Goodness of Fit of Probability Distributions for Sightings as Species Approach Extinction

  • Richard M. Vogel
  • Jonathan R. M. Hosking
  • Chris S. Elphick
  • David L. Roberts
  • J. Michael Reed
Original Article

DOI: 10.1007/s11538-008-9377-3

Cite this article as:
Vogel, R.M., Hosking, J.R.M., Elphick, C.S. et al. Bull. Math. Biol. (2009) 71: 701. doi:10.1007/s11538-008-9377-3


Estimating the probability that a species is extinct and the timing of extinctions is useful in biological fields ranging from paleoecology to conservation biology. Various statistical methods have been introduced to infer the time of extinction and extinction probability from a series of individual sightings. There is little evidence, however, as to which of these models provide adequate fit to actual sighting records. We use L-moment diagrams and probability plot correlation coefficient (PPCC) hypothesis tests to evaluate the goodness of fit of various probabilistic models to sighting data collected for a set of North American and Hawaiian bird populations that have either gone extinct, or are suspected of having gone extinct, during the past 150 years. For our data, the uniform, truncated exponential, and generalized Pareto models performed moderately well, but the Weibull model performed poorly. Of the acceptable models, the uniform distribution performed best based on PPCC goodness of fit comparisons and sequential Bonferroni-type tests. Further analyses using field significance tests suggest that although the uniform distribution is the best of those considered, additional work remains to evaluate the truncated exponential model more fully. The methods we present here provide a framework for evaluating subsequent models.


L-moments Extinct birds Field significance test Biological records Extirpation 

Copyright information

© Society for Mathematical Biology 2008

Authors and Affiliations

  • Richard M. Vogel
    • 1
  • Jonathan R. M. Hosking
    • 2
  • Chris S. Elphick
    • 3
  • David L. Roberts
    • 4
    • 5
  • J. Michael Reed
    • 6
  1. 1.Department of Civil and Environmental EngineeringTufts UniversityMedfordUSA
  2. 2.IBM Research DivisionThomas J. Watson Research CenterYorktown HeightsUSA
  3. 3.Department of Ecology and Evolutionary Biology, and Center for Conservation and BiodiversityUniversity of ConnecticutStorrsUSA
  4. 4.Museum of Comparative ZoologyHarvard UniversityCambridgeUSA
  5. 5.Royal Botanic GardensRichmondUK
  6. 6.Department of BiologyTufts UniversityMedfordUSA

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