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Hierarchical linear modeling of the tempo and mode of evolution

Published online by Cambridge University Press:  08 April 2016

Fred L. Bookstein
Center for Human Growth and Development and Departments of Statistics and Biostatistics, The University of Michigan; Ann Arbor, Michigan 48109
Philip D. Gingerich
Museum of Paleontology and Department of Geology and Mineralogy, The University of Michigan; Ann Arbor, Michigan 48109
Arnold G. Kluge
Museum of Zoology and Department of Ecology and Evolutionary Biology, The University of Michigan; Ann Arbor, Michigan 48109


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.

Research Article
Copyright © The Paleontological Society 

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