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A general approach to modeling and analysis of species abundance data with extra zeros

Article

Abstract

A general method for the analysis of ecological count data with extra zeros is presented using a Markov birth process representation of discrete distributions. The method uses a non parametric formulation of the birth process to model the residual variation and therefore allows the data to play a greater role in determining an appropriate distribution. This enables a more critical assessment of covariate effects and more accurate predictions to be made. The approach is also presented as a useful diagnostic tool for suggesting appropriate parametric models or verifying standard models. As an ill ustrative example, data describing a bundance of a species of possum from the montane ash forests of the central highlands of Victoria, southeast Australia, is considered.

Key Words

Covariate effects Extended Poisson process model Penalized likelihood Prediction 

References

  1. Cox, D. R., and Miller, H. D. (1965), The Theory of Stochastic Processes, London: Methuen.MATHGoogle Scholar
  2. Daniels, H. E. (1982), “The Saddlepoint Approximation for a General Birth Process,” Journal of Applied Probability, 19, 20–38.MATHCrossRefMathSciNetGoogle Scholar
  3. Faddy, M. J. (1997), “Extended Poisson Process Modelling and Analysis of Count Data,” Biometrical Journal, 39, 431–440.MATHCrossRefGoogle Scholar
  4. Faddy, M. J. (1998), “Stochastic Models for Analysis of Species Abundance Data,” in Statistics in Ecology and Environmental Monitoring (Vol. 2), eds. D. J. Fletcher, L. Kavalieris, and B. F. J. Manly, Dunedin: University of Otago Press, pp. 33–40.Google Scholar
  5. Green, P. J., and Silverman, B. W. (1994), Nonparametric Regression and Generalized Linear Models, London: Chapman and Hall.MATHGoogle Scholar
  6. Lambert, D. (1992), “Zero-Inflated Poisson Regression, With an Application to Defects in Manufacturing,” Technometrics 34, 1–14.MATHCrossRefGoogle Scholar
  7. Podlich, H. M., Faddy, M. J., and Smyth, G. K. (1999), “Likelihood Computations for Extended Poisson Process Models,” InterStat, September No. 1, 15 pp.Google Scholar
  8. Sidje, R. B. (1998), “EXPOKIT: Software Package for Computing Matrix Exponentials,” ACM Transactions on Mathematical Software, 24, 130–156.MATHCrossRefGoogle Scholar
  9. Welsh, A. H., Cunningham, R. B., Donnelly, C. F., and Lindenmayer, D. B. (1996), “Modelling the Abundance of Rare Species: Statistical Models for Counts With Extra Zeros,” Ecological Modelling, 88, 297–308.CrossRefGoogle Scholar

Copyright information

© International Biometric Society 2002

Authors and Affiliations

  1. 1.School of Land and Food SciencesThe University of QueenslandAustralia
  2. 2.School of Mathematics and StatisticsThe University of BirminghamU.K.
  3. 3.Walter and Eliza Hall Institute for Medical ResearchMelbourneAustralia

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