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Life Cycles

Are there periodic booms and busts in the diversity of life on Earth? Hear a tale of fossils and Fourier transforms

Brian Hayes

Answers and More Questions

The question that launched me on this adventure was whether evidence of periodicity is something blatant and robust and unmistakable, or whether the procedures needed to detect it are subtle, temperamental and subjective. My answers remain murky.

On the one hand, it was a relief to find that no careful selection or heavy-handed mistreatment of the data were needed to bring forth the two signals reported by Muller and Rohde. The peaks emerged clearly from the entire data set or from many different subsets, and the positions of the peaks along the frequency axis were quite stable, unaffected by variations in analytic method. Even the extraneous Vendian data altered only the heights of the peaks, not their positions at 62 and 140 million years.

But my troubles with the heights of the peaks were chastening. In the end the cause turned out to be a simple error; but, then again, I knew that something was amiss only because I had the right answer given to me. Under other circumstances, the decision to keep or to discard the Vendian genera might be an open question. The choice made about this seemingly minor component of the data—it amounts to 0.2 percent—can have a visually conspicuous effect on the outcome. (Whether the effect is also statistically significant is a question I have not addressed.)

Mathematically, the Fourier transform is well-defined and deterministic, with no more room for subjectivity than, say, the conversion of rectangular to polar coordinates. The same input always yields the same output. In practice, though, there are knobs and dials to twiddle—choices to be made in preparing the input and presenting the output. As with many other methods, it's these niggling details—how to deal with outliers, how to correct for systematic biases—that cause most of the trouble.

Perhaps it is foolish for an untrained amateur even to attempt using such tools; certainly the tools are not to be blamed just because a neophyte fails to get the right answer on the first try. But still I cherish the notion that ordinary readers can assess a scientific claim for themselves, by analyzing the evidence and working through the steps of the argument, not by appeals to authority or consensus.

Apart from my methodological muddles, what should we make of the oscillations in fossil diversity? A tall, sharp peak in a Fourier spectrum implies that the underlying wave has a very steady frequency and phase. Such long-term regularity is unusual in biological systems, and so Muller and Rohde argue that there must be some external driving force. Muller favors an astronomical explanation, perhaps something related to the motion of the solar system through the galaxy. Rohde is more partial to geological causes, such as recurrent episodes of volcanism caused by periodic events in the Earth's mantle.

Muller and Rohde have looked for correlations between the cycles in fossil diversity and various geophysical phenomena, such as indicators of past climate and sea level. They note a 135-million-year-cycle in glaciation, statistically indistinguishable from the wavelength of their 140-million-year cycle. There are several other possible matches as well, but none of them is compelling enough for Muller and Rohde to endorse one candidate cause among all the contenders.

© Brian Hayes

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