Hostname: page-component-7c8c6479df-xxrs7 Total loading time: 0 Render date: 2024-03-27T08:14:33.469Z Has data issue: false hasContentIssue false

On a conservative Bayesian method of inferring extinction

Published online by Cambridge University Press:  05 May 2016

John Alroy*
Affiliation:
Department of Biological Sciences, Macquarie University, New South Wales 2109, Australia. E-mail: john.alroy@mq.edu.au.

Abstract

Few methods exist that put a posterior probability on the hypothesis that a thing is gone forever given its sighting history. A recently proposed Bayesian method is highly accurate but aggressive, generating many near-zero or near-one probabilities of extinction. Here I explore a Bayesian method called the agnostic equation that makes radically different assumptions and is much more conservative. The method assumes that the overall prior probability of extinction is 50% and that slices of the prior are exponentially distributed across the time series. The conditional probability of the data given survival is based on a simple, long-known combinatorial expression that captures the chance all presences would fall at random before or within the last sighting’s interval (L) given that they could fall anywhere. The same equation is used to compute the conditional probability given extinction at the start of each interval i, that is, the chance that all sightings would fall before or within L given that none could equal or postdate i. The conditional probability is zero for all hypothesized extinction intervals through L. Bayes’s theorem is then used to compute the posterior extinction probability. It is noted that recycling the mean posterior for a population as a prior improves the method’s accuracy. The agnostic equation differs from an earlier, related one, because it explicitly includes a term to represent the hypothesis of survival, and it therefore does not assume that the species has necessarily gone extinct within the sampling window. Simulations demonstrate that the posterior extinction probabilities are highly accurate when considered as a suite but individually indecisive, rarely approaching one. This property is advantageous whenever inferring extinction would have dangerous consequences. The agnostic method is therefore advocated in cases where conservative estimates are desired.

Type
Methods in Paleobiology
Copyright
Copyright © 2016 The Paleontological Society. All rights reserved 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Literature Cited

Alroy, J. 2014. A simple Bayesian method of inferring extinction. Paleobiology 40:584607.Google Scholar
Alroy, J. 2015. Current extinction rates of reptiles and amphibians. Proceedings of the National Academy of Sciences USA 112:1300313008.Google Scholar
Alroy, J. 2016. A simple Bayesian method of inferring extinction: reply. Ecology (in press).CrossRefGoogle Scholar
Bradshaw, C. J. A., Cooper, A., Turney, C. S. M., and Brook, B. W.. 2012. Robust estimates of extinction time in the geological record. Quaternary Science Reviews 33:1419.Google Scholar
Burgman, M. A., Grimson, R. C., and Ferson, S.. 1995. Inferring threat from scientific collections. Conservation Biology 9:923928.Google Scholar
Caley, P., and Barry, S. C.. 2014. Quantifying extinction probabilities from sighting records: inference and uncertainties. PLoS ONE 9:e95857.CrossRefGoogle ScholarPubMed
Collen, B., Purvis, A., and Mace, G. M.. 2010. When is a species really extinct? Testing extinction inference from a sighting record to inform conservation assessment. Diversity and Distributions 16:755764.Google Scholar
Goodman, L. A. 1952. Serial number analysis. Journal of the American Statistical Association 47:622634.CrossRefGoogle Scholar
Höhle, M., and Held, L.. 2006. Bayesian estimation of the size of a population. Ludwig-Maximilians-Universität München Institut für Statistik Sonderforschungsbereich 386:112.Google Scholar
Marshall, C. R. 1999. Fossil gap analysis supports early Tertiary origin of trophically diverse avian orders: comment. Geology, 2795.Google Scholar
Marshall, C. R. 2010. Using confidence intervals to quantify the uncertainty in the end-points of stratigraphic ranges. Paleontological Society Papers 16:291316.CrossRefGoogle Scholar
Marshall, C. R., and Ward, P. D.. 1996. Sudden and gradual molluscan extinctions in the latest Cretaceous of western European Tethys. Science 274:13601363.CrossRefGoogle ScholarPubMed
Rivadeneira, M. M., Hunt, G., and Roy, K.. 2009. The use of sighting records to infer species extinction: an evaluation of different methods. Ecology 90:12911300.Google Scholar
Roberts, D. L., and Solow, A. R.. 2003. Flightless birds: when did the dodo become extinct? Nature 426:245.Google Scholar
Solow, A. 2016. A simple Bayesian method for inferring extinction: comment. Ecology (in press). doi:10.1890/15-0336.1.CrossRefGoogle Scholar
Strauss, D., and Sadler, P. M.. 1989. Classical confidence intervals and Bayesian probability estimates for ends of local taxon ranges. Mathematical Geology 21:411427.CrossRefGoogle Scholar