Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-27T14:04:28.731Z Has data issue: false hasContentIssue false

Estimation of stratigraphic ranges when fossil finds are not randomly distributed

Published online by Cambridge University Press:  08 April 2016

Andrew R. Solow*
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543. E-mail: [email protected]

Abstract

Existing methods for point and interval estimation of the endpoints of the stratigraphic range of a fossil taxon under continuous sampling assume that the mean density of finds is constant over the stratigraphic range. These methods can perform badly when this mean density is not constant. Most seriously, if mean density declines toward the endpoint of interest, then the true coverage of the confidence interval for the true endpoint can be far below its nominal level, giving a false impression of estimation precision. Simple point and interval estimates that are designed to avoid this problem are presented. These methods are illustrated with the fossil record of two species of the Caribbean bryozoan Metrarabdotos.

Type
Articles
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

Cox, D. R., and Lewis, P. A. W. 1978. The statistical analysis of series of events. Chapman and Hall, London.Google Scholar
Hall, P., and Wang, J. Z. 1999. Estimating the end-point of a probability distribution using minimum-distance methods. Bernoulli 5:177189.Google Scholar
Marshall, C. R. 1990. Confidence intervals on stratigraphic ranges. Paleobiology 16:110.Google Scholar
Marshall, C. R. 1994. Confidence intervals on stratigraphic ranges: partial relaxation of the assumption of randomly distributed fossil horizons. Paleobiology 20:459469.Google Scholar
Marshall, C. R. 1995. Stratigraphy, the true order of species originations and extinctions, and testing ancestor-descendent hypotheses among Caribbean Neogene bryozoans. Pp. 208235in 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. 1997. Confidence intervals on stratigraphic ranges with nonrandom distributions of fossil horizons. Paleobiology 23:165173.Google Scholar
McKinney, M. L. 1986. Biostratigraphic gap analysis. Journal of Geology 14:3638.Google Scholar
Paul, C. R. C. 1982. The adequacy of the fossil record. In Joysey, K. A. and Friday, A. E., eds. Problems of phylogenetic reconstruction. Systematics Association Special Volume 21:75117. Academic Press, London.Google Scholar
Quenouille, M. H. 1956. Notes on bias in estimation. Biometrika 43:353360.Google Scholar
Robson, D. S., and Whitlock, J. H. 1964. Estimation of a truncation point. Biometrika 51:3339.Google Scholar
Smith, R. L. 1987. Estimating the tails of probability distributions. Annals of Statistics 15:11741207.Google Scholar
Springer, M. S. 1990. The effect of random range truncations on patterns of evolution in the fossil record. Paleobiology 16:512520.Google Scholar
Springer, M. S., and Lilje, A. 1988. Biostratigraphy and gap analysis: the expected sequence of biostratigraphic events. Journal of Geology 96:228236.Google Scholar
Strauss, D., and Sadler, P. M. 1989. Classical confidence intervals and Bayesian probability estimates for ends of local taxon ranges. Mathematical Geology 21:411427.Google Scholar
Weissman, I. 1981. Confidence intervals for the threshold parameter. II. Unknown shape parameter. Communications in Statistics A11:24512474.Google Scholar
Wise, K. 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