Hostname: page-component-6bf8c574d5-qdpjg Total loading time: 0 Render date: 2025-02-18T21:17:17.410Z Has data issue: false hasContentIssue false
  • English
  • Français

Hierarchical linear modeling of the tempo and mode of evolution

Published online by Cambridge University Press:  08 April 2016

Fred L. Bookstein ,
Philip D. Gingerich  and
Arnold G. Kluge
Fred L. Bookstein
Affiliation:
Center for Human Growth and Development and Departments of Statistics and Biostatistics, The University of Michigan; Ann Arbor, Michigan 48109
Philip D. Gingerich
Affiliation:
Museum of Paleontology and Department of Geology and Mineralogy, The University of Michigan; Ann Arbor, Michigan 48109
Arnold G. Kluge
Affiliation:
Museum of Zoology and Department of Ecology and Evolutionary Biology, The University of Michigan; Ann Arbor, Michigan 48109
Get access Rights & Permissions [Opens in a new window]

Abstract

Punctuated equilibrium and phyletic gradualism are alternative hypotheses that purport to explain the tempo and mode of evolution. We evaluate the two hypotheses, as they apply to the fossil record, on both theoretical and empirical grounds. Hidden randomness in data increases as a function of greater aggregation, and the hypothesis of punctuated equilibrium should not be applied to those examples where randomness is likely to occur. False stasis can result from a sustained pattern of emigration and immigration, and geographic variation must be studied in order to posit an unambiguous case of punctuated equilibrium. We describe a statistical method based on the general linear model for testing the relative fit of the alternative hypotheses to any set of temporally ordered metric data. Our method is hierarchical in the sense that subsets of the total explained variance can themselves be explained. The size of the first molar of the primate Pelycodus and of the condylarth Hyopsodus are analyzed. There are 17 tests in the two data sets, and we discover 12 instances of gradualism, four of punctuation and one of equilibrium.

Type
Research Article
Information
Paleobiology , Volume 4 , Issue 2 , Spring 1978 , pp. 120 - 134
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

Bookstein, F. L. 1975. On a form of piecewise linear regression. Am. Stat. 29:116–117.Google Scholar
Draper, N. and Smith, H. 1966. Applied Regression Analysis. Wiley; New York.Google Scholar
Eldredge, N. and Gould, S. J. 1972. Punctuated equilibria: an alternative to phyletic gradualism. Pp. 82–115 In: Schopf, T. J. M., ed. Models in Paleobiology. Freeman, Cooper and Co.; San Francisco, California.Google Scholar
Gardner, M. 1976. In which “monster” curves force redefinition of the word “curve.” Sci. Am. 235:124–133.Google Scholar
Gingerich, P. D. 1974. Stratigraphic record of early Eocene Hyopsodus and the geometry of mammalian phylogeny. Nature. 248:107–109.CrossRefGoogle Scholar
Gingerich, P. D. 1976. Paleontology and phylogeny: patterns of evolution at the species level in early Tertiary mammals. Am. J. Sci. 276:1–28.Google Scholar
Gingerich, P. D. 1978. Evolutionary transition from ammonite Subprionocyclus to Reesidites—punctuated or gradual? Evolution. In press.CrossRefGoogle Scholar
Gingerich, P. D. and Simons, E. L. 1977. Systematics, phylogeny, and evolution of early Eocene Adapidae (Mammalia, Primates) in North America. Contrib. Paleontol. Univ. Mich. 24:245–279.Google Scholar
Gould, S. J. 1977a. Evolution's erratic pace. Nat. Hist. 86(5):12–16.Google Scholar
Gould, S. J. 1977b. The return of hopeful monsters. Nat. Hist. 86(6):22–30.Google Scholar
Gould, S. J. and Eldredge, N. 1977. Punctuated equilibria: the tempo and mode of evolution reconsidered. Paleobiology. 3:115–151.CrossRefGoogle Scholar
Harper, C. W. Jr. 1975. Origin of species in geologic time: alternatives to the Eldredge-Gould model. Science. 190:47–48.Google Scholar
Hickey, L. J. 1977. Stratigraphy and paleobotany of the Golden Valley Formation (early Tertiary) of Western North Dakota. Geol. Soc. Am. Mem. 150:1–181.Google Scholar
Kellogg, D. E. 1975. The role of phyletic change in the evolution of Pseudocubus vema (Radiolaria). Paleobiology. 1:359–370.CrossRefGoogle Scholar
Lande, R. 1976. Natural selection and random genetic drift in phenotypic evolution. Evolution. 30:314–344.CrossRefGoogle ScholarPubMed
Lewontin, R. C. 1970. The units of selection. Annu. Rev. Ecol. Syst. 1:1–18.Google Scholar
Mandelbrot, B. B. 1977. Fractals: Form, Chance, and Dimension. W. H. Freeman Co.; San Francisco, California.Google Scholar
Ozawa, T. 1975. Evolution of Lepidolina multiseptata (Permian foraminifer) in East Asia. Mem. Fac. Sci. Kyushu Univ., Ser. D. Geol. 23:117–164.Google Scholar
Reyment, R. A. 1975. Analysis of a generic level transition in Cretaceous ammonites. Evolution. 28:665–676.CrossRefGoogle Scholar
Stanley, S. M. 1975a. Clades versus clones in evolution: why we have sex. Science. 190:382–383.Google Scholar
Stanley, S. M. 1975b. A theory of evolution above the species level. Proc. Natl. Acad. Sci. 72:646–650.Google Scholar
Stanley, S. M. 1976. Stability of species in geologic time. Science. 192:267–269.CrossRefGoogle ScholarPubMed
Steinhaus, H. 1954. Length, shape, and area. Colloq. Math. 3:1–13.Google Scholar