Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-23T18:10:53.033Z Has data issue: false hasContentIssue false
  • English
  • Français

Confidence intervals on stratigraphic ranges: partial relaxation of the assumption of randomly distributed fossil horizons

Published online by Cambridge University Press:  08 February 2016

Charles R. Marshall
Charles R. Marshall*
Affiliation:
Department of Earth and Space Sciences, University of California, Los Angeles, California 90024-1567
Get access Rights & Permissions [Opens in a new window]

Abstract

The equations for calculating classical confidence intervals on the end points of stratigraphic ranges are based on the restrictive assumption of randomly distributed fossil finds. Herein, a method is presented for calculating confidence intervals on the end-points of stratigraphic ranges that partially relaxes this assumption: the method will work for any continuous distribution of gap sizes, not just those generated by random processes. The price paid for the generality of the new approach is twofold: (1) there are uncertainties associated with the sizes of the confidence intervals, and (2) for large confidence values (e.g., 95%) a rich fossil record is required to place upper bounds on the corresponding confidence intervals. This new method is not universal; like the method for calculating classical confidence intervals it is based on the assumption that there is no correlation between gap size and stratigraphic position. The fossil record of the Neogene Caribbean bryozoan Metrarabdotos is analyzed with the new approach. The equations developed here, like those for classical confidence intervals, should not be applied to stratigraphic ranges based on discrete sampling regimes, such as those typically established from deep-sea drilling cores, though there are exceptions to this rule.

Type
Research Article
Information
Paleobiology , Volume 20 , Issue 4 , Fall 1994 , pp. 459 - 469
Copyright
Copyright © The Paleontological Society 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Literature Cited

Cheetham, A. H. 1986. Tempo of evolution in a Neogene bryozoan: rates of morphologic change within and across species boundaries. Paleobiology 2:190–202.CrossRefGoogle Scholar
Hogg, T. V., and Tanis, E. A. 1977. Probability and statistical inference. Macmillan, New York.Google Scholar
Kreyszig, E. 1979. Advanced engineering mathematics. Wiley & Sons, New York.Google Scholar
Marshall, C. R. 1990a. Confidence intervals on stratigraphic ranges. Paleobiology 16:1–10.CrossRefGoogle Scholar
Marshall, C. R. 1990b. The fossil record and estimating divergence times between lineages: maximum divergence times and the importance of reliable phylogenies. Journal of Molecular Evolution 30:400–408.CrossRefGoogle ScholarPubMed
Marshall, C. R.In press. Stratigraphy, the true order of species' originations and extinctions, and testing ancestor-descendent hypotheses among Caribbean Neogene bryozoans. In Erwin, D. H. and Anstey, R., eds. Speciation and the fossil record. Columbia University Press, New York.Google Scholar
McKinney, M. L. 1986. Biostratigraphic gap analysis. Journal of Geology 14:36–38.2.0.CO;2>CrossRefGoogle Scholar
Paul, C. R. C. 1982. The adequacy of the fossil record. Pp. 75–117in Joysey, K. A. and Friday, A. E., eds. Problems of phylogenetic reconstruction. Systematics Association Special Volume 21. Academic Press, London.Google Scholar
Springer, M. S. 1990. The effect of random range truncations on patterns of evolution in the fossil record. Paleobiology 16:512–520.CrossRefGoogle Scholar
Springer, M. S., and Lilje, A. 1988. Biostratigraphy and gap analysis: the expected sequence of biostratigraphic events. Journal of Geology 96:228–236.CrossRefGoogle 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
Wise, K. P. 1991. The use of fossil occurrence data to distinguish between instantaneous and stepwise extinction. Geological Society of America, Abstracts with Programs 23:A184.Google Scholar