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Adaptive credible intervals on stratigraphic ranges when recovery potential is unknown

Published online by Cambridge University Press:  19 February 2016

Steve C. Wang ,
Philip J. Everson ,
Heather Jianan Zhou ,
Dasol Park  and
David J. Chudzicki
Steve C. Wang*
Affiliation:
Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081.
Philip J. Everson
Affiliation:
Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081.
Heather Jianan Zhou
Affiliation:
Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081.
Dasol Park
Affiliation:
Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081.
David J. Chudzicki
Affiliation:
Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081.
*
E-mail: [email protected].
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Abstract

Numerous methods exist for estimating the true stratigraphic range of a fossil taxon based on the stratigraphic positions of its fossil occurrences. Many of these methods require the assumption of uniform fossil recovery potential—that fossils are equally likely to be found at any point within the taxon's true range. This assumption is unrealistic, because factors such as stratigraphic architecture, sampling effort, and the taxon's abundance and geographic range affect recovery potential. Other methods do not make this assumption, but they instead require a priori quantitative knowledge of recovery potential that may be difficult to obtain. We present a new Bayesian method, the Adaptive Beta method, for estimating the true stratigraphic range of a taxon that works for both uniform and non-uniform recovery potential. In contrast to existing methods, we explicitly estimate recovery potential from the positions of the occurrences themselves, so that a priori knowledge of recovery potential is not required. Using simulated datasets, we compare the performance of our method with existing methods. We show that the Adaptive Beta method performs well in that it achieves or nearly achieves nominal coverage probabilities and provides reasonable point estimates of the true extinction in a variety of situations. We demonstrate the method using a dataset of the Cambrian mollusc Anabarella.

Type
Articles
Information
Paleobiology , Volume 42 , Issue 2 , May 2016 , pp. 240 - 256
Copyright
Copyright © 2016 The Paleontological Society. All rights reserved 

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References

Literature Cited

Akmentins, M. S., Pereyra, L. C., and Vaira, M.. 2012. Using sighting records to infer extinction in three endemic Argentinean marsupial frogs. Animal Conservation 15:142–151.Google Scholar
Alroy, J. 2014. A simple Bayesian method of inferring extinction. Paleobiology 40:584–607.Google Scholar
Berk, R., Brown, L., Buja, A., Zhang, K., and Zhao, L.. 2013. Valid post-selection inference. Annals of Statistics 41:802–837.Google Scholar
Brusatte, S. L., Butler, R. J., Barrett, P. M., Carrano, M. T., Evans, D. C., Lloyd, G. T., Mannion, P. D., Norell, M. A., Peppe, D. J., Upchurch, P., and Williamson, T. W.. 2015. The extinction of the dinosaurs. Biological Reviews 90:628–642.Google Scholar
Caley, P., and Barry, S. C.. 2014. Quantifying extinction probabilities from sighting records: inference and uncertainties. PLoS ONE 9:e95857. doi: 10.1371/journal.pone.0095857.Google Scholar
Clements, C. F., Worsfold, N. T., Warren, P. H., Collen, B., Clark, N., Blackburn, T. M., and Petchey, O. L.. 2013. Experimentally testing the accuracy of an extinction estimator: Solow’s optimal linear estimation model. Journal of Animal Ecology 82:345–354.Google Scholar
Clements, C. F., Collen, B., Blackburn, T. M., and Petchey, O. L.. 2014. Effects of recent environmental change on accuracy of inferences of extinction status. Conservation Biology 28:971–981.Google Scholar
Cohen, K.M., Finney, S.C., Gibbard, P. L., and Fan, J.-X.. 2013. The ICS International Chronostratigraphic Chart. Episodes 36:199–204.CrossRefGoogle 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
Cooke, P. 1980. Optimal linear estimation of bounds of random variables. Biometrika 67:257–258.Google Scholar
Foote, M. 2007. Symmetric waxing and waning of marine animal genera. Paleobiology 33:517–529.CrossRefGoogle Scholar
Gingerich, P. D., and Uhen, M. D.. 1998. Likelihood estimation of the time of origin of Cetacea and the time of divergence of Cetacea and Artiodactyla. Palaeontologia Electronica 1(2), 47 pp.Google Scholar
Holland, S. M. 1995. The stratigraphic distribution of fossils. Paleobiology 21:92–109.Google Scholar
Holland, S. M 2000. The quality of the fossil record: a sequence stratigraphic perspectivein D. H. Erwin and S. L. Wing, eds. Deep Time: Paleobiology’s Perspective. Paleobiology 26(Suppl. to No. 4) 148–168.Google Scholar
Holland, S. M 2003. Confidence limits on fossil ranges that account for facies changes. Paleobiology 29:468–479.Google Scholar
Holland, S. M., and Patzkowsky, M. E.. 2002. Stratigraphic variation in the timing of first and last occurrences. Palaios 17:134–146.Google Scholar
Holland, S. M., and Patzkowsky, M. E.. 2004. Ecosystem structure and stability: Middle Upper Ordovician of central Kentucky, USA. Palaios 19:316–331.Google Scholar
Holland, S. M., and Patzkowsky, M. E.. 2007. Gradient ecology of a biotic invasion: Biofacies of the type Cincinnatian series (Upper Ordovician), Cincinnati, Ohio region. USA. Palaios 22:392–407.Google Scholar
Holland, S. M., and Patzkowsky, M. E.. 2009. The stratigraphic distribution of fossils in a tropical carbonate succession: Ordovician Bighorn Dolomite, Wyoming, USA. Palaios 25:303–317.Google Scholar
Jaric, I., and Ebenhard, T.. 2010. A method for inferring extinction based on sighting records that change in frequency over time. Wildlife Biology 16:267–275.Google Scholar
Jin, Y. G., Wang, Y., Wang, W., Shang, Q. H., Cao, C. Q., and Erwin, D. H.. 2000. Pattern of marine mass extinction near the Permian-Triassic boundary in South China. Science 289:432–436.Google Scholar
Liow, L. H., and Stenseth, N. C.. 2007. The rise and fall of species: implications for macroevolutionary and macroecological studies. Proceedings of the Royal Society of London, Series B 274:2745–2752.Google Scholar
Liow, L. H., Skaug, H. J., Ergon, T. H., and Schweder, T.. 2010. Environmental volatility and the global occupancy trajectory of microfossils. Paleobiology 36:224–252.Google Scholar
Maloof, A.C., Porter, S. M., Moore, J. L., Dudas, F. O., Bowring, S. A., Higgins, J. A., Fike, D. A., and Eddy, M.. 2010. The earliest Cambrian record of animals and ocean geochemical change. Geological Society of America Bulletin 122:1731–1774.Google 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 1995. Distinguishing between sudden and gradual extinctions in the fossil record: Predicting the position of the Cretaceous-Tertiary iridium anomaly using the ammonite fossil record on Seymour Island, Antarctica. Geology 23:731–734.Google Scholar
Marshall, C. R 1997. Confidence intervals on stratigraphic ranges with nonrandom distributions of fossil horizons. Paleobiology 23:165–173.Google Scholar
Marshall, C. R., and Ward, P. D.. 1996. Sudden and gradual molluscan extinctions in the latest Cretaceous in western European Tethys. Science 274:1360–1363.Google Scholar
McCarthy, M. A. 1998. Identifying declining and threatened species with museum data. Biological Conservation 83:9–17.CrossRefGoogle 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
McPherson, J. M., and Myers, R. A.. 2009. How to infer population trends in sparse data: examples with opportunistic sighting records for great white sharks. Diversity and Distributions 15:880–890.Google Scholar
Patzkowsky, M.E., and Holland, S.M.. 2012. Stratigraphic Paleobiology: Understanding the Distribution of Fossil Taxa in Time and Space. The University of Chicago Press.Google Scholar
Paul, C. R. C. 1982. The adequacy of the fossil record. Pp. 75–117in K. A. Joysey and A. E. Friday, eds. Problems of phylogenetic reconstruction. Systematics Association Special Volume 21. Academic Press, London.Google Scholar
Pimiento, C., and Clements, C. F.. 2014. When did Carcharocles megalodon become extinct? A new analysis of the fossil record. PLoS ONE 10(1), e0117877. doi: 10.1371/journal.pone.0111086.Google Scholar
Rivadeneira, M. M., Hunt, G., and Roy, K.. 2009. The use of sighting records to infer species extinctions: 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
Robson, D. S., and Whitlock, J. H.. 1964. Estimation of a truncation point. Biometrika 51:33–39.Google Scholar
Scarponi, D., and Kowalewski, M.. 2004. Stratigraphic paleoecology: Bathymetric signatures and sequence overprint of mollusk associations from upper Quaternary sequences of the Po Plain, Italy. Geology 32:989–992.Google Scholar
Shaw, A. B. 1964. Time in stratigraphy. McGraw-Hill, New York.Google Scholar
Solow, A. R. 1993. Inferring extinction in a declining population. Journal of Mathematical Biology 32:79–82.Google Scholar
Solow, A. R 1996. Tests and confidence intervals for a common upper endpoint in fossil taxa. Paleobiology 22:406–410.Google Scholar
Solow, A. R 2003. Estimation of stratigraphic ranges when fossil finds are not randomly distributed. Paleobiology 29:181–185.Google Scholar
Solow, A. R 2005. Inferring extinction from a sighting record. Mathematical Biosciences 195:47–55.Google Scholar
Solow, A. R., and Smith, W. K.. 2000. Testing for a mass extinction without selecting taxa. Paleobiology 26:647–650.Google Scholar
Solow, A. R., and Roberts, D. L.. 2003. A nonparametric test for extinction based on a sighting record. Ecology 84:1329–1332.CrossRefGoogle Scholar
Solow, A. R., Roberts, D. L., and Robbirt, K. M.. 2006. On the Pleistocene extinctions of Alaskan mammoths and horses. Proceedings of the National Academy of Sciences USA 103:7351–7353.CrossRefGoogle ScholarPubMed
Song, H., Wignall, P. B., Tong, J., and Yin, H.. 2013. Two pulses of extinction during the Permian-Triassic crisis. Nature Geoscience 6:52–56.Google Scholar
Springer, M. S. 1990. The effect of random range truncations on patterns of evolution in the fossil record. Paleobiology 16:512–520.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
Thompson, C. J., Lee, T. E., Stone, L., McCarthy, M. A., and Burgman, M. A.. 2013. Inferring extinction risks from sighting records. Journal of Theoretical Biology 338:16–22.Google Scholar
Vogel, R. M., Hosking, J. R. M., Elphick, C. S., Roberts, D. L., and Reed, J. M.. 2009. Goodness of fit of probability distributions for sightings as species approach extinction. Bulletin of Mathematical Biology 71:701–719.CrossRefGoogle ScholarPubMed
Wang, S. C. 2010. Principles of statistical inference: Likelihood and the Bayesian paradigmin Quantitative Methods in Paleobiology. J. Alroy and G. Hunt, eds. Paleontological Society Papers 16. 1–18.Google Scholar
Wang, S. C., and Dodson, P.. 2006. Estimating the diversity of dinosaurs. Proceedings of the National Academy of Sciences USA 103:13601–13605.Google Scholar
Wang, S. C., and Everson, P. J.. 2007. Confidence intervals for pulsed mass extinction events. Paleobiology 33:324–336.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