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Scaling the Cycles

To the Editor:

In "Life Cycles" (Computing Science, July-August), Brian Hayes gives an excellent discussion of a number of the difficulties encountered in studying purported cycles in the fossil record. However, he seems to have missed a discussion in the literature on two additional problems that make the statistical demonstration of such cycles particularly problematic: The evident serial correlation in the fossil record (due in part to measurement error) and the patterns and uncertainties in the time scale.

Nearly 20 years ago, a student and I argued that the appearance of a 26-million-year (myr) cycle—in a version of the same fossil record that Hayes discusses—was a statistical artifact due to these two problems (Science 238:940–945; 241:96–99). The time scale used then was the Harland time scale, which fairly arbitrarily assigned 20 epochs to the period from 238 million years ago (mya) to 113 mya. Lacking a better way to make the assignment, the system aimed for equal divisions, but the scale was rounded off to give this sequence of millions of years for the 20 epoch lengths: 7, 6, 6, 6, 7, 6, 6, 6, 7, 6, 6, 6, 7, 6, 6, 6, 7, 6, 6, 6. This rounding artificially created a periodic sequence of 25 myr, which together with the more irregular remainder of the scale, led to the appearance of a 26-myr cycle in the extinction record, and its significance was then exaggerated by the serial correlation in the data.

The study by Robert A. Rohde and Richard A. Muller that Hayes discusses uses an improved time scale, although its span is twice as long as in the earlier study and is subject to large uncertainties and unanalyzed patterns in the earliest portion. Also, the significance claimed for the 62-myr cycle is based upon an analysis much like that used to find the purported 26-myr cycle.

The basic difficulty—that noncyclic but serially correlated processes can produce misleading pseudo-cycles—has been known since at least 1926, when the British statistician G. Udny Yule gave his Presidential Address to the Royal Statistical Society with the evocative title, "Why do we sometimes get Nonsense-Correlations between Time-Series?"

Stephen Stigler
University of Chicago

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