Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-27T00:55:34.342Z Has data issue: false hasContentIssue false
  • English
  • Français

Probabilities of origination, persistence, and extinction of families of marine invertebrate life

Published online by Cambridge University Press:  08 February 2016

Norman L. Gilinsky  and
I. J. Good
Norman L. Gilinsky
Affiliation:
Department of Geological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
I. J. Good
Affiliation:
Department of Statistics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we model the process of taxonomic evolution as a Galton-Watson branching process in discrete time and, using maximum likelihood, develop methods to estimate the probabilities of origination, persistence, and extinction of fossil taxa. We use the methods to estimate the probabilities of origination, persistence, and extinction of families (1) within 135 orders of marine invertebrate organisms, (2) within 12 phyla, and (3) within all marine invertebrate life (independently of the suprafamilial classification).

Most orders, including the arcoid bivalves, the dentaloid scaphopods, the orders of chitins, and many others, have relatively low probabilities of familial origination and extinction. The various ammonoid and trilobite orders, and some others, have high probabilities of origination and extinction. Among the phyla, the Archaeocyatha have the highest probabilities of familial origination and extinction, and the Annelida the lowest, with the more typical phyla of shelly organisms clustering near the high end of the probability scale. The Porifera and Protozoa also have low probabilities but not as low as the Annelida. The estimated origination and extinction probabilities for families within all marine invertebrate life are 0.470 and 0.452 per stage, respectively, values that are at the high end of the probability scale. We have also estimated the probabilities of ultimate extinction (extinction of all families) of the supertaxa.

By analyzing the changes of the diversity during each stratigraphic stage separately, we have also determined the trajectories of the estimated origination and extinction probabilities for families within all marine invertebrate life. The estimated origination probability is relatively high in association with the expansion of the Cambrian and Paleozoic evolutionary faunas and declines to more normal levels for the remainder of the Phanerozoic. The trajectory of the estimated extinction probability is from nearly zero early in the Phanerozoic to more normal levels later, showing clearly defined peaks in association with the five Phanerozoic mass-extinction events. The terminal Cretaceous mass extinction is the only one of the five that was not preceded by a monotonic decline of origination probability or by a series of stages with low origination probability. It appears to have been a unique, singular event.

Because the mathematical theory we employ as a model corresponds so closely to the processes of taxonomic evolution as we understand them, we believe that the theory provides a reasonable model of biological reality.

Type
Articles
Information
Paleobiology , Volume 17 , Issue 2 , Spring 1991 , pp. 145 - 166
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

Alvarez, L., Alvarez, W., Asaro, F., and Michel, H. V. 1980. Extraterrestrial cause for the Cretaceous-Tertiary extinction. Science 208:1095–1108.CrossRefGoogle ScholarPubMed
Bailey, N.T.J. 1964. The Elements of Stochastic Processes. Wiley; New York.Google Scholar
Bartlett, M. S. 1949. Some evolutionary stochastic processes. Journal of the Royal Statistical Society, Series B 11:211–229.Google Scholar
Bienaymé, I. J. 1845. De la loi de multiplication et de la durée des families. Société de la Philomatique de Paris Extraits des Procès-Verbaux des Sciences 5:37–39.Google Scholar
Feller, W. 1968. Introduction to Probability Theory and its Applications. Wiley; New York.Google Scholar
Fisher, R. A. 1922. On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London, A 222:309–368.Google Scholar
Foote, M. 1988. Survivorship analysis of Cambrian and Ordovician trilobites. Paleobiology 14:258–271.CrossRefGoogle Scholar
Galton, F. 1873. Problem 4001. Educational Times (London). 1 April 1873, p. 17.Google Scholar
Galton, F. 1889. Natural Inheritance. Macmillan; London.Google Scholar
Ghiselin, M. T. 1974. A radical solution to the species problem. Systematic Zoology 23:536–544.CrossRefGoogle Scholar
Gilinsky, N. L., and Good, I. J. 1989. Analysis of clade shape using queueing theory and the fast Fourier Transform. Paleobiology 15:321–333.CrossRefGoogle Scholar
Good, I. J. 1969. Polynomial algebra: an application of the fast Fourier Transform. Nature 222:1302.CrossRefGoogle Scholar
Good, I. J. 1987. A survey of the use of the fast Fourier Transform for computing distributions. Journal of Statistical Computation and Simulation 28:87–93.CrossRefGoogle Scholar
Good, I. J. 1990. Isolikelihoods. Journal of Statistical Computation and Simulation 36:45–47.Google Scholar
Good, I. J., and Gilinsky, N. L. 1990. A simple comment concerning the Galton-Watson-Bienaymé process. Journal of Statistical Computation and Simulation 34:165–166.CrossRefGoogle Scholar
Gould, S. J. 1985. The paradox of the first tier: an agenda for paleobiology. Paleobiology 11:2–12.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.CrossRefGoogle Scholar
Harris, T. E. 1963. The Theory of Branching Processes. Springer; Berlin.CrossRefGoogle Scholar
Hoffman, A., and Ghiold, J. 1985. Randomness in the pattern of “mass extinctions” and “waves of originations.” Geological Magazine 122:1–4.CrossRefGoogle Scholar
Hull, D. L. 1978. A matter of individuality. Philosophy of Science 45:335–360.CrossRefGoogle Scholar
Kendall, D. G. 1966. Branching processes since 1873. Journal of the London Mathematical Society 41:385–406.CrossRefGoogle Scholar
Kendall, D. G., and Stuart, A. 1969. The Advanced Theory of Statistics, Vol. 1, 3rd ed.Griffin; London.Google Scholar
Kitchell, J. A., and MacLeod, .N. 1988. Macroevolutionary interpretations of symmetry and synchroneity in the fossil record. Science 240:1190–1193.CrossRefGoogle ScholarPubMed
Kurten, B. 1960. Chronology and faunal evolution of the earlier European glaciations. Soc Scient Fennica Comm Biol 21:40–62.Google Scholar
Lehman, E. L. 1983. Theory of Point Estimation. Wiley; New York.CrossRefGoogle Scholar
Levinton, J. S., and Farris, J. S. 1987. On the estimation of taxonomic longevity from Lyellian curves. Paleobiology 13:479–483.CrossRefGoogle Scholar
Lotka, A. J. 1939. Theórie Analytique des Associations Biologiques. Herman; Paris.Google Scholar
Mode, C. J. 1971. Multitype Branching Processes. Elsevier; New York.Google Scholar
Pease, C. M. 1987. Lyellian curves and mean taxonomic durations. Paleobiology 13:484–487.CrossRefGoogle Scholar
Raup, D. M. 1978. Cohort analysis of generic survivorship. Paleobiology 4:1–15.CrossRefGoogle Scholar
Raup, D. M. 1985. Mathematical models of cladogenesis. Paleobiology 11:42–52.CrossRefGoogle 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. Journal of Geology 81:525–542.CrossRefGoogle Scholar
Raup, D. M., and Sepkoski, J. J. Jr. 1982. Mass extinctions in the marine fossil record. Science 215:1501–1503.CrossRefGoogle ScholarPubMed
Raup, D. M., and Sepkoski, J. J. Jr. 1986a. Periodic extinctions of families and genera. Science 231:833–836.CrossRefGoogle ScholarPubMed
Raup, D. M., and Sepkoski, J. J. Jr. 1986b. Periodicity in marine extinction events. Pp. 3–36. In Elliott, D. K. (ed.), Dynamics of Extinction. Wiley; New York.Google Scholar
Sepkoski, J. J. Jr. 1979. A kinetic model of Phanerozoic taxonomic diversity II. Early Phanerozoic families and multiple equilibria. Paleobiology 5:222–251.CrossRefGoogle Scholar
Sepkoski, J. J. Jr. 1981. A factor analytic description of the Phanerozoic marine fossil record. Paleobiology 7:36–53.CrossRefGoogle Scholar
Sepkoski, J. J. Jr. 1982. A compendium of fossil marine families. Milwaukee Public Museum Contributions to Biology and Geology 51.Google Scholar
Sepkoski, J. J. Jr. 1984. A kinetic model of Phanerozoic taxonomic diversity. III. Post-Paleozoic families and mass extinctions. Paleobiology 20:246–267.CrossRefGoogle Scholar
Sepkoski, J. J. Jr. 1986. Phanerozoic overview of mass extinction. Pp. 277–295. In Raup, D. M., and Jablonski, D. (eds.), Patterns and Processes in the History of Life. Springer-Verlag; Berlin.CrossRefGoogle Scholar
Signor, P. W., and Lipps, J. H. 1982. Sampling bias, gradual extinction patterns, and catastrophes in the fossil record. Pp. 291–296. In Silver, L. T., and Schultz, P. H. (eds.), Geological Implications of Impacts of Large Asteroids and Comets on the Earth. Geological Society of America Special Paper 190.CrossRefGoogle Scholar
Simpson, G. G. 1944. Tempo and Mode in Evolution. Columbia University Press; New York.Google Scholar
Stanley, S. M. 1979. Macroevolution: Pattern and Process. W. H. Freeman and Company; San Francisco.Google Scholar
Stanley, S. M. 1985. Rates of evolution. Paleobiology 11:13–26.CrossRefGoogle 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.CrossRefGoogle Scholar
Van Valen, L. 1973. A new evolutionary law. Evolutionary Theory 1:1–30.Google Scholar
Van Valen, L. 1979. Taxonomic survivorship curves. Evolutionary Theory 4:129–142.Google Scholar
Yule, G. U. 1924. A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, F. R. S. Proceedings of the Royal Society of London 213(B):21–87.Google Scholar