COMPUTING SCIENCE
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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