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Using Confidence Intervals to Quantify the Uncertainty in the End-Points of Stratigraphic Ranges

Published online by Cambridge University Press:  21 July 2017

Charles R. Marshall
Charles R. Marshall*
Affiliation:
University of California Museum of Paleontology, Department of Integrative Biology University of California, Berkeley, 1101 Valley Life Sciences Building #4780 Berkeley, CA 94720-4780
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Abstract

One of the many contributions paleontology makes to our understanding of the biosphere and its evolution is a direct temporal record of biotic events. However, assuming fossils have been correctly identified and accurately dated, stratigraphic ranges underestimate true temporal ranges: observed first occurrences are too young, and observed last occurrences are too old. Here I introduce the techniques developed for placing confidence intervals on the end-points of stratigraphic ranges. I begin with the analysis of single taxa in local sections – with the simplest of assumptions – random fossilization. This is followed by a discussion of the methods developed to handle the fact that the recovery of fossils is often non-random in space and time. After discussion of how confidence intervals can be used to test for simultaneous origination and extinctions, I conclude with an example application of confidence intervals to unravel the relative importance of background extinction, environmental change and mass extinction of ammonite species at the end of the Cretaceous in western Tethys.

Type
Stratigraphic Data
Information
The Paleontological Society Papers , Volume 16: Quantitative Methods in Paleobiology , October 2010 , pp. 291 - 316
Copyright
Copyright © 2010 by the Paleontological Society 

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References

Alroy, J. 2008. Dynamics of origination and extinction in the marine fossil record. Proceedings National Academy of Sciences, USA, 105(suppl. 1):11536–11542.Google Scholar
Alvarez, L. W. 1984. Experimental evidence that an asteroid impact led to the extinction of many species 65 million years ago. Proceedings National Academy of Sciences, USA, 80:627–642.Google Scholar
Bleiweiss, R. 1998. Fossil gap analysis supports early Tertiary origin of trophically diverse avian orders. Geology, 26:323–326.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
Bergman, M. A., Grimson, R. C., and Ferson, S. 1995. Inferring threat from scientific collections. Conservation Biology, 9:923–928.CrossRefGoogle Scholar
Cheetham, A. H. 1986. Tempo of evolution in a Neogene bryozoan: rates of morphologic change within and across species boundaries. Paleobiology, 2:190–202.Google Scholar
Foote, M. 2007. Symmetric waxing and waning of marine animal genera. Paleobiology, 333:517–529.Google Scholar
Foote, M. and Miller, A. I. 2006. Principles of Paleontology. 3rd Ed. W. H. Freeman and Company, New York, New York, 354.Google Scholar
Foote, M., Hunter, J. P., Jams, C. M., and Sepkoski, J. J. 1999. Evolutionary and preservational constraints on origins of biologic groups: Divergence times of eutherian mammals. Science, 283:1310–1314.Google Scholar
Foote, M., Crampton, J. S., Beu, A. G., Marshall, B. A., Cooper, R. A., Maxwell, P. A., and Matcham, I. 2007. Rise and fall of species occupancy in Cenozoic fossil molluscs. Science, 318:1131–1134.CrossRefGoogle Scholar
Foote, M., Crampton, J. S., Beu, A. G., and Cooper, R. A. 2008. On the bidirectional relationship between geographic range and taxonomic duration. Paleobiology, 34:421–433.Google Scholar
Gingerich, P. D., and Uhen, M. D. 1994. Time of origin of primates. Journal of Human Evolution, 27:443–445.Google 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), 45 p.Google Scholar
Hayek, L. C., and Bura, E. 2001. On the ends of the taxon range problem, p. 221–244. In Jackson, J. B. C., Lidgard, S., and McKinney, F. K. (eds.), Evolutionary Patterns: Growth, Form, and Tempo in the Fossil Record. University of Chicago Press, Chicago.Google Scholar
Holland, S. M. 2003. Confidence limits on fossil ranges that account for fades changes. Paleobiology, 29:468–479.Google Scholar
Holland, S. M., and Patzkowsky, M. E. 1999. Models for simulating the fossil record. Geology, 27:491–494.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
Jaanusson, V. 1976. Faunal dynamics in the Middle Ordovician (Viruan) of Balto-Scandia, p. 301–326. In Bassett, M.G. (ed.), The Ordovician System: Proceedings of a Paleontological Association Symposium, Birmingham. University of Wales Press and National Museum of Wales, Cardiff.Google Scholar
Labandiera, C. C., Johnson, K. R., and Wilf, P. 2002. Impact of the terminal Cretaceous event on plant–insect associations. Proceedings National Academy Sciences, USA, 99:2061–2066.Google Scholar
Liow, L. H., and Stenseth, N. C. 2007. The rise and fall of species: implications for macroevolutionary and macroecological studies. Proceedings Royal Society of London B, 274:2745–2752.Google Scholar
Liow, L. H., Skaug, H. J., Ergon, T., and Schweder, T. 2010. Global occurrence trajectories of microfossils: environmental volatility and the rise and fall of individual species. Paleobiology, 36:224–252.Google Scholar
Macellari, C. E. 1986. Late Campanian-Maastrichtian ammonite fauna from Seymour Island (Antarctic Peninsula), Journal of Paleontology, 60 (supplement), 55 p.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.CrossRefGoogle Scholar
Marshall, C. R. 1995a. Stratigraphy, the true order of species originations and extinctions, and testing ancestor-descendent hypotheses among Caribbean Neogene bryozoans, p. 208–235. In Erwin, 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. 1995b. 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, 23:731–734.2.3.CO;2>CrossRefGoogle Scholar
Marshall, C. R. 1997. Confidence intervals on stratigraphic ranges with non-random distributions of fossil horizons. Paleobiology, 23:165–173.Google Scholar
Marshall, C. R. 1998. Determining stratigraphic ranges, p. 23–53. In Donovan, S. K. and Paul, C. R. C. (eds.), The Adequacy of the Fossil Record. John Wiley and Sons, London.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. 2005. Comment on “Abrupt and gradual extinction among Late Permian land vertebrates in the Karoo Basin, South Africa”. Science, 308:1413b.CrossRefGoogle Scholar
Marshall, C.R. 2008. A simple method for bracketing absolute divergence times on molecular phylogenies using multiple fossil calibration points. The American Naturalist, 171:726–742.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.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.CrossRefGoogle ScholarPubMed
Paul, C. R. C. 1982. The adequacy of the fossil record, p. 75–117. In Joysey, K. A. and Friday, A. E. (eds.), Problems of Phylogenetic Reconstruction. Systematic Association Special Volume 21, Academic Press, London.Google Scholar
Payne, J. L. 2003. Applicability and resolving power of statistical tests for simultaneous extinction events in the fossil record. Paleobiology, 29:37–51.Google Scholar
Quental, T. B., and Marshall, C. R. 2010. Diversity dynamics: molecular phylogenies need the fossil record. Trends in Ecology and Evolution, (in press).Google Scholar
Raup, D. M. 1991. Extinction: Bad Genes or Bad Luck? W. W. Norton and Company, New York, New York, 210 p.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. 2006. Extinct or possibly extinct? Science, 312:997–998.Google Scholar
Roberts, D. L., and Solow, A. R. 2003. Flightless birds: When did the dodo become extinct? Nature, 426:245.Google Scholar
Saunders, J. B., Jung, P., and Biju-Duval, B. 1986. Neogene paleontology in the northern Dominican Republic. 1. Field surveys, lithology, environment, and age. Bulletins of American Paleontology, 89(323):1–79.Google Scholar
Shaw, A. B. 1964. Time in Stratigraphy. McGraw Hill, New York, New York, 365 p.Google Scholar
Signor, P. W., and Lipps, J. H. 1982. Sampling bias, gradual extinction patterns, and catastrophes in the fossil record, p. 291–296. In Silver, L. T. and Schultz, P. H. (eds.), Geological Implications of Large Asteroids and Comets on the Earth. Geological Society of America Special Paper, 190.Google Scholar
Soligo, C., Will, O., Tavaré, S., Marshall, C. R., and Martin, R. D. 2007. New light on the dates of primate origins and divergence. p. 29–49. In Ravosa, M. J. and Dagosto, M. (eds.), Primate Origins: Adaptations and Evolution, Springer-Verlag, New York.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. 1996. A test for a common upper endpoint in fossil taxa. Paleobiology, 22:406–410.Google Scholar
Solow, A. R. 2005. Inferring extinction from a sighting record. Mathematical Biosciences, 195:47–55.Google Scholar
Solow, A. R., Kitchener, A. C., Roberts, D. L., and Birks, J. D. S. 2006a. Rediscovery of the Scottish polecat, Mustela putorius: Survival or reintroduction? Biological Conservation, 128:574–575.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
Solow, A. R., Roberts, D. L., and Robbirt, K. M. 2006. On the Pleistocene extinctions of Alaskan mammoths and horses. Proceedings National Academy of Sciences, USA, 103:7351–7353.Google Scholar
Solow, A. R., and Smith, W. K. 2000. Testing for a mass extinction without selecting taxa. Paleobiology, 26:647–650.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
Tavaré, S., Marshall, C. R., Will, O., Soligo, C., and Martin, R. D. 2002. Using the fossil record to estimate the age of the last common ancestor of extant primates. Nature, 416:726–729.Google Scholar
Thomas, R. C. 1993. The Marjumiid-Pterocephaliid (Upper Cambrian) Mass Extinction Event in the Western United States. Unpublished Ph.D. dissertation, University of Washington, 352 p.Google Scholar
Thomas, R. C. 1995. Cambrian mass extinction “Biomere” boundaries: a summary of thirty years of research. Northwest Geology, 24:67–75.Google Scholar
Wang, S. C., and Marshall, C. R. 2004. Improved confidence intervals for estimating the position of a mass extinction boundary. Paleobiology, 30:5–18.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., and Kennedy, W. J. 1993. Maastrichtian Ammonites from the Biscay Region (France, Spain). Paleontological Society Memoir Number 34, 58 p.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, 307:709–714.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. p. 215–232. In: Buck, C. E. and Millard, A. R. (eds.), Tools for Constructing Chronologies: Crossing Disciplinary Boundaries. Springer-Verlag, London.Google Scholar
Wolfram Research, Inc. 2002. Mathematica, Version 4.2. Champaign, Illinois.Google Scholar