Environmental and Ecological Statistics

, Volume 4, Issue 1, pp 31–48 | Cite as

Modelling the distribution of plant species using the autologistic regression model

  • Hulin Wu
  • F Red W. Huffer


For modeling the distribution of plant species in terms of climate covariates, we consider an autologistic regression model for spatial binary data on a regularly spaced lattice. This model belongs to the class of autologistic models introduced by Besag (1974). Three estimation methods, the coding method, maximum pseudolikelihood method and Markov chain Monte Carlo method are studied and comparedvia simulation and real data examples. As examples, we use the proposed methodology to model the distributions of two plant species in the state of Florida.

binary data coding method ecological data environmental statistics Markov chain Monte Carlo plant species pseudolikelihood spatial data 


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  1. Arnold, B.C. and Strauss, D. (1991) Pseudolikelihood estimation: some examples. Sankhyã: The Indian Journal of Statistics, 53, B, 233–243.Google Scholar
  2. Austin, M.P., Nicholls, A.O. and Margules, C.R. (1990) Measurement of the realized qualitative niche: environmental niches of five eucalyptus species. Ecological Monographs, 60 (2), 161–177.Google Scholar
  3. Bartlein, P.J., Prentice, I.C. and Webb, T. (1986) Climatic response surfaces from pollen data for some eastern North American taxa. Journal of Biogeography, 13, 35–57.Google Scholar
  4. Besag, J. (1972) Nearest-neighbour systems and the auto-logistic model for binary data (with Discussion). Journal of the Royal Statistical Society, Series B, 34, 75–83.Google Scholar
  5. Besag, J. (1974) Spatial interaction and the statistical analysis of lattice systems (with Discussion). Journal of the Royal Statistical Society, Series B, 36, 192–236.Google Scholar
  6. Besag, J. (1975) Statistical analysis of non-lattice data. The Statistician, 24, 179–195.Google Scholar
  7. Besag, J. (1977) Efficiency of pseudolikelihood estimators for simple Gaussian fields. Biometrika, 64, 616–8.Google Scholar
  8. Besag, J. and Moran, P.A.P. (1975) On the estimation and testing of spatial interaction in Gaussian Lattice Processes, Biometrika, 62, 555–562.Google Scholar
  9. Box, E.O., Crumpacker, D.W. and Hardin E.D. (1993) A climatic model for location of plant species in Florida, U.S.A. Journal of Biogeography, 20, 629–44.Google Scholar
  10. Chalmond, B. (1986) Image restoration using an estimated Markov model. Preprint, Mathematics Dept., University of Paris, Orsay.Google Scholar
  11. Comets, F. (1992) On consistency of a class of estimators for exponential families of Markov random fields on the lattice. The Annals of Statistics, 20, (1), 455–568.Google Scholar
  12. Cressie, N. (1993) Statistics for Spatial Data (revised edition). Wiley, New York.Google Scholar
  13. Geman, S. and Geman, D. (1984) Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–41.Google Scholar
  14. Geman, S. and Graffine, C. (1987) Markov random field image models and their applications to computer vision. Proceedings of the 1986 International Congress of Mathematicians, (A.M. Gleason, ed.) Vol. 2, pp. 1496–1517. American Mathematical Society, Providence, R.I.Google Scholar
  15. Geyer, C.J. (1991) Markov chain Monte Carlo maximum likelihood. Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface (E.M. Keramides, ed.), pp. 156–63.Google Scholar
  16. Geyer, C.J. (1992) Practical Markov chain Monte Carlo (with discussion). Statistical Science, 7, (4), 473–511.Google Scholar
  17. Geyer, C.J. (1994) On the convergence of Monte Carlo maximum likelihood calculations. Journal of the Royal Statistical Society, Series B, 56, 261–74.Google Scholar
  18. Geyer, C.J. and Thompson, E.A. (1992) Constrained Monte Carlo maximum likelihood for dependent data (with discussion). Journal of the Royal Statistical Society, Series B, 54 657–99.Google Scholar
  19. Gidas, B. (1986) Consistency of maximum likelihood and pseudolikelihood estimators for Gibbs distributions. Proceedings of the Workshop on Stochastic Differential Systems with Applications in Electrical/Computer Engineering, Control Theory, and Operations Research, IMA, University of Minnesota. 129–45.Google Scholar
  20. Gidas, B. (1991) Parameter estimation for Gibbs distributions from fully observed data. Markov Random Fields: Theory and Applications, (R. Chellappa and A. Jain, eds), Academic, New York. 471–98.Google Scholar
  21. Huffer, F.W. and Wu, H. (1995) Markov chain Monte Carlo for autologistic regression models with applica-tion to the distribution of plant species, (submitted for publication).Google Scholar
  22. Huntley, B., Bartlein, P.J. and Prentice, I.C. (1989) Climatic control of the distribution and abundance of beech (Fagus L.) in Europe and North America. Journal of Biogeography, 16, 551–60.Google Scholar
  23. Jensen, J.L. and Mùoller, J. (1991) Pseudolikelihood for exponential family models of spatial point processes. The Annals of Applied Probability, 1, (3), 445–61.Google Scholar
  24. Little, Jr., E.L. (1978) Atlas of United States Trees, Volume 5. Florida. Misc. Publ. No. 1361, USDA Forest Service. Washington, D.C.: U.S. Government Printing Office. 256 maps, with indices of common and scientific names.Google Scholar
  25. Preisler, H.K. (1993) Modelling spatial patterns of trees attacked by bark beetles. Applied Statistics, 42, 501–14.Google Scholar
  26. Ripley, B.D. (1988) Statistical Inference for Spatial Processes, Cambridge University Press, Cambridge.Google Scholar
  27. Schwartz, M.W. (1988) Species diversity patterns in woody flora on three north American peninsulas. Journal of Biogeography, 15, 759–74.Google Scholar
  28. Strauss, D. and Ikeda, M. (1990) Pseudolikelihood estimation for social networks. Journal of the American Statistical Association, 85, 204–12.Google Scholar
  29. Winkler, G. (1995) Image Analysis, Random Fields and Dynamic Monte Carlo Methods: A Mathematical Introduction, Springer-Verlag, Berlin.Google Scholar
  30. Wu, H. (1994) Regression models for spatial binary data with application to the distribution of plant species. Ph.D. Dissertation, Department of Statistics, The Florida State University.Google Scholar
  31. Zhao, L.P. and Prentice, R.L. (1990) Correlated binary regression using a quadratic exponential model. Biometrika, 77, 642–48.Google Scholar

Copyright information

© Chapman and Hall 1997

Authors and Affiliations

  • Hulin Wu
    • 1
  • F Red W. Huffer
    • 2
  1. 1.Frontier Science & Technology Research Foundation, Inc.BrooklineUSA
  2. 2.Department of StatisticsThe Florida State UniversityTallahasseeUSA

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