Environmental and Ecological Statistics

, Volume 5, Issue 4, pp 391–402

Non-parametric MLE for Poisson species abundance models allowing for heterogeneity between species

  • James L. Norris
  • Kenneth H Pollock

DOI: 10.1023/A:1009659922745

Cite this article as:
Norris, J.L. & Pollock, K.H. Environmental and Ecological Statistics (1998) 5: 391. doi:10.1023/A:1009659922745


The proper management of an ecological population is greatly aided by solid information about its species' abundances. For the general heterogeneous Poisson species abundance setting, we develop the non-parametric mle for the entire probability model, namely for the total number N of species and the generating distribution F for the expected values of the species' abundances. Solid estimation of the entire probability model allows us to develop generator-based measures of ecological diversity and evenness which have inferences over similar regions. Also, our methods produce a solid goodness-of-fit test for our model as well as a likelihood ratio test to examine if there is heterogeneity in the expected values of the species' abundances. These estimates and tests are examined, in detail, in the paper. In particular, we apply our methods to important data from the National Breeding Bird Survey and discuss how our methods can also be easily applied to sweep net sampling data. To further examine our methods, we provide simulations for several illustrative situations.

bootstrap ecological diversity and evenness goodness-of-fit test likelihood ratio test mixture model 

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • James L. Norris
    • 1
  • Kenneth H Pollock
    • 2
  1. 1.Department of Mathematics and Computer ScienceWake Forest UniversityWinston-SalemUSA
  2. 2.Biostatistics ProgramNorth Carolina State UniversityRaleighUSA

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