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Mathematical models of cladogenesis

Published online by Cambridge University Press:  08 April 2016

David M. Raup
David M. Raup*
Affiliation:
Department of Geophysical Sciences, University of Chicago, Chicago, Illinois 60637
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Abstract

The evolutionary pattern of speciation and extinction in any biologic group may be described by a variety of mathematical models. These models provide a framework for describing the history of taxonomic diversity (clade shape) and other aspects of larger evolutionary patterns. The simplest model assumes time homogeneity: that is, speciation and extinction probabilities are constant through time and within taxonomic groups. In some cases the homogeneous model provides a good fit to real world paleontological data, but in other cases the model serves only as a null hypothesis that must be rejected before more complex models can be applied. In cases where the homogeneous model does not fit the data, time-inhomogeneous models can be formulated that specify change, regular or episodic, in speciation and extinction probabilities. An appendix provides a list of the most useful equations based on the homogeneous model.

Type
Research Article
Information
Paleobiology , Volume 11 , Issue 1 , Winter 1985 , pp. 42 - 52
Copyright
Copyright © The Paleontological Society 

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References

Literature Cited

Ashlock, P. D. 1971. Monophyly and associated terms. Syst. Zool. 20:63–69.Google Scholar
Bailey, N. T. J. 1964. The Elements of Stochastic Processes, with Applications to the Natural Sciences. 249 pp. Wiley; New York.Google Scholar
Fischer, A. G. and Arthur, M. A. 1977. Secular variations in the pelagic realm. Soc. Econ. Paleontol. and Mineral., Publ. 25, Pp. 19–50.Google Scholar
Galton, F. and Watson, H. W. 1875. On the problem of the extinction of families. J. Anthropol. Soc. London. 4:138–144.Google Scholar
Gilinsky, N. L. and Bambach, R. K. 1984. A new look at patterns of taxonomic diversity: evidence for extrinsic biotic control. Geol. Soc. Amer. Abstracts with Program. 16:519.Google Scholar
Gillespie, J. H. and Ricklefs, R. E. 1979. A note on the estimation of species duration distributions. Paleobiology. 5:60–62.CrossRefGoogle Scholar
Gould, S. J., Raup, D. M., Sepkoski, J. J. Jr., Schopf, T. J. M., and Simberloff, D. S. 1977. The shape of evolution: a comparison of real and random clades. Paleobiology. 3:23–40.Google Scholar
Hoffman, A. and Kitchell, J. A. 1984. Evolution in a pelagic, planktic system: a paleobiologic test of models of multispecies evolution. Paleobiology. 10:9–33.Google Scholar
Holman, E. W. 1983. Time scale and taxonomic survivorship. Paleobiology. 9:20–25.Google Scholar
Kendall, D. G. 1948. On the generalized “birth-death” process. Ann. Math. Statist. 19:1–15.CrossRefGoogle Scholar
Müller, A. H. 1961. Grossablaüfe der Stammesgeschichte. 116 pp. Fischer; Jena.Google Scholar
Müller, A. H. 1970. Eine phylogenetische Regel. Monatsb. Dt. Akad. Wiss. Berlin. 12:521–531.Google Scholar
Müller, A. H. 1974. Regelhafte und systemgebundene Verlagerung der Formenmaxima sich stammesgeschichtlich ablössender gleichrangiger Taxa. Biol. Zentralbl. 93:265–288.Google Scholar
Raup, D. M. 1975. Taxonomic survivorship curves and Van Valen's law. Paleobiology. 1:82–96.Google Scholar
Raup, D. M. 1978. Cohort analysis of generic survivorship. Paleobiology. 4:1–15.Google Scholar
Raup, D. M. 1981. Extinction: bad genes or bad luck? Acta Geol. Hisp. 16:25–33.Google Scholar
Raup, D. M., Gould, S. J., Schopf, T. J. M., and Simberloff, D. S. 1973. Stochastic models of phylogeny and the evolution of diversity. J. Geol. 81:525–542.CrossRefGoogle Scholar
Raup, D. M. and Sepkoski, J. J. Jr. 1984. Periodicity of extinctions in the geologic past. Proc. Nat. Acad. Sci. USA. 81:801–805.Google Scholar
Raup, D. M. and Valentine, J. W. 1983. Multiple origins of life. Proc. Nat. Acad. Sci. USA. 80:2981–2984.Google Scholar
Ricklefs, R. E. 1980. Phyletic gradualism vs. punctuated equilibrium: applicability of neontological data. Paleobiology. 6:271–275.Google Scholar
Salthe, S. N. 1975. Some comments on Van Valen's law of extinction. Paleobiology. 4:356–358.CrossRefGoogle Scholar
Sepkoski, J. J. Jr. 1978. A kinetic model of Phanerozoic taxonomic diversity. I. Analysis of marine orders. Paleobiology. 4:223–252.CrossRefGoogle Scholar
Sepkoski, J. J. Jr. 1979. A kinetic model of Phanerozoic taxonomic diversity. II. Early Phanerozoic families and multiple equilibria. Paleobiology. 5:222–251.Google Scholar
Stanley, S. M. 1979. Macroevolution. 332 pp. W. H. Freeman; San Francisco.Google Scholar
Stanley, S. M. and Newman, W. A. 1980. Competitive exclusion in evolutionary time: the case of the acorn barnacles. Paleobiology. 6:173–183.Google Scholar
Stanley, S. M., Signor, P. W. III, Lidgard, S., and Karr, A. F. 1981. Natural clades differ from “random” clades: simulations and analyses. Paleobiology. 7:115–127.Google Scholar
Stoyan, D. 1980. Estimation of transition rates of inhomogeneous birth-death processes with a paleontological application. Elecktonische Informationsverarbeitung u. Kybernetik. 16:647–649.Google Scholar
Stoyan, D. and Stoyan, G. 1980. Über die Formen-Maxima-Regel von A. H. Müller. Freiberger Forschungsheft. 357:105–110.Google Scholar
Thomson, K. S. 1976. Explanation of large scale extinctions of lower vertebrates. Nature. 261:578–580.Google Scholar
Thomson, K. S. 1977. The pattern of diversification among fishes. Pp. 377–404. In: Hallam, A., ed. Patterns of Evolution as Illustrated by the Fossil Record. 591 pp. Elsevier; Amsterdam.CrossRefGoogle Scholar
Van Valen, L. 1973. A new evolutionary law. Evol. Theory. 1:1–30.Google Scholar
Wilson, M. V. H. 1983. Is there a characteristic rate of radiation for insects? Paleobiology. 9:79–85.Google Scholar
Yule, G. U. 1924. A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, F.R.S. R. Soc. London, Philos. Trans. (B). 213:21–87.Google Scholar