1251-1281.

  • Podlaski, R. 2008. Characterization of diameter distribution data in near-natural forests using the Birnbaum-Saunders distribution. Can. J. For. Res. 38: 518-527.

  • Taubert, F., Hartig, F., Dobner, H. J. and Huth, A. 2013. On the challenge of fitting tree size distributions in ecology. PLoS One 8: e58036.

  • Zhang, L., Packard, K. C. and Liu, C. 2003. A comparison of estimation methods for fitiing Weibull and Johnson’s SB distributions to mixed spruce-fir stands in northeastern North America. Can. J. For. Res., 33: 1340-1347.

  • Zhang, X., Duan, A., Zhang, J. and Xiang, C. 2014. Estimating tree height-diameter models with the Bayesian method. Scientific World J. ID: 683691.


Abstract Views: 415

PDF Views: 1




  • Modelling Tree Diameter Distribution With a Case Study from Garhbeta Sal Coppice Forest, Paschim Medinipur District, West Bengal

Abstract Views: 415  |  PDF Views: 1

Authors

Sumanta Pasari
Birla Institute of Technology and Science, Pilani, Jhunjhunu, Rajasthan, India
N. C. Nandi
Social Environmental and Biological Association, Kolkata, India

Abstract


In forestry, statistical modelling has long been an effective tool in quantitative assessment of tree sizes using probability distributions on tree diameters at breast height (dbh). It is however still unclear that which family of probability distributions, viz., symmetric, skewed, or heavy-tailed models are more flexible to this end, especially in forests within a small area like Garhbeta sal (Shorea robusta) coppice forest of Paschim Medinipur district, West Bengal. Thus, a comprehensive analysis of several descriptive and inferential statistics is provided here to identify the best-fit probability distribution in tree diameter estimation. The sample dataset comprises tree diameters (22 cm-44 cm) of 80 randomly selected sal trees, aged between 40-50 years. Twelve candidate probability distributions are evaluated in this study. The Maximum Likelihood Estimation (MLE) method is used for parameter estimation. Results from two goodness-of-fit criteria reveal that (i) the exponentiated exponential distribution provides the best fit, (ii) the Frechet (inverse Weibull), gamma, Gaussian, inverse Gaussian, lognormal and Weibull distributions provide the intermediate fit, and (iii) the rest, namely, exponential, Levy, Maxwell, Pareto and Rayleigh distributions fit poorly to the observed tree diameters in the study area. Finally, some theoretical issues related to the selection of appropriate models are discussed. However, further studies encompassing multi-variable tree diameter data are recommended to strengthen the modelling results towards commercial timber production assessment in forests.

Keywords


Garhbeta Forest, Probability Distributions, Diameter Modelling, Model Selection.

References