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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

Doubts about Detrending

When I first read about the practice of selecting and detrending the data, it seemed highly manipulative: First you throw away half the data, then you suppress the most conspicuous features in what remains. The choice of a cubic polynomial for the detrending curve was particularly troubling. Why a cubic, rather than, say, a linear or an exponential trend line? The obvious answer is that the cubic curve fits the data very well, and other curves don't, but that seemed rather ad hoc. If you're allowed to invent any detrending curve you please, then you can generate any result you want.

Muller and Rohde have persuaded me that these concerns were unfounded. The exclusion of genera with uncertain dates was not a way of enhancing the signal—which in fact is just as clear in the complete data set as it is in the well-resolved subset—but rather addressed concerns that poor-quality data might be seen as contaminating their result. And the detrending method has long been standard procedure in Fourier analysis. The polynomial curve is not meant to represent any meaningful trend in the data; it is simply a device for filtering out the lowest-frequency components of the signal, which would otherwise dominate the spectrum and obscure everything else. The long-period trends in diversity—especially the dramatic rise since the Cretaceous—may well be the most intriguing aspects of the fossil record, but they are not the subject of study here. The Fourier analysis is confined to a specific band of frequencies, corresponding to periods of roughly 200 down to 20 million years. The detrending process imposes the long-period limit, and a short-period cutoff comes from the finite resolution of the geologic time scale. Only features within this band are to be examined.

Subsets of the Sepkoski collection...Click to Enlarge Image

It is the nature of the Fourier transform to highlight the strongest periodicities in any signal, whatever they might be. Because some peaks are bound to emerge even in a spectrum made from random data, a crucial question is whether the 62- and 140-million-year peaks climb far enough above the background level to be considered statistically significant. Muller and Rohde address this issue through Monte Carlo simulation, generating thousands of random histograms and running them through their Fourier-analysis mill. In essence they ask: If we had 10,000 planets like the Earth and we could dig up fossils on all of them, how often would we see spectral features as strong as those observed in the real fossil record? They conclude that a peak as tall and narrow as the 62-million-year signal would turn up randomly no more than 1 percent of the time; the case for the 140-million-year peak is less compelling. I have not attempted to reproduce the Monte Carlo analysis, although it is clearly key to evaluating claims of periodicity.

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