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Uncorrelated change produces the apparent dependence of evolutionary rate on interval

Published online by Cambridge University Press:  08 April 2016

H. David Sheets  and
Charles E. Mitchell
H. David Sheets
Affiliation:
Department of Physics, Canisius College, 2001 Main Street, Buffalo, New York 14208. E-mail: [email protected]
Charles E. Mitchell
Affiliation:
Department of Geology, State University of New York at Buffalo, Amherst, New York 14260. E-mail: [email protected]
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Abstract

An intriguing phenomenon in the study of evolutionary rates of morphological change measured from fossil lineages has been the dependence of these rates on the inverse of the measurement interval. This effect has been reported across wide ranges of species as well as within single lineages, and has been interpreted as representing a smooth extension of evolutionary rate from generational timescales to paleontological timescales, suggesting that macroevolution may be simply microevolution extended over longer intervals. There has been some debate about whether this inverse dependence is a real feature of evolutionary change, or a mathematical or psychological artifact associated with the interpretation of data.

Our analysis indicates that the strong inverse dependence of rate on interval is an artifact produced by the phenomenon of spurious self-correlation. Spurious self-correlation can appear in any calculation when a ratio is plotted against its denominator, as is done in plotting rate versus interval, and when these two quantities are not well correlated with one another. We demonstrate that the effect of spurious self-correlation appears in seven published data sets of evolutionary rate that range from taxonomically broad compendia to studies of single families. The effect obscures the underlying information about the dependence of evolutionary change on interval that is present in the data sets. In five of the seven data sets examined there is no significant correlation between the extent of evolutionary change and elapsed time. Where such a correlation does exist, the inverse dependence of rate on interval length is weakened. We describe the role played by taxonomic, dynamic, and character inhomogeneity in producing the lack of correlation of change with interval in each of these data sets. This lack of correlation of change with interval, and the accompanying inverse correlation of rate with interval, most likely arises from discontinuous modes of evolutionary change in which a distinct long-term dynamic dominates net change over geological time spans. It is poorly explained by the extrapolationary microevolutionary models that have been said to account for this phenomenon.

Type
Articles
Information
Paleobiology , Volume 27 , Issue 3 , Summer 2001 , pp. 429 - 445
Copyright
Copyright © The Paleontological Society 

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References

Literature Cited

Arnold, A. J., Kelly, D. C., and Parker, W. C. 1995. Causality and Cope's Rule: evidence from the planktonic foraminifera. Journal of Paleontology 69:203–210.Google Scholar
Bookstein, F. L. 1987. Random walk and the existence of evolutionary rates. Paleobiology 13:446–464.CrossRefGoogle Scholar
Bookstein, F. L. 1988. Random walk and the biometrics of morphological characters. Evolutionary Biology 23:369–398.Google Scholar
Bowring, S. A., and Erwin, D. H. 1998. A new look at evolutionary rates in deep time: Uniting paleontology and high-precision geochronology. GSA Today 8:1–8.Google Scholar
Clyde, W. C., and Gingerich, P. D. 1994. Rates of evolution in the dentition of early Eocene Cantius: comparison of size and shape. Paleobiology 20:506–522.Google Scholar
Efron, B., and Tibshirani, R. J. 1993. An introduction to the bootstrap. Chapman and Hall, New York.CrossRefGoogle Scholar
Freund, J. E., and Walpole, R. E. 1980. Mathematical statistics, 3d ed.Prentice-Hall, Englewood Cliffs, N.J.Google Scholar
Gingerich, P. D. 1983. Rates of evolution: effects of time and temporal scaling. Science 222:159–161.Google Scholar
Gingerich, P. D. 1984. Smooth curve of evolutionary rates: a psychological and mathematical artifact (response). Science 226:995.Google Scholar
Gingerich, P. D. 1993. Quantification and comparison of evolutionary rates. American Journal of Science 293A:453–478.Google Scholar
Gould, S. J. 1984. Smooth curve of evolutionary rate: a psychological and mathematical artifact. Science 226:994.Google Scholar
Haldane, J. B. S. 1949. Suggestions as to quantitative measure of rates of evolution. Evolution 3:51–56.CrossRefGoogle ScholarPubMed
Hallam, A. 1975. Evolutionary size increase and longevity in Jurassic bivalves and ammonites. Nature 258:493–496.Google Scholar
Hallam, A. 1978. How rare is phyletic gradualism and what is its evolutionary significance? Evidence from Jurassic bivalves. Paleobiology 4:16–25.CrossRefGoogle Scholar
Hendry, A. P., and Kinnison, M. T. 1999. Perspective: the pace of modern life: measuring rates of contemporary microevolution. Evolution 53:1637–1653.CrossRefGoogle ScholarPubMed
Kenney, B. C. 1982. Beware of spurious self-correlations! Water Resources Research 18:1041–1048.Google Scholar
Kurtén, B. 1959. Rates of evolution in fossil mammals. Cold Springs Harbor Symposium on Quantitative Biology 24:205–215.Google Scholar
Lewontin, R. C. 1966. On the measurement of relative variability. Systematic Zoology 15:141–142.CrossRefGoogle Scholar
MacFadden, B. J. 1985. Patterns of phylogeny and rates of evolution in fossil horses: hipparions from the Miocene and Pliocene of North America. Paleobiology 11:245–257.Google Scholar
MacFadden, B. J. 1986. Fossil horses from “Eohippus” (Hyracotherium) to Equus: scaling, Cope's Law, and the evolution of body size. Paleobiology 12:355–369.Google Scholar
MacFadden, B. J. 1988. Fossil horses from “Eohippus” (Hyracotherium) to Equus, 2: rates of dental evolution revisited. Biological Journal of the Linnean Society 35:37–48.Google Scholar
MacFadden, B. J. 1992. Fossil horses: systematics, paleobiology, and evolution of the Family Equidae. Cambridge University Press, New York.Google Scholar
Mandelbrot, B. B. 1997. Fractals and scaling in finance: discontinuity, concentration, risk. Springer, New York.Google Scholar
Mandelbrot, B. B. 1998. Multifractals and 1/f Noise: wild self-affinity in physics. Springer, New York.Google Scholar
Maurer, B. A., Brown, J. H., and Rusler, R. D. 1992. The micro and macro in body size evolution. Evolution 46:939–953.Google Scholar
Middleton, G. W. 2000. Data analysis in the earth sciences using Matlab. Prentice-Hall, Upper Saddle River, N.J.Google Scholar
Pearson, K. 1897. On a form of cpurious correlation which may arise when indices are used in the measurement of organs. Proceedings of the Royal Society of London 60:489–502.Google Scholar
Plotnick, R. E. 1986. A fractal model for the distribution of stratigraphic hiatuses. Journal of Geology 95:885–890.Google Scholar
Plotnick, R. E. 1988. A fractal model for the distribution of stratigraphic hiatuses: a reply. Journal of Geology 96:102–103.Google Scholar
Plotnick, R. E., and Sepkoski, J. J. Jr. 1998. A multifractal model for macroevolution. Geological Society of America Abstracts with Programs 30:A37.Google Scholar
Rice, W. R. 1989. Analyzing tables of statistical tests. Evolution 43:223–225.Google Scholar
Ridley, M. 1983. Evolution. Blackwell Scientific, Cambridge, Mass.Google Scholar
Roopnarine, P. D., Byars, G., and Fitzgerald, P. 1999. Anagenetic evolution, stratophenetic patterns, and random walk models. Paleobiology 25:41–57.Google Scholar
Sadler, P. M. 1981. Sediment accumulation rates and the completeness of stratigraphic sections. Journal of Geology 89:569–584.CrossRefGoogle Scholar
Sadler, P. M. 1993. Time scale dependence of the rates of unsteady geologic processes. In Armentrout, J. M., Bloch, R., Olson, H. C., and Perkins, B. F., eds. Rates of geologic processes, tectonics, sedimentation, eustasy and climate. Gulf Coast Section SEPM Research Conference 14:221–228.Google Scholar
Sadler, P. M. 1999. The influence of hiatuses on sediment accumulation rates. GeoResearch Forum 5:15–40.Google Scholar
Sadler, P. M., and Strauss, D. J. 1990. Estimation of completeness of stratigraphical sections using empirical data and theoretical models. Journal of the Geological Society, London 147:471–485.Google Scholar
Schlager, W., Marsal, D., van der Geest, P. A. G., and Sprenger, A. 1998. Sedimentation rates, observation span, and the problem of spurious correlation. Mathematical Geology 30:547–556.Google Scholar
Sheldon, P. R. 1996. Plus ca change—a model for stasis and evolution in different environments. Palaeogeography, Palaeoclimatology, Palaeoecology 127:209–227.Google Scholar
Stanley, S. M. 1985. Rates of evolution. Paleobiology 11:13–26.Google Scholar
Stanley, S. M., and Yang, X. 1987. Approximate evolutionary stasis for bivalve morphology over millions of years: a multivariate, multilineage study. Paleobiology 13:113–139.Google Scholar
Waythomas, C. F., and Williams, G. P. 1988. Sediment yield and spurious correlation—toward a better portrayal of the annual suspended-sediment load of rivers. Geomorphology 1:309–316.Google Scholar
Wing, S. L. 1998. Rates of floral change scale to duration of measurement. Geological Society of America Abstracts with Programs 30:A37.Google Scholar