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Estimating the number of pulses in a mass extinction

  • Steve C. Wang (a1) and Ling Zhong (a1)

The Signor-Lipps effect states that even a sudden mass extinction will invariably appear gradual in the fossil record, due to incomplete fossil preservation. Most previous work on the Signor–Lipps effect has focused on testing whether taxa in a mass extinction went extinct simultaneously or gradually. However, many authors have proposed scenarios in which taxa went extinct in distinct pulses. Little methodology has been developed for quantifying characteristics of such pulsed extinction events. Here we introduce a method for estimating the number of pulses in a mass extinction, based on the positions of fossil occurrences in a stratigraphic section. Rather than using a hypothesis test and assuming simultaneous extinction as the default, we reframe the question by asking what number of pulses best explains the observed fossil record.

Using a two-step algorithm, we are able to estimate not just the number of extinction pulses but also a confidence level or posterior probability for each possible number of pulses. In the first step, we find the maximum likelihood estimate for each possible number of pulses. In the second step, we calculate the Akaike information criterion and Bayesian information criterion weights for each possible number of pulses, and then apply a k-nearest neighbor classifier to these weights. This method gives us a vector of confidence levels for the number of extinction pulses—for instance, we might be 80% confident that there was a single extinction pulse, 15% confident that there were two pulses, and 5% confident that there were three pulses. Equivalently, we can state that we are 95% confident that the number of extinction pulses is one or two. Using simulation studies, we show that the method performs well in a variety of situations, although it has difficulty in the case of decreasing fossil recovery potential, and it is most effective for small numbers of pulses unless the sample size is large. We demonstrate the method using a data set of Late Cretaceous ammonites.

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Akaike H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19:716723.
Algeo T., Henderson C. M., Ellwood B., Rowe H., Elswick E., Bates S., Lyons T., Hower J. C., Smith C., Maynard B., Hays L. E., Summons R. E., Fulton J., and Freeman K. H.. 2012. Evidence for a diachronous Late Permian marine crisis from the Canadian Arctic region. Geological Society of America Bulletin 124:14241448.
Amati L., and Westrop S. R.. 2006. Sedimentary facies and trilobite biofacies along an Ordovician shelf to basin gradient, Viola Group, south-central Oklahoma. Palaios 21:516529.
Anderson D. R., Burnham K. P., and Thompson W. L.. 2000. Null hypothesis testing: problems, prevalence, and an alternative. Journal of Wildlife Management 64:912923.
Angiolini L., Checconi A., Gaetani M., and Rettori R.. 2010. The latest Permian mass extinction in the Alborz Mountains (North Iran). Geological Journal 45:216229.
Baarli B. G. 2014. The early Rhuddanian survival interval in the Lower Silurian of the Oslo Region: a third pulse of the end-Ordovician extinction. Palaeogeography, Palaeoclimatology, Palaeoecology 395:2941.
Brenchley P. J., Carden G. A., Hints L., Kaljo D., Marshall J. D., Martma T., Meidla T., and Nolvak J.. 2003. High-resolution stable isotope stratigraphy of Upper Ordovician sequences: constraints on the timing of bioevents and environmental changes associated with mass extinction and glaciation. Geological Society of America Bulletin 115:89104.
Breiman L., Friedman J. H., Olshen R. A., and Stone C. J.. 1984. Classification and regression trees. Chapman and Hall/CRC, Boca Raton, Fla.
Casella G., and Berger R. L.. 2002. Statistical inference, 2nd ed. Duxbury, Pacific Grove, Calif.
Darroch S. A. F., and Wagner P. J.. 2015. Response of beta diversity to pulses of Ordovician–Silurian mass extinction. Ecology 96:532549.
Garbelli C., Angiolini L., Brand U., Shen S.-Z., Jadoul F., Posenato R., Azmy K., and Cao C.-Q.. 2015. Neotethys seawater chemistry and temperature at the dawn of the end Permian mass extinction. Gondwana Research 35:272285.
Graham R. L., Knuth D. E., and Patashnik O.. 1994. Concrete mathematics: a foundation for computer science, 2nd ed. Addison-Wesley, Reading, Mass.
Groves J. R., Rettori R., Payne J. L., Boyce M. D., and Altiner D.. 2007. End-Permian mass extinction of Lagenide foraminifers in the southern Alps (northern Italy). Journal of Paleontology 81:415434.
Hastie T., Tibshirani R., and Friedman J.. 2009. The elements of statistical learning, 2nd ed. Springer, New York.
He W.-H., Shi G. R., Twitchett R. J., Zhang Y., Zhang K.-X., Song H.-J., Yue M.-L., Wu S.-B., Wu H.-T., Yang T.-L., and Xiao Y.-F.. 2015. Late Permian marine ecosystem collapse began in deeper waters: evidence from brachiopod diversity and body size changes. Geobiology 13:123138.
Holland S. M. 1995. The stratigraphic distribution of fossils. Paleobiology 21:92109.
Holland S. M. 2000. The quality of the fossil record: a sequence stratigraphic perspective. Pp. 148–168 in D. H. Erwin, and S. L. Wing, eds. Deep time: paleobiology’s perspective. Paleontological Society, Lawrence, Kans.
Holland S. M. 2003. Confidence limits on fossil ranges that account for facies changes. Paleobiology 29:468479.
Holland S. M., and Patzkowsky M. E.. 2002. Stratigraphic variation in the timing of first and last occurrences. Palaios 17:134146.
Holland S. M., and Patzkowsky M. E.. 2004. Ecosystem structure and stability: Middle Upper Ordovician of central Kentucky. USA. Palaios 19:316331.
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 22:392407.
Holland S. M., and Patzkowsky M. E.. 2009. The stratigraphic distribution of fossils in a tropical carbonate succession: Ordovician Bighorn Dolomite, Wyoming, USA. Palaios 25:303317.
Holland S. M., and Patzkowsky M. E.. 2015. The stratigraphy of mass extinction. Palaeontology 58:903924.
Horton B. P., Edwards R. J., and Lloyd J. M.. 1999. UK intertidal foraminiferal distributions: implications for sea-level studies. Marine Micropaleontology 36:205223.
Hunt G. 2006. Fitting and comparing models of phyletic evolution: random walks and beyond. Paleobiology 32:578601.
Isozaki Y. 2002. End-Permian double-phased mass extinction and killer volcanism. Geological Society of America Abstracts with Programs 34:360.
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 289:432436.
Keller G., Stinnesbeck W., Adatte T., and Stüben D.. 2003. Multiple impacts across the Cretaceous–Tertiary boundary. Earth-Science Reviews 62:327363.
Keller G., Adatte T., Bhowmick P. K, Upadhyay H., Dave A., Reddy A. N., and Jaiprakash B. C.. 2012. Nature and timing of extinctions in Cretaceous–Tertiary planktic foraminifera preserved in Deccan intertrappean sediments of the Krishna–Godavari Basin, India. Earth and Planetary Science Letters 341–344:211221.
Knoll A. H., Bambach R. K., Canfield D. E., and Grotzinger J. P.. 1996. Comparative Earth history and late Permian mass extinction. Science 273:452457.
Konar B., Iken K., and Edwards M.. 2008. Depth-stratified community zonation patterns on Gulf of Alaska rocky shores. Marine Ecology 30:6373.
Lindström S., and McLoughlin S.. 2007. Synchronous palynofloristic extinction and recovery after the end-Permian event in the Prince Charles Mountains, Antarctica: implications for palynofloristic turnover across Gondwana. Review of Palaeobotany and Palynology 145:89122.
Macellari C. E. 1986. Late Campanian–Maastrichtian ammonite fauna from Seymour Island (Antarctic Peninsula). Paleontological Society Memoir 18. Journal of Paleontology 60(Suppl. to No. 2), 155.
Marshall C. R. 1990. Confidence intervals on stratigraphic ranges. Paleobiology 16:110.
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 23:731734.
Marshall C. R. 1995b. Stratigraphy, the true order of species originations and extinctions, and testing ancestor-descendent hypotheses among Caribbean Neogene bryozoans. Pp. 208235 in D. H. Erwin, and R. L. Anstey, eds. New approaches to speciation in the fossil record. Columbia University Press, New York.
Marshall C. R., and Ward P. D.. 1996. Sudden and gradual molluscan extinctions in the latest Cretaceous in western European Tethys. Science 274:13601363.
McGhee G. R. Jr. 2001. The “multiple impacts hypothesis” for mass extinction: a comparison of the Late Devonian and the late Eocene. Palaeogeography, Palaeoclimatology, Palaeoecology 176:4758.
Olabarria C. 2006. Faunal change and bathymetric diversity gradient in deep-sea prosobranchs from northeastern Atlantic. Biodiversity and Conservation 15:36853702.
Patzkowsky M. E., and Holland S. M.. 2012. Stratigraphic paleobiology: understanding the distribution of fossil taxa in time and space. University of Chicago Press, Chicago.
Paul C. R. C., Lamolda M. A., Mitchell S. F., Vaziri M. R., Gorostidi A., and Marshall J. D.. 1999. The Cenomanian–Turonian boundary at Eastbourne (Sussex, UK): a proposed European reference section. Palaeogeography, Palaeoclimatology, Palaeoecology 150:83121.
Payne J. L. 2003. Applicability and resolving power of statistical tests for instantaneous extinction events in the fossil record. Paleobiology 29:3751.
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 26:415418.
R Core Team. 2013. R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
Rivadeneira M. M., Hunt G., and Roy K.. 2009. The use of sighting records to infer species extinctions: an evaluation of different methods. Ecology 90:12911300.
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 32:989992.
Schwarz G. E. 1978. Estimating the dimension of a model. Annals of Statistics 6:461464.
Signor P. W., and Lipps J. H.. 1982. Sampling bias, gradual extinction patterns, and catastrophes in the fossil record. In L. T. Silver and P. H. Schultz, eds. Geological implications of large asteroids and comets on the Earth. Geological Society of America Special Paper 190:291–296.
Smale D. A. 2008. Continuous benthic community change along a depth gradient in Antarctic shallows: evidence of patchiness but not zonation. Polar Biology 31:189198.
Solow A. R. 1996. Tests and confidence intervals for a common upper endpoint in fossil taxa. Paleobiology 22:406410.
Solow A. R. 2003. Estimation of stratigraphic ranges when fossil finds are not randomly distributed. Paleobiology 29:181185.
Solow A. R., and Smith W. K.. 2000. Testing for a mass extinction without selecting taxa. Paleobiology 26:647650.
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 103:73517353.
Song H., Tong J., and Chen Z. Q.. 2009. Two episodes of foraminiferal extinction near the Permian–Triassic boundary at the Meishan section, South China. Australian Journal of Earth Sciences 56:765773.
Song H. J., Wignall P. B., Tong J. N., and Yin H. F.. 2013. Two pulses of extinction during the Permian–Triassic crisis. Nature Geoscience 6:5256.
Springer M. S. 1990. The effect of random range truncations on patterns of evolution in the fossil record. Paleobiology 16:512520.
Stanley S. M., and Yang X.. 1994. A double mass extinction at the end of the Paleozoic Era. Science 266:13401344.
Strauss D., and Sadler P. M.. 1989. Classical confidence intervals and Bayesian probability estimates for ends of local taxon ranges. Mathematical Geology 21:411427.
Tobin T. S., Ward P. D., Steig E. J., Olivero E. B., Hilburn I. A., Mitchell R. N., Diamond M. R., Raub T. D., and Kirschvink J. L.. 2012. Extinction patterns, δ18O trends, and magnetostratigraphy from a southern high-latitude Cretaceous–Paleogene section: links with Deccan volcanism. Palaeogeography, Palaeoclimatology, Palaeoecology 350–352:180188.
Varian H. R. 2006. Intermediate microeconomics: a modern approach, 7th ed. Norton, New York.
Wagner P. J. 2000. Likelihood tests of hypothesized durations: determining and accommodating biasing factors. Paleobiology 26:431449.
Wang S. C., and Everson P. J.. 2007. Confidence intervals for pulsed mass extinction events. Paleobiology 33:324336.
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.
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 38:265277.
Wang S. C., Wang C., Gai L., Moore J. L., Porter S. M., and Maloof A. C.. 2014. Estimating the duration and tempo of the Cambrian explosion. Geological Society of America Abstracts with Programs 46:367.
Wang S. C., Everson P. J., Zhou H. J., Park D., and Chudzicki D. J.. 2016. Adaptive credible intervals on stratigraphic ranges when recovery potential is unknown. Paleobiology 42:240256.
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 307:709713.
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 31:435453.
Xie S., Pancost R. D., Yin H., Wang H., and Evershed R. P.. 2005. Two episodes of microbial change coupled with Permo/Triassic faunal mass extinction. Nature 434:494497.
Yin H. F., Feng Q. L., Lai X. L., Baud A., and Tong J. N.. 2007. The protracted Permo-Triassic crisis and multi-episode extinction around the Permian–Triassic boundary. Global and Planetary Change 55:120.
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