LETTERS TO THE EDITORS

# 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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