Function Approximation and Documentation of Sampling Data Using Artificial Neural Networks

  • Wenjun Zhang
  • Albert Barrion


Biodiversity studies in ecology often begin with the fitting and documentation of sampling data. This study is conducted to make function approximation on sampling data and to document the sampling information using artificial neural network algorithms, based on the invertebrate data sampled in the irrigated rice field.

Three types of sampling data, i.e., the curve species richness vs. the sample size, the curve rarefaction, and the curve mean abundance of newly sampled species vs.the sample size, are fitted and documented using BP (Backpropagation) network and RBF (Radial Basis Function) network. As the comparisons, The Arrhenius model, and rarefaction model, and power function are tested for their ability to fit these data. The results show that the BP network and RBF network fit the data better than these models with smaller errors.

BP network and RBF network can fit non-linear functions (sampling data) with specified accuracy and don't require mathematical assumptions. In addition to the interpolation, BP network is used to extrapolate the functions and the asymptote of the sampling data can be drawn. BP network cost a longer time to train the network and the results are always less stable compared to the RBF network. RBF network require more neurons to fit functions and generally it may not be used to extrapolate the functions. The mathematical function for sampling data can be exactly fitted using artificial neural network algorithms by adjusting the desired accuracy and maximum iterations. The total numbers of functional species of invertebrates in the tropical irrigated rice field are extrapolated as 140 to 149 using trained BP network, which are similar to the observed richness.


artificial neural networks documentation function approximation rice invertebrates sampling data 


  1. Brown, K. S. Jr.: 1991, Conservation of Neotropical insects: Insects as indicators. In: Collins, N. M., Thomas, J. A. (eds.), The Conservation of Insects and Their Habitats. Academic Press, London, pp.349–404.Google Scholar
  2. Bunge, J., Fitzpatrick, M.: 1993, Estimating the number of species: a review. Journal of American Statistician Association, 88, 364–373.CrossRefGoogle Scholar
  3. Cohen, J. E.: 1978, Food webs and niche space. Monographs in Population Biology 11, Princeton University Press, Princeton, USA.Google Scholar
  4. Cohen, J. E. et al.: 1993, Improving food webs. Ecology, 74, 252–258.CrossRefGoogle Scholar
  5. Coleman, B. D., Mares, M. A., Willig, M. R., Hsieh, Y. H.: 1982, Randomness, area, and species richness. Ecology, 63, 1121–1133.CrossRefGoogle Scholar
  6. Colwell, R. K., Coddington, J. A.: 1994. Estimating terrestrial biodiversity through extrapolation. Phil. Trans. Roy. Soc. London B, 345, 101–108.Google Scholar
  7. Gotelli, N. J., Graves, G. R.: 1996, Null Models in Ecology. Smithsonian Institution Press, Washington, D.C., USA.Google Scholar
  8. Hagan, M. T., Demuth, H. B., Beale, M. H.: 1996, Neural Network Design. PWS Publishing Company.Google Scholar
  9. Heong, K. L., Aquino, G. B., Barrion, A. T.: 1991, Invertebrate community structures of rice ecosystems in the Philippines. Bulletin of Entomological Research, 81, 407–416.Google Scholar
  10. Hurlbert, S. H.: 1971, The concept of species diversity: a critique and alternative parameters. Ecology, 52, 577–585.CrossRefGoogle Scholar
  11. James, F. C., Rathbun, S.: 1981, Rarefaction, relative abundance, and diversity of avian communities. Auk, 98, 785–800.Google Scholar
  12. Krebs, C. J.: 1989, Ecological Methodology. HarperCollinsPublishers, New York, USA, pp. 1–654.Google Scholar
  13. Kremen, C., Colwell, R. K., Erwin, T. L., Murphy, D. D.: 1993, Invertebrate assemblges: their use as indicators in conservation planning. Conservation Biology, 7, 796–808.CrossRefGoogle Scholar
  14. Mathworks, 2002. Neural Network Toolbox, MATLAB 6.5.Google Scholar
  15. May, R. M.: 1981, Patterns in multi-species communities. In: May, R.M. (ed.) Theoretical Ecology. Sinauer Associates, Sunderland, MASS., USA, pp. 197–227.Google Scholar
  16. Miller, R. J., White, P. S.: 1986, Condiderations for preserve design based on the distribution of rare plants in Great Smoky Mountains National Park. U.S.A. Journal of Environmental Management, 10, 119–124.CrossRefGoogle Scholar
  17. Miller, R. J., and R. G. Wiegert.: 1989, Documenting completeness, species-area relations, and the species-abundance distribution of a regional flora. Ecology, 1, 16–22.CrossRefGoogle Scholar
  18. Moreno, C. E., Halffter, G.: 2000, Assessing the completeness of bat biodiversity inventories using species accumulation curves. Journal of Applied Ecology, 37, 149–158.CrossRefGoogle Scholar
  19. Ooi, P., Shepard, M.: 1994, Predators and parasitoids of rice insect pests. In: Pedigo, L. P., Buntin, G. D. (eds.), Handbook of Sampling Methods for Arthropods in Agriculture. CRC Press, Boca Raton, Fla., USA.Google Scholar
  20. Sanders, H. L.: 1968, Marine benthic diversity: a comparative study. Am. Nat., 102, 243–282.CrossRefGoogle Scholar
  21. Schoenly, K. G., Cohen, M. B., Barrion, A. T., Zhang, W. J., Gaolach, B., Viajante, V. D.: 2003, Effects of Bacillus thuringiensison non-target herbivore and natural enemy assemblages in tropical irrigated rice. Environment and Biosafety Research, 3, 181–206.CrossRefGoogle Scholar
  22. Schoenly, K. G., Cohen, J. E., Heong, K. L., Litsinger, J. A., Aquino, G. B., Barrion, A. T., Arida, G.: 1996, Food web dynamics of irrigated rice fields at five elevations in Luzon, Philippines. Bulletin of Entomological Research, 86, 451–466.Google Scholar
  23. Schoenly, K. G., Justo, J. D. Jr., Barrion, A. T., Harris, M. K., Bottrell, D. G.: 1998, Analysis of invertebrate biodiversity in a Philippine farmer's irrigated rice field. Environmental Entomology, 27, 1125–1136.Google Scholar
  24. Schoenly, K. G., Zhang, W. J.: 1999, IRRI Biodiversity Software Series. V. RARE, SPPDISS, and SPPANK: programs for detecting between-sample difference in community structure. IRRI Technical Bulletin No.5. International Rice Research Ins titute, Manila, Philippines, pp. 1–17.Google Scholar
  25. Shahid, S. A., Schoenly, K. G., Haskell, N. H., Hall, R. D., Zhang, W. J.: 2003, Carcass enrichment does not alter decay rates or arthropod community structure: a test of the arthropod saturation hypothesis at the anthropology research facility in Knoxville, Tennessee. Journal of Medical Entomology, 4, 559–569.CrossRefGoogle Scholar
  26. Shannon, C. E., Weaver, W.: 1963, The Mathematical Theory of Communication. University of Illinois Press, Urbana, Illinois, USA.Google Scholar
  27. Simberloff, D.: 1972, Properties of the rarefaction diversity measurements. Am. Nat., 196, 414–418.CrossRefGoogle Scholar
  28. Simberloff, D.: 1978, Rarefaction as a distribution-free method of expressing and estimating diversity. In: Grassle, J. F., Patil, G. P., Smith, W. K., Taillie, C. (eds.), Ecological Diversity in Theory and Practice. International Cooperative Publishing House, Fairland, Md., USA, pp. 159–176.Google Scholar
  29. Steele, B. B., Bayn, R. L. Jr., ValGrant, C.: 1984. Environmental monitoring using populations of birds and small mammals: analysis of sampling effort. Biological Conservation, 30, 157–172.CrossRefGoogle Scholar
  30. Sutherland, W. J.: 1996, Ecological Census Techniques. Cambridge University Press, Cambridge, UK.Google Scholar
  31. Way, M. J., Heong, K. L.: 1994, The role of biodiversity in the dynamics and management of insect pests of tropical irrigated rice-a review. Bulletin of Entomological Research, 84, 567–587.CrossRefGoogle Scholar
  32. Zhang, W. J., Schoenly, K. G.: 1999, IRRI Biodiversity Software Series. II. COLLECT1 and COLLECT2: programs for calculating statistics of collectors' curves. IRRI Technical Bulletin No.2. International Rice Research Institute, Manila, Philippines, pp. 1–15.Google Scholar
  33. Zhang, W. J., Schoenly, K. G.: 2001, A randomization test and software to compare ecological communities. International Rice Research Notes, 2, 48–49.Google Scholar
  34. Zhang, W. J., Qi, Y. H.: 2002, Functional link artificial neural network and agri-biodiversity analysis. Biodiversity Science, 3, 345–350.Google Scholar
  35. Zhang, W. J., Qi, Y. H., Schoenly, K. G.: 2002, Randomization tests and computational software on significance of community biodiversity and evenness. Biodiversity Science, 4, 431–437.Google Scholar
  36. Zhang, W. J., Qi, Y. H., Barrion, A. T.: 2004, Neural network approximation of sampling yield-effort curves of rice invertebrates. International Rice Research Notes, 2: 34–36.Google Scholar
  37. Zhang, W. J., Schoenly, K. G.: 2004, Lumping and correlation analyses of invertebrate taxa in tropical irrigated rice field. International Rice Research Notes, 1: 41–43.Google Scholar
  38. Zhao, Z. M., Guo, Y. Q.: 1990, Community Ecology: Principles and Methods. Chongqing Branch Press of Science and Technology Literature Press, Chongqing, China, pp. 129–130.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Research Institute of Entomology and School of Life SciencesZhongshan UniversityGuangzhouP.R. China
  2. 2.International Rice Research InstituteMetro ManilaPhilippines

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