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A simple Bayesian method of inferring extinction

Published online by Cambridge University Press:  08 April 2016

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

Determining whether a species has gone extinct is a central problem in both paleobiology and conservation biology. Past literature has mostly employed equations that yield confidence intervals around the endpoints of temporal ranges. These frequentist methods calculate the chance of not having seen a species lately given that it is still alive (a conditional probability). However, any reasonable person would instead want to know the chance that a species is extinct given that it has not been seen (the posterior probability). Here, I present a simple Bayesian equation that estimates posteriors. It uninterestingly assumes that the sampling probability equals the frequency of sightings within the range. It interestingly sets the prior probability of going extinct during any one time interval (E) by assuming that extinction is an exponential decay process and there is a 50% chance a species has gone extinct by the end of its observed range. The range is first adjusted for undersampling by using a routine equation. Bayes' theorem is then used to compute the posterior for interval 1 (ε1), which becomes the prior for interval 2. The following posterior ε2 again incorporates E because extinction might have happened instead during interval 2. The posteriors are called “creeping-shadow-of-a-doubt values” to emphasize the uniquely iterative nature of the calculation. Simulations show that the method is highly accurate and precise given moderate to high sampling probabilities and otherwise conservative, robust to random variation in sampling, and able to detect extinction pulses after a short lag. Improving the method by having it consider clustering of sightings makes it highly resilient to trends in sampling. Example calculations involving recently extinct Costa Rican frogs and Maastrichtian ammonites show that the method helps to evaluate the status of critically endangered species and identify species likely to have gone extinct below some stratigraphic horizon.

Type
Articles
Information
Paleobiology , Volume 40 , Issue 4 , Fall 2014 , pp. 584 - 607
Copyright
Copyright © The Paleontological Society 

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References

Literature Cited

Anchukaitis, K. J., Evans, M. N., and Graumlich, L. 2010. Tropical cloud forest climate variability and the demise of the Monteverde golden toad. Proceedings of the National Academy of Sciences USA 107:5036–5040.CrossRefGoogle ScholarPubMed
Bayes, T., and Price, R. 1763. An essay towards solving a problem in the doctrine of chance. By the late Rev. Mr. Bayes, communicated by Mr. Price, in a letter to John Canton, M. A. and F. R. S. Philosophical Transactions of the Royal Society of London 53:370–418.Google Scholar
Bottjer, D. J., and Jablonski, D. 1988. Paleoenvironmental patterns in the evolution of post-Paleozoic benthic marine invertebrates. Palaios 3:540–560.Google 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 33:14–19.Google Scholar
Burgman, M. A., Grimson, R. C., and Ferson, S. 1995. Inferring threat from scientific collections. Conservation Biology 9:923–928.Google Scholar
Chapman, P. 2007. Bananas: how the United Fruit Company shaped the world. Canongate, New York.Google Scholar
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 16:755–764.Google Scholar
Diamond, J. M. 1987. Extant unless proven extinct? Or extinct unless proven extant? Conservation Biology 1:77–79.Google Scholar
Gotelli, N. J., Chao, A., Colwell, R. K., Hwang, W.-H., and Graves, G. R. 2011. Specimen-based modeling, stopping rules, and the extinction of the ivory-billed woodpecker. Conservation Biology 26:47–56.Google Scholar
Gott, J. R. III. 1993. Implications of the Copernican principle for our future prospects. Nature 363:315–319.Google Scholar
Holland, S. M. 2003. Confidence limits on fossil ranges that account for facies changes. Paleobiology 29:469–479.Google Scholar
Labandeira, C. C., Johnson, K. R., and Wilf, P. 2002. Impact of the terminal Cretaceous event on plant-insect interactions. Proceedings of the National Academy of Sciences USA 99:2061–2066.CrossRefGoogle Scholar
Marshall, C. R. 1990. Confidence intervals on stratigraphic ranges. Paleobiology 16:1–10.Google Scholar
Marshall, C. R. 1994. Confidence intervals on stratigraphic ranges: partial relaxation of the assumption of randomly distributed fossil horizons. Paleobiology 20:459–469.Google Scholar
Marshall, C. R. 1999. Fossil gap analysis supports early Tertiary origin of trophically diverse avian orders: Comment. Geology 27:95.Google Scholar
Marshall, C. R. 2008. A simple method for bracketing absolute divergence times using multiple fossil calibration points. American Naturalist 171:726–742.Google Scholar
Marshall, C. R. 2010. Using confidence intervals to quantify the uncertainty in the end-points of stratigraphic ranges. Paleontological Society Papers 16:291–316.Google Scholar
Marshall, C. R., and Ward, P. D. 1996. Sudden and gradual molluscan extinctions in the latest Cretaceous of western European Tethys. Science 274:1360–1363.CrossRefGoogle ScholarPubMed
McCarthy, M. A. 1998. Identifying declining and threatened species with museum data. Biological Conservation 83:9–17.Google Scholar
McInerny, G. J., Roberts, D. L., Davy, A. J., and Cribb, P. J. 2006. Significance of sighting rate in inferring extinction and threat. Conservation Biology 20:562–567.Google Scholar
Pounds, J. A., Bustamante, M. R., Coloma, L. A., Consuegra, J. A., Fogden, M. P. L., Foster, P. N., La Marca, E., Masters, K. L., Merino-Viteri, A., Puschendorf, R., Ron, S. R., Sánchez-Azofeifa, G. A., Still, C. J., and Young, B. E. 2006. Widespread amphibian extinctions from epidemic disease driven by global warming. Nature 439:161–167.Google Scholar
Raup, D. M., Gould, S. J., Schopf, T. J. M., and Simberloff, D. S. 1973. Stochastic models of phylogeny and the evolution of diversity. Journal of Geology 81:525–542.Google Scholar
Rivadeneira, M. M., Hunt, G., and Roy, K. 2009. The use of sighting records to infer species extinction: an evaluation of different methods. Ecology 90:1291–1300.Google Scholar
Roberts, D. L., and Kitchener, A. C. 2006. Inferring extinction from biological records: were we too quick to write off Miss Waldron's Red Colobus Monkey (Piliocolobus badius waldronae)? Biological Conservation 128:285–287.Google Scholar
Roberts, D. L., and Solow, A. R. 2003. Flightless birds: when did the dodo become extinct? Nature 426:245–246.Google Scholar
Schankler, D. M. 1980. Faunal zonation of the Willwood Formation in the central Bighorn Basin, Wyoming. University of Michigan Museum, Papers on Paleontology 24:99–114.Google Scholar
Signor, P. W. III, and Lipps, J. H. 1982. Sampling bias, gradual extinction patterns, and catastrophes in the fossil record. InSilver, Leon T. and Schultz, Peter H., eds. Geological implications of impacts of large asteroids and comets on the earth. Geological Society of America Special Publication 190:291–296.Google Scholar
Smith, F. D. M., May, R. M., Pellew, R., Johnson, T. H., and Walter, K. R. 1993. How much do we know about the current extinction rate? Trends in Ecology and Evolution 8:375–378.Google Scholar
Solow, A. R. 1993a. Inferring extinction from sighting data. Ecology 74:962–964.Google Scholar
Solow, A. R. 1993b. Inferring extinction in a declining population. Journal of Mathematical Biology 32:79–82.Google Scholar
Solow, A. R. 2005. Inferring extinction from a sighting record. Mathematical Biosciences 195:47–55.Google Scholar
Solow, A. R., and Roberts, D. L. 2003. A nonparametric test for extinction based on a sighting record. Ecology 84:1329–1332.Google Scholar
Stanley, S. M. 1985. Rates of evolution. Paleobiology 11:13–26.Google Scholar
Stork, N. 2010. Re-assessing current extinction rates. Biodiversity and Conservation 19:357–371.Google Scholar
Strauss, D., and Sadler, P. M. 1989. Classical confidence intervals and Bayesian probability estimates for ends of local taxon ranges. Mathematical Geology 21:411–427.Google Scholar
Stuart, S. N., Chanson, J. S., Cox, N. A., Young, B. E., Rodrigues, A. S. L., Fischman, D. L., and Waller, R. W. 2004. Status and trends of amphibian declines and extinctions worldwide. Science 306:1783–1786.Google Scholar
Szabo, J. K., Khwaja, N., Garnett, S. T., and Butchart, S. H. M. 2012. Global patterns and drivers of avian extinctions at the species and subspecies level. PLoS ONE 7:e47080.Google Scholar
Van Valen, L. 1973. A new evolutionary law. Evolutionary Theory 1:1–30.Google Scholar
Wang, S. C. 2010. Principles of statistical inference: likelihood and the Bayesian paradigm. Paleontological Society Papers 16:1–18.Google Scholar
Wang, S. C., and Everson, P. J. 2007. Confidence intervals for pulsed mass extinction events. Paleobiology 33:324–336.Google Scholar
Wang, S. C., Zimmerman, A. E., McVeigh, B. S., Everson, P. J., and Wong, H. 2012. Confidence intervals for the duration of a mass extinction. Paleobiology 38:265–277.Google Scholar
Weiss, R. E., and Marshall, C. R. 1999. The uncertainty in the true end point of a fossil's stratigraphic range when stratigraphic sections are sampled discretely. Mathematical Geology 31:435–453.Google Scholar
Weiss, R. E., Basu, S., and Marshall, C. R. 2003. A framework for analyzing fossil record data. Pp. 215–232inBuck, C. E. and Millard, A. R., eds. Tools for constructing chronologies: crossing disciplinary boundaries. Springer, London.Google Scholar