Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-03T00:50:51.722Z Has data issue: false hasContentIssue false
  • English
  • Français

Biases in the durations and diversities of fossil taxa

Published online by Cambridge University Press:  08 February 2016

Craig M. Pease
Craig M. Pease*
Affiliation:
Committee on Evolutionary Biology, University of Chicago, Chicago, Illinois 60637
Get access Rights & Permissions [Opens in a new window]

Abstract

The theoretical framework developed here delineates the biological and paleontological circumstances under which the observed durations and diversities of fossil taxa will be significantly affected by three time-dependent sampling biases. The pull of the Recent and the loss of fossiliferous sediments shorten the observed durations of ancient taxa, as compared to the observed durations of Recent taxa. By contrast, the duration truncation mechanism lengthens the observed durations of ancient, as compared to more recent, taxa. Both the pull of the Recent and loss of fossiliferous sediments decrease the observed diversity of ancient, as compared to contemporary, communities.

This theoretical framework is built on four parameters: the extinction and origination rates q and p; the fossilization rate, v; and the fossil loss rate, h. I derive formulas for the observed durations and diversities of fossil taxa in terms of these parameters and develop a method of estimating these parameters. The estimation procedure is applied to the bivalve families, and I provide statistical evidence for the conclusion that q – p < 0 for bivalve families, and hence that bivalve diversity has been increasing through time. The theory predicts that a certain fraction of an extinct fauna will be represented by only one fossil, and hence will have an observed duration of zero. As the record becomes poorer, this fraction increases. For bivalves I assume that families known from only one stage have an observed duration of zero, and exploit this assumption to estimate h and v/p.

To evaluate the errors made in applying the model to the bivalves, I estimate several parameters in two different ways and find the estimates to be consistent. Additionally, I argue that the errors caused by the simplifying assumptions of the model are less than the sampling errors inherent in estimating p, q, h, and v.

Type
Research Article
Information
Paleobiology , Volume 11 , Issue 3 , Summer 1985 , pp. 272 - 292
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

Bambach, R. K. 1977. Species richness in marine benthic habitats through the Phanerozoic. Paleobiology. 3:152–167.CrossRefGoogle Scholar
Bender, C. M. and Orszag, S. A. 1978. Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill; New York.Google Scholar
Blank, R. G. 1979. Applications of probabilistic biostratigraphy to chronostratigraphy. J. Geol. 87:647–670.CrossRefGoogle Scholar
Blank, R. G. and Ellis, C. H. 1982. The probable range concept applied to the biostratigraphy of marine microfossils. J. Geol. 90:415–433.CrossRefGoogle Scholar
Blatt, H. and Jones, R. L. 1975. Proportions of exposed igneous, metamorphic, and sedimentary rocks. Geol. Soc. Am. Bull. 86:1085–1088.2.0.CO;2>CrossRefGoogle Scholar
Bretsky, P. W. 1973. Evolutionary patterns in the Paleozoic Bivalvia: documentation and some theoretical considerations. Geol. Soc. Am. Bull. 84:2079–2096.2.0.CO;2>CrossRefGoogle Scholar
Bulmer, M. G. 1980. The Mathematical Theory of Quantitative Genetics. Clarendon; Oxford.Google Scholar
Chen, C. T. 1970. Introduction to Linear Systems Theory. Holt, Rinehart & Winston; New York.Google Scholar
Cutbill, J. L. and Funnel, B. M. 1967. Computer analysis of the fossil record. Pp. 791–820. In: Harland, W. B. et al., eds. The Fossil Record. Geol. Soc. London; London.Google Scholar
Drooger, C. W. 1974. The boundaries and limits of stratigraphy. Proc. Konink. Neder. Akad. Wetensch. 77B:159–176.Google Scholar
Efron, B. 1982. The Jacknife, the Bootstrap and Other Resampling Plans. Soc. Indust. Appl. Math.; Philadelphia.CrossRefGoogle Scholar
Garrels, R. M. and MacKenzie, F. T. 1971. Gregor's denudation of the continents. Nature. 231:382–383.CrossRefGoogle Scholar
Gautschi, W. 1959. Exponential integral ∫1∞ e–xtt–n dt for large values of n. J. Res. Natl. Bur. Stand. 62:123–125.CrossRefGoogle Scholar
Gould, S. J., Raup, D. M., Sepkoski, J. J., Schopf, T. J. M., and Simberloff, D. S. 1977. The shape of evolution: a comparison of real and random clades. Paleobiology. 3:23–40.CrossRefGoogle Scholar
Gregor, C. B. 1968. The rate of denudation in post-Algonkian time. Proc. Konink. Ned. Akad. Van Wetensch. 71:22–30.Google Scholar
Gregor, C. B. 1980. Weathering rates of sedimentary and crystalline rocks. Geol. Proc. 83B:173–181.Google Scholar
Guilley, J. 1969. Geological perspective on the completeness of the fossil record. Geol. Soc. Am. Bull. 80:2303–2312.Google Scholar
Harper, C. W. 1975. Standing diversity of fossil groups in successive intervals of geologic time: a new measure. J. Paleontol. 49:752–757.Google Scholar
Harland, W. B., Cox, A. V., Llewellyn, P. G., Pickton, C. A. G., Smith, A. G., and Walters, R. 1982. A Geologic Time Scale. Cambridge Univ. Press; Cambridge.Google Scholar
Higgs, D. V. 1949. Quantitative areal geology of the United States. Am. J. Sci. 247:575–583.CrossRefGoogle Scholar
Kurtén, B. 1954. Population dynamics—a new method in paleontology. J. Paleontol. 28:286–292.Google Scholar
Lasker, H. R. 1976. Effects of differential preservation on the measurement of taxonomic diversity. Paleobiology. 2:84–93.CrossRefGoogle Scholar
Li, Y. H. 1972. Geochemical mass balance among lithosphere, hydrosphere, and atmosphere. Am. J. Sci. 272:119–137.CrossRefGoogle Scholar
Lin, C. C. and Segel, L. A. 1974. Mathematics Applied to Deterministic Problems in the Natural Sciences. Macmillan; New York.Google Scholar
Moore, R. C. and Teichert, C., eds. 1953–1983. Treatise on Invertebrate Paleontology. Geol. Soc. Am. and Univ. Kansas Press; Lawrence, Kans.Google Scholar
Newell, N. D. 1967. Revolutions in the history of life. Pp. 63–91. In: Albritton, C. C. Jr., ed. Uniformity and Simplicity: A Symposium on the Uniformity of Nature. Geol. Soc. Am. Spec. Paper 89.Google Scholar
Nichols, J. D. and Pollock, K. H. 1983. Estimating taxonomic diversity, extinction rates, and origination rates from fossil data using capture-recapture models. Paleobiology. 9:150–163.CrossRefGoogle Scholar
Odin, G. S. 1982. Introduction: uncertainities in evaluating the numerical time scale. Pp. 3–16. In: Odin, G. S., ed. Numerical Dating in Stratigraphy. I. Wiley; New York.Google Scholar
Odin, G. S., Curry, D., Gale, N. H., and Kennedy, W. J. 1982. The Phanerozoic time scale in 1981. Pp. 957–960. In: Odin, G. S., ed. Numerical Dating in Stratigraphy. II. Wiley; New York.Google Scholar
Palmer, A. R. 1983. The decade of North American geology 1983 geologic time scale. Geology. 11:503–504.2.0.CO;2>CrossRefGoogle Scholar
Papoulis, A. 1965. Probability, Random Variables and Stochastic Processes. McGraw-Hill; New York.Google Scholar
Raup, D. M. 1972. Taxonomic diversity during the Phanerozoic. Science. 177:1065–1071.CrossRefGoogle ScholarPubMed
Raup, D. M. 1976. Species diversity in the Phanerozoic: an interpretation. Paleobiology. 2:289–297.CrossRefGoogle Scholar
Raup, D. M. 1978. Cohort analysis of generic survivorship. Paleobiology. 4:1–15.CrossRefGoogle Scholar
Raup, D. M. 1979. Biases in the fossil record of species and genera. Bull. Carnegie Mus. Nat. Hist. 13:85–91.Google Scholar
Raup, D. M. and Sepkoski, J. J. 1982. Mass extinctions in the marine fossil record. Science. 215:1501–1503.CrossRefGoogle ScholarPubMed
Raup, D. M. and Sepkoski, J. J. 1984. Periodicity of extinctions in the geologic past. Proc. Natl. Acad. Sci. (USA). 81:801–805.CrossRefGoogle ScholarPubMed
Rohr, D. M. and Boucot, A. J. 1974. Evolutionary patterns in the Paleozoic Bivalvia: documentation and some theoretical considerations: discussion. Geol. Soc. Am. Bull. 85:665–666.2.0.CO;2>CrossRefGoogle Scholar
Romer, A. S. 1966. Vertebrate Paleontology. Univ. Chicago Press; Chicago.Google Scholar
Ronov, A. B. 1959. Contribution to the post-Cambrian geochemical history of the atmosphere and hydrosphere. Geokhimiia. Pp. 397–409.Google Scholar
Schopf, T. J. M. 1978. Fossilization potential of an intertidal fauna: Friday Harbor, Washington. Paleobiology. 4:261–270.CrossRefGoogle Scholar
Schopf, T. J. M. 1981. Evidence from findings of molecular biology with regard to the rapidity of genomic change: implications for species durations. Pp. 135–192. In: Niklas, K. J., ed. Paleobotany, Paleoecology and Evolution. Vol. 1. Praeger; New York.Google Scholar
Schopf, T. J. M. 1982. A critical assessment of punctuated equilibria. I. Duration of taxa. Evolution. 36:1144–1157.Google ScholarPubMed
Sepkoski, J. J. 1975. Stratigraphic biases in the analysis of taxonomic survivorship. Paleobiology. 1:343–355.CrossRefGoogle Scholar
Sepkoski, J. J. 1978. A kinetic model of Phanerozoic taxonomic diversity. I. Analysis of marine orders. Paleobiology. 4:223–251.CrossRefGoogle Scholar
Sepkoski, J. J. 1979. A kinetic model of Phanerozoic taxonomic diversity. II. Early Phanerozoic families and multiple equilibria. Paleobiology. 5:222–251.Google Scholar
Sepkoski, J. J. 1982. A Compendium of Fossil Marine Families. Milwaukee Public Mus. Contr. Biol. Geol. no. 51. 125 pp.Google Scholar
Sepkoski, J. J., Bambach, R. K., Raup, D. M., and Valentine, J. W. 1981. Phanerozoic marine diversity and the fossil record. Nature. 293:435–437.CrossRefGoogle Scholar
Signor, P. W. 1978. Species richness in the Phanerozoic: an investigation of sampling effects. Paleobiology. 4:394–406.CrossRefGoogle Scholar
Simpson, G. G. 1944. Tempo and Mode in Evolution. Columbia Univ. Press; New York.Google Scholar
Simpson, G. G. 1960. The history of life. Pp. 117–180. In: Tax, S., ed. Evolution after Darwin. Vol. 1. The Evolution of Life. Univ. Chicago Press; Chicago.Google Scholar
Stanley, S. M. 1977. Trends, rates and patterns of evolution in the bivalvia. Pp. 209–250. In: Halman, A., ed. Patterns of Evolution. Elsevier; Amsterdam.Google Scholar
Stanley, S. M. 1979. Macroevolution, Pattern and Process. W. H. Freeman; San Francisco.Google Scholar
Valentine, J. W. 1970. How many marine invertebrate fossil species? A new approximation. J. Paleontol. 44:410–415.Google Scholar
Valentine, J. W. 1972. Phanerozoic taxonomic diversity: a test of two alternative models. Science. 180:1078–1079.CrossRefGoogle Scholar
Van Valen, L. 1973. A new evolutionary Law. Evol. Theory. 1:1–30.Google Scholar
Van Valen, L. 1979. Taxonomic survivorship curves. Evol. Theory. 4:129–142.Google Scholar
Wonnacott, T. H. and Wonnacott, R. J. 1977. Introductory Statistics. 3d ed.Wiley; New York.Google Scholar