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
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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 Lmoment 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 Bonferronitype 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.
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 Title
 Goodness of Fit of Probability Distributions for Sightings as Species Approach Extinction
 Journal

Bulletin of Mathematical Biology
Volume 71, Issue 3 , pp 701719
 Cover Date
 20090401
 DOI
 10.1007/s1153800893773
 Print ISSN
 00928240
 Online ISSN
 15229602
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Lmoments
 Extinct birds
 Field significance test
 Biological records
 Extirpation
 Industry Sectors
 Authors

 Richard M. Vogel ^{(1)}
 Jonathan R. M. Hosking ^{(2)}
 Chris S. Elphick ^{(3)}
 David L. Roberts ^{(4)} ^{(5)}
 J. Michael Reed ^{(6)}
 Author Affiliations

 1. Department of Civil and Environmental Engineering, Tufts University, Medford, MA, 02155, USA
 2. IBM Research Division, Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY, 10598, USA
 3. Department of Ecology and Evolutionary Biology, and Center for Conservation and Biodiversity, University of Connecticut, 75 North Eagleville Rd. U3043, Storrs, CT, 06269, USA
 4. Museum of Comparative Zoology, Harvard University, 26 Oxford St., Cambridge, MA, 02138, USA
 5. Royal Botanic Gardens, Kew, Richmond, Surrey, TW9 3AB, UK
 6. Department of Biology, Tufts University, Medford, MA, 02155, USA