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Confidence intervals for the duration of a mass extinction

Published online by Cambridge University Press:  08 April 2016

Steve C. Wang ,
Aaron E. Zimmerman ,
Brendan S. McVeigh ,
Philip J. Everson  and
Heidi Wong
Steve C. Wang
Affiliation:
Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081, U.S.A. E-mail: [email protected]
Aaron E. Zimmerman
Affiliation:
Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081, U.S.A. E-mail: [email protected]
Brendan S. McVeigh
Affiliation:
Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081, U.S.A. E-mail: [email protected]
Philip J. Everson
Affiliation:
Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081, U.S.A. E-mail: [email protected]
Heidi Wong
Affiliation:
Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081, U.S.A. E-mail: [email protected]
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Abstract

A key question in studies of mass extinctions is whether the extinction was a sudden or gradual event. This question may be addressed by examining the locations of fossil occurrences in a stratigraphic section. However, the fossil record can be consistent with both sudden and gradual extinctions. Rather than being limited to rejecting or not rejecting a particular scenario, ideally we should estimate the range of extinction scenarios that is consistent with the fossil record. In other words, rather than testing the simplified distinction of “sudden versus gradual,” we should be asking, “How gradual?”

In this paper we answer the question “How gradual could the extinction have been?” by developing a confidence interval for the duration of a mass extinction. We define the duration of the extinction as the time or stratigraphic thickness between the first and last taxon to go extinct, which we denote by Δ. For example, we would like to be able to say with 90% confidence that the extinction took place over a duration of 0.3 to 1.1 million years, or 24 to 57 meters of stratigraphic thickness. Our method does not deny the possibility of a truly simultaneous extinction; rather, in this framework, a simultaneous extinction is one whose value of Δ is equal to zero years or meters.

We present an algorithm to derive such estimates and show that it produces valid confidence intervals. We illustrate its use with data from Late Permian ostracodes from Meishan, China, and Late Cretaceous ammonites from Seymour Island, Antarctica.

Type
Articles
Information
Paleobiology , Volume 38 , Issue 2 , Spring 2012 , pp. 265 - 277
Copyright
Copyright © The Paleontological Society 

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References

Literature Cited

Alvarez, L. W., Alvarez, W., Asaro, F., and Michel, H. V. 1980. Extraterrestrial cause for the Cretaceous-Tertiary extinction. Science 208:1095–1108.Google Scholar
De Veaux, R. D., Velleman, P. F., and Bock, D. E. 2012. Stats: data and models, 3rd ed. Addison-Wesley, Boston.Google Scholar
Groves, J. R., Altiner, D., and Rettori, R. 2005. Extinction, survival and recovery of lagenide foraminifers in the Permian-Triassic boundary interval, central Taurides, Turkey. Paleontological Society Memoir 62. Journal of Paleontology 79(Suppl.):1–38.Google Scholar
Holland, S. M. 2003. Confidence limits on fossil ranges that account for facies changes. Paleobiology 29:468–479.Google Scholar
Jablonski, D. 2002. Survival without recovery after mass extinctions. Proceedings of the National Academy of Sciences USA 99:8139–8144.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
Macellari, C. E. 1986. Late Campanian-Maastrichtian ammonite fauna from Seymour Island (Antarctic Peninsula). Journal of Paleontology 60(Suppl.).Google Scholar
Marshall, C. R. 1990. Confidence intervals on stratigraphic ranges. Paleobiology 16:1–10.Google Scholar
Marshall, C. R. 1995a. 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. 1995b. Stratigraphy, the true order of species originations and extinctions, and testing ancestor-descendent hypotheses among Caribbean Neogene bryozoans. Pp. 208–235inErwin, D. H.and Anstey, R. L., eds. New approaches to speciation in the fossil record. Columbia University Press, New York.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
Meldahl, K. H. 1990. Sampling, species abundance, and the stratigraphic signature of mass extinction: a test using Holocene tidal flat molluscs. Geology 18:890–893.Google Scholar
Moore, D. S., McCabe, G. P., and Craig, B. 2012. Introduction to the practice of statistics, seventh edition. W. H. Freeman, New York.Google Scholar
Payne, J. L. 2003. Applicability and resolving power of statistical tests for instantaneous extinction events in the fossil record. Paleobiology 29:37–51.Google Scholar
Rampino, M. R., and Adler, A. C. 1998. Evidence for abrupt latest Permian mass extinction of foraminifera: results of tests for the Signor-Lipps effect. Geology 26:415–418.Google Scholar
Roberts, D. L., and Solow, A. R. 2003. Flightless birds: When did the dodo become extinct? Nature 426:245.Google Scholar
Roopnarine, P. D. 2006. Extinction cascades and catastrophe in ancient food webs. Paleobiology 32:1–19.Google Scholar
Roopnarine, P. D., Angielczyk, K. D., Wang, S. C., and Hertog, R. 2007. Trophic network models explain instability of Early Triassic terrestrial communities. Proceedings of the Royal Society of London B 274:1622, 2077–2086.Google Scholar
Signor, P. W., and Lipps, J. H. 1982. Sampling bias, gradual extinction patterns, and catastrophes in the fossil record. InSilver, L. T.and Schultz, P. H., eds. Geological implications of large asteroids and comets on the Earth. Geological Society of America Special Paper 190:291–296.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., and Smith, W. K. 2000. Testing for a mass extinction without selecting taxa. Paleobiology 26:647–650.Google 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.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.CrossRefGoogle Scholar
Wang, S. C. 2001. Optimal methods for estimating the stratigraphic position of a mass extinction boundary. Geological Society of America Abstracts with Programs 33:A–142.Google Scholar
Wang, S. C. 2003. On the continuity of background and mass extinctions. Paleobiology 29:455–467.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., Everson, P. J., Chudzicki, D. J., and Park, D. 2008. Confidence Intervals on stratigraphic ranges when recovery potential is unknown. Geological Society of America Abstracts with Programs 40:222.Google Scholar
Wang, S. C., Chudzicki, D. J., and Everson, P. J. 2009. Optimal estimators of the position of a mass extinction when recovery potential is uniform. Paleobiology 35:447–459.Google Scholar
Ward, P. D., Botha, J., Buick, R., de Kock, M. O., Erwin, D. H., Garrison, G. H., Kirschvink, J. L., and Smith, R. 2005. Abrupt and gradual extinction among Late Permian land vertebrates in the Karoo Basin, South Africa. Science 307:709–713.Google Scholar