Table of Contents 
ISRN Forestry
Volume 2013, Article ID 196832, 12 pages
http://dx.doi.org/10.1155/2013/196832
Research Article

Individual Growth Model for Eucalyptus Stands in Brazil Using Artificial Neural Network

Renato Vinícius Oliveira Castro,1 Carlos Pedro Boechat Soares,2 Helio Garcia Leite,2 Agostinho Lopes de Souza,2 Gilciano Saraiva Nogueira,3 and Fabrina Bolzan Martins4

1Department of Forestry, Faculty of Technology, University of Brasília, Campus Darcy Ribeiro, 70904-970 Brasília, DF, Brazil
2Department of Forestry, Federal University of Viçosa, Campus UFV, 36570-000 Viçosa, MG, Brazil
3Department of Forestry, Federal University of the Valleys of Jequitinhonha and Mucuri, Campus Diamantina, 39100-000 Diamantina, MG, Brazil
4Natural Resources Institute, Federal University of Itajubá, Campus Itajubá, 37500-903 Itajubá, MG, Brazil

Received 13 December 2012; Accepted 14 February 2013

Academic Editors: J. Kaitera, P. Newton, T. L. Noland, and P. Robakowski

Copyright © 2013 Renato Vinícius Oliveira Castro et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. L. Clutter, J. C. Fortson, L. V. Pienaar, G. H. Brister, and R. L. Bailey, Timber Management: A Quantitative Approach, John Wiley & Sons, New York, NY, USA, 1983.
  2. L. S. Davis and K. N. Johnson, Forest Management, McGraw-Hill, New York, NY, USA, 1987.
  3. J. K. Vanclay, Modeling Forest Growth and Yield: Aplications to Mixed Tropical Forest, CAB International, Wallingford, UK, 1994.
  4. D. D. Munro, “Forest growth models—a prognosis,” in Growth Models for Tree and Stand Simulation, J. Fries, Ed., pp. 1–21, Royal College of Forestry, Stockholm, Sweden, 1974. View at Google Scholar
  5. R. M. Newnham, The development of a stand model for Douglas-fir [Ph.D. thesis], University of British Columbia, Canada, 1964.
  6. P. Soares and M. Tomé, “A distance dependent diameter growth model for first rotation eucalyptus plantation in Portugal,” in Empirical and Process—Bases Models for Forest Tree and Stand Growth Simulation, A. Amaro and M. Tomé, Eds., pp. 267–270, Salamandra, 1997. View at Google Scholar
  7. F. Crescente-Campo, P. Soares, M. Tomé, and U. Diéguez-Aranda, “Modeling noncatastrophic individual tree mortality for Pinus radiate plantations in northwestern Spain,” Forest Ecology and Management, vol. 257, no. 6, pp. 1542–1550, 2010. View at Google Scholar
  8. B. R. Mendes, N. Calegario, C. E. S. Volpato, and A. A. Melo, “Desenvolvimento de modelos de crescimento de árvores individuais fundamentado em equações diferenciais,” Cerne, vol. 12, pp. 254–263, 2006. View at Google Scholar
  9. F. B. Martins, Modelagem de crescimento em nível de árvore individual para plantios comerciais de eucaliptos [Ph.D. thesis], Universidade Federal de Viçosa, Brazil, 2011.
  10. ABRAF-Associação Brasileira de Florestas Plantadas, “Anuário estatístico da ABRAF: ano base 2010. Brasília,” 2011, http://www.abraflor.org.br/estatisticas/ABRAF11/ABRAF11-BR.pdf.
  11. M. A. Durlo, “Relações morfométricas para Cabralea canjerana (Well.) Mart,” Ciencia Florestal, vol. 11, no. 1, pp. 141–149, 2001. View at Google Scholar
  12. J. B. Della Flora, M. A. Durlo, and P. Soathelf, “Modelo de crescimento para árvores singulares—Nectandra megapotamica (Spreng.) Mez,” Ciencia Florestal, vol. 14, no. 1, pp. 165–177, 2004. View at Google Scholar
  13. M. A. Durlo, F. J. Sutili, and L. Denardi, “Modelagem da copa de Cedrela fissilis Vellozo,” Ciencia Florestal, vol. 14, no. 2, pp. 79–89, 2004. View at Google Scholar
  14. T. Chassot, Modelos de crescimento em diâmetro de árvores individuais de Araucaria angustifólia (Bertol.) Kuntze na floresta ombrófila mista [Ph.D. thesis], Universidade Federal de Santa Maria, Brazil, 2009.
  15. J. C. C. Campos and H. G. Leite, Mensuração Florestal: Perguntas e Respostas, Universidade Federal de Viçosa, Viçosa, Brazil, 2009.
  16. P. Miehle, M. Battaglia, P. J. Sands et al., “A comparison of four process-based models and a statistical regression model to predict growth of Eucalyptus globulus plantations,” Ecological Modelling, vol. 220, no. 5, pp. 734–746, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. D. Merkl and H. Hasenauer, “Using neural networks to predict individual tree mortality,” in Proceedings of the Int’l Conference on Engineering Applications of Neural Networks, pp. 10–12, Gibraltar, UK, 1998.
  18. M. Weingartner, D. Merkl, and H. Hasenauer, “Improving tree mortality predictions of Norway Spruce stands with neural networks,” in Proceedings of the Symposiun on Integration in Environmental Information Systems, Austria, 2000.
  19. H. Hasenauer, D. Merkl, and M. Weingartner, “Estimating tree mortality of Norway spruce stands with neural networks,” Advances in Environmental Research, vol. 5, no. 4, pp. 405–414, 2001. View at Publisher · View at Google Scholar · View at Scopus
  20. M. J. Diamantopoulou, “Artificial neural networks as an alternative tool in pine bark volume estimation,” Computers and Electronics in Agriculture, vol. 48, no. 3, pp. 235–244, 2005. View at Publisher · View at Google Scholar · View at Scopus
  21. E. Görgens, Estimação do volume de árvores utilizando redes neurais artificiais [Ph.D. thesis], Universidade Federal de Viçosa, Brazil, 2006.
  22. M. L. M. Silva, D. H. B. Binoti, J. M. Gleriani, and H. G. Leite, “Ajuste do modelo de Schumacher e Hall e aplicações de redes neurais artificiais para estimar volumes de árvores de eucalipto,” Árvore, vol. 33, no. 6, pp. 1133–1139, 2009. View at Google Scholar
  23. J. M. Paruelo and F. Tomasel, “Prediction of functional characteristics of ecosystems: a comparison of artificial neural networks and regression models,” Ecological Modelling, vol. 98, no. 2-3, pp. 173–186, 1997. View at Publisher · View at Google Scholar · View at Scopus
  24. M. Gevrey, I. Dimopoulos, and S. Lek, “Review and comparison of methods to study the contribution of variables in artificial neural network models,” Ecological Modelling, vol. 160, no. 3, pp. 249–264, 2003. View at Publisher · View at Google Scholar · View at Scopus
  25. H. G. Leite, M. L. M. da Silva, D. H. B. Binoti, L. Fardin, and F. H. Takizawa, “Estimation of inside-bark diameter and heartwood diameter for Tectona grandis Linn. trees using artificial neural networks,” European Journal of Forest Research, vol. 130, no. 2, pp. 263–269, 2011. View at Publisher · View at Google Scholar · View at Scopus
  26. A. P. Braga, Carvalho, A. C. P. L. F, and T. B. Ludemir, “Redes neurais artificiais,” in Sistemas Inteligentes, S. O. Rezende, Ed., pp. 141–168, Manole, Barueri, Brazil, 2003. View at Google Scholar
  27. A. K. Jain, J. Mao, and K. M. Mohiuddin, “Artificial neural networks: a tutorial,” Computer, vol. 29, no. 3, pp. 31–44, 1996. View at Google Scholar · View at Scopus
  28. S. Haykin, Redes Neurais: Princípios e Prática, Bookman, Porto Alegre, Brazil, 2001.
  29. J. M. Barreto, Introdução às Redes Neurais Artificiais, Universidade Federal de Santa Catarina, Florianópolis, Brazil, 2002.
  30. B. T. Guan and G. Gertner, “Using a parallel distributed processing system to model individual tree mortality,” Forensic Science, vol. 37, pp. 871–885, 1991. View at Google Scholar
  31. B. T. Guan and G. Gertner, “Modeling red pine tree survival with an artificial neural network,” Forensic Science, vol. 37, pp. 1429–1440, 1991. View at Google Scholar
  32. D. L. Schomoudt, P. Li, and A. L. Abbot, “Machine vision using artificial neural networks with local 3d neighborhoods,” Computers and Electronics in Agriculture, vol. 97, pp. 101–119, 1997. View at Google Scholar
  33. Q. B. Zhang, R. I. Hebda, Q. J. Zhang, and R. I. Alfaro, “Modeling tree-ring growth responses to climatic variables using artificial neural networks,” Forest Science, vol. 46, no. 2, pp. 229–239, 2000. View at Google Scholar · View at Scopus
  34. C. Liu, L. Zhang, C. J. Davis, D. S. Solomon, T. B. Brann, and L. E. Caldwell, “Comparison of neural networks and statistical methods in classification of ecological habitats using FIA data,” Forest Science, vol. 49, no. 4, pp. 619–631, 2003. View at Google Scholar · View at Scopus
  35. S. A. Corne, S. J. Carver, W. E. Kunin, J. J. Lennon, and A. W. S. van Hees, “Predicting forest attributes in Southeast Alaska using artificial neural networks,” Forest Science, vol. 50, no. 2, pp. 259–276, 2004. View at Google Scholar · View at Scopus
  36. R. Özçelik, M. J. Diamantopoulou, J. R. Brooks, and H. V. Wiant Jr., “Estimating tree bole volume using artificial neural network models for four species in Turkey,” Journal of Environmental Management, vol. 91, no. 3, pp. 742–753, 2010. View at Publisher · View at Google Scholar · View at Scopus
  37. R. A. Demolinari, Crescimento de povoamentos de eucalipto não-desbastados [Ph.D. thesis], Universidade Federal de Viçosa, Viçosa, Brazil, 2006.
  38. M. G. Silva, Produtividade, idade e qualidade da madeira de Eucalyptus destinada à produção de polpa celulósica branqueada [Ph.D. thesis], Universidade de São Paulo, São Paulo, Brazil, 2011.
  39. T. D. Keister and G. R. Tidwell, “Competition ratio dynamics for improved mortality estimates in simulated growth of forests stands,” Forest Science, vol. 21, pp. 46–51, 1975. View at Google Scholar
  40. G. R. Glover and J. N. Hool, “A basal area ratio predictor of loblolly pine plantation mortality,” Forest Science, vol. 25, pp. 275–282, 1979. View at Google Scholar
  41. R. C. de Miranda, J. C. C. Campos, F. de Paula Neto, and L. M. de Oliveira, “Predição da mortalidade regular para eucalipto,” Árvore, vol. 13, pp. 152–173, 1989. View at Google Scholar
  42. S. A. Machado, A. E. Tonon, A. F. Filho, and E. B. Oliveira, “Comportamento da mortalidade natural em bracatingais nativos em diferentes densidades iniciais e classes de sítio,” Ciencia Florestal, vol. 12, pp. 41–50, 2002. View at Google Scholar
  43. R. Maestri, C. R. Sanquetta, and J. C. Arce, “Modelagem do crescimento de povoamentos de Eucalyptus grandisatravés de processos de difusão,” Floresta, vol. 33, pp. 169–182, 2003. View at Google Scholar
  44. L. M. B. Rossi, H. S. Koehler, C. R. Sanquetta, and J. E. Arce, “Modelagem da mortalidade em florestas naturais,” Floresta, vol. 37, pp. 275–291, 2007. View at Google Scholar
  45. D. Zhao, B. Borders, M. Wang, and M. Kane, “Modeling mortality of second-rotation loblolly pine plantations in the Piedmont/Upper coastal plain and lower coastal plain of the southern United States,” Forest Ecology and Management, vol. 252, no. 1–3, pp. 132–143, 2007. View at Publisher · View at Google Scholar · View at Scopus
  46. A. R. Stage, “Prognosis model for stand development,” USDA Forest Service Research Papers INT-137, USDA, Washington, DC, USA, 1973. View at Google Scholar
  47. StatSoft Inc, STATISTICA (data analysis software system), version 8. 0, 2007.
  48. R. P. Lippmann, “An introduction to computing with neural nets,” IEEE ASSP Magazine, vol. 4, no. 2, pp. 4–22, 1987. View at Google Scholar · View at Scopus
  49. A. P. Braga, Carvalho, A. P. L. F, and T. B. Ludemir, Redes Neurais Artificiais: Teoria e Aplicações, Rio de Janeiro, Rio de Janeiro, Brazil, 2000.
  50. R. G. D. Steel and J. H. Torrie, Principles and Procedures of Statistics, McGraw-Hill, New York, NY, USA, 1960.
  51. P. A. Murphy and H. S. Sternitzke, Growth and Yield Estimation for Loblolly Pine in the West Gulf, Southern Forest Experiment Station, New Orleans, La, USA, 1979.
  52. J. Siipilehto, “A comparison of two parameter prediction methods for stand structure in Finland,” Silva Fennica, vol. 34, no. 4, pp. 331–349, 2000. View at Google Scholar · View at Scopus
  53. A. Monty, P. Lejeune, and J. Rondeux, “Individual distance-independent girth increment model for Douglas-fir in southern Belgium,” Ecological Modelling, vol. 212, no. 3-4, pp. 472–479, 2008. View at Publisher · View at Google Scholar · View at Scopus
  54. H. Pretzsch, P. Biber, and J. Ďurský, “The single tree-based stand simulator SILVA: construction, application and evaluation,” Forest Ecology and Management, vol. 162, no. 1, pp. 3–21, 2002. View at Publisher · View at Google Scholar · View at Scopus
  55. F. A. Graybill, Theory and Application of Linear Model, Duxbury, North Scituate, Mass, USA, 1976.
  56. D. A. Hamilton Jr., “A logistic model of mortality in thinned and unthinned mixed conifer stands of northern Idaho,” Forest Science, vol. 32, no. 4, pp. 989–1000, 1986. View at Google Scholar · View at Scopus
  57. I. E. Bella, “A new competition model for individual tree,” Forest Science, vol. 17, pp. 364–372, 1971. View at Google Scholar
  58. R. F. Daniels, “Simple competition indices and their correlation with annual loblolly pine tree growth,” Forest Science, vol. 22, pp. 454–456, 1976. View at Google Scholar
  59. H. Hasenauer and R. A. Monserud, “A crown ratio model for Austrian Forests,” Forest Ecology and Management, vol. 84, no. 1–3, pp. 49–60, 1996. View at Publisher · View at Google Scholar · View at Scopus
  60. S. Vospernik, R. A. Monserud, and H. Sterba, “Do individual-tree growth models correctly represent height: diameter ratios of Norway spruce and Scots pine?” Forest Ecology and Management, vol. 260, no. 10, pp. 1735–1753, 2010. View at Publisher · View at Google Scholar · View at Scopus
  61. H. Hasenauer, “Princípios para a modelagem de ecossistemas florestais,” Revista Ciência & Ambiente, vol. 20, pp. 53–69, 2000. View at Google Scholar
  62. Q. V. Cao, “Predictions of individual-tree and whole-stand attributes for loblolly pine plantations,” Forest Ecology and Management, vol. 236, no. 2-3, pp. 342–347, 2006. View at Publisher · View at Google Scholar · View at Scopus
  63. M. Tome and H. E. Burkhart, “Distance-dependent competition measures for predicting growth of individual trees,” Forest Science, vol. 35, no. 3, pp. 816–831, 1989. View at Google Scholar · View at Scopus
  64. H. Hasenauer, R. A. Monserud, and T. G. Gregoire, “Using simultaneous regression techniques with individual-tree growth models,” Forest Science, vol. 44, no. 1, pp. 87–95, 1998. View at Google Scholar · View at Scopus
  65. M. S. González, RÍO, M. del, I. Cañellas, and G. Montero, “Distance independent tree diameter growth model for cork oak stands,” Forest Ecology and Management, vol. 225, no. 1–3, pp. 262–270, 2006. View at Google Scholar
  66. K. Andreassen and S. M. Tomter, “Basal area growth models for individual trees of Norway spruce, Scots pine, birch and other broadleaves in Norway,” Forest Ecology and Management, vol. 180, no. 1–3, pp. 11–24, 2003. View at Publisher · View at Google Scholar · View at Scopus
  67. C. H. Peng and X. Wen, Recent Applications of Artificial Neural Networks in Forest Resource Management: An Overview, American Association for Artificial Intelligence Technical, Menlo Park, Calif, USA, 1999.
  68. E. Dogan, B. Sengorur, and R. Koklu, “Modeling biological oxygen demand of the Melen River in Turkey using an artificial neural network technique,” Journal of Environmental Management, vol. 90, no. 2, pp. 1229–1235, 2009. View at Publisher · View at Google Scholar · View at Scopus
  69. P. W. West, “Simulation of diameter growth and mortality in regrowth eucalypt forest of southern Tasmania,” Forensic Science, vol. 27, pp. 603–616, 1981. View at Google Scholar
  70. D. W. Hann and C. H. Wang, Mortality Equations for Individual Trees in the Mixed-Conifer Zone of Southwest Oregon, vol. 67 of Research Bulletin, Forest Research Laboratory, Oregon, Wash, USA, 1990.
  71. R. A. Monserud and H. Sterba, “Modeling individual tree mortality for Austrian forest species,” Forest Ecology and Management, vol. 113, no. 2-3, pp. 109–123, 1999. View at Publisher · View at Google Scholar · View at Scopus
  72. F. Crecente-Campo, P. Soares, M. Tomé, and U. Diéguez-Aranda, “Modelling annual individual-tree growth and mortality of Scots pine with data obtained at irregular measurement intervals and containing missing observations,” Forest Ecology and Management, vol. 260, no. 11, pp. 1965–1974, 2010. View at Publisher · View at Google Scholar · View at Scopus
  73. M. Palahí and T. Pukkala, “Optimising the management of Scots pine (Pinus sylvestris L.) stands in Spain based on individual-tree models,” Annals of Forest Science, vol. 60, no. 2, pp. 105–114, 2003. View at Google Scholar · View at Scopus
  74. F. C. C. Uzoh and W. W. Oliver, “Individual tree height increment model for managed even-aged stands of ponderosa pine throughout the western United States using linear mixed effects models,” Forest Ecology and Management, vol. 221, no. 1–3, pp. 147–154, 2006. View at Publisher · View at Google Scholar · View at Scopus