JULY/AUGUST 2007 THIS ARTICLE HAS BEEN PEER-REVIEWED. 61 R esearchers recently analyzed marine di- versity data from the past 542 million years with Fourier transform methods that strongly signal a periodic variation about a cubic trend of 62 million years. Gauss- Vaníc ˇek (GV) analysis on the nondetrended data, however, shows that no 62-million-year periodic- ity exists in it. In this article, I show that GV analysis of this di- versity data detrended with a cubic also strongly signals a 62-million-year periodicity. Furthermore, I’ve found that neither GV analysis nor Fourier transform analysis of the nondetrended data leads to any statistically significant periodicity. Marine Diversity Data From J. John Sepkoski’s record 1 of marine animal genera from the past 542 million years, researchers Robert Rohde and Richard Muller 2 extracted a time series, , of marine animal diversity. The pairs (t i , G i ) appear in a Web supplement to their article. 2 The first and last three terms of the series are (–0.001, 4115), (0.0, 4166), (1.8, 4063), …, (532.0, 99), (534.0, 47), (538.0, 16). Time is measured as millions of years ago (Myr), so (534.0, 47) means that the presently known fossils of marine animals that lived sometime between 538 and 534 Myr are grouped into 47 genera (47 is likely a small fraction of the number of genera ac- tually present). To compare GV analysis with Fourier transform (FT) analysis, we need to apply them to comparable sequences. Following Rohde and Muller, I computed the cubic polynomial P(t) that’s the least-squares fit to and computed the detrended time se- ries with D i = G i – P(t i ). I computed the GV power spectrum (GVPS) of , and Ro- hde and Muller computed the FT power spectrum (FTPS) of a series similar to . Mensur Omerbashich 3 examined the GVPS of , and I computed the FTPS of . GV analysis is sometimes called the Lomb 4 or Lomb-Scargle 5 method; researchers have applied it in such diverse disciplines as astrophysics 6 and medicine. 7 Its value at a frequency f is a measure of the variance reduction obtained from fitting by least squares a sine function of frequency f to the data. A full discussion of the GVPS appears else- where. 4,5 I’ve placed the equations for computing the GVPS in a Web supplement at http://opac. ieeecomputersociety.org/opac?year=2007&volume =9&issue=4&acronym=cise. Monte Carlo Analysis A peak in a power spectrum can accurately signal a periodic variation in the underlying series or could be a computational artifact. To measure the statis- { , } t G i ii =1 167 { , } t G i ii =1 167 { , } t D i ii =1 167 { , } t D i ii =1 167 { , } t D i ii =1 167 { , } t G i ii =1 167 { , } t G i ii =1 167 Gauss-Vaníc ˇ ek and Fourier Transform Spectral Analyses of Marine Diversity T ECHNICAL N OTE The author compares Gauss-Vaníc ˇ ek analysis of historical marine diversity data with a Fourier transform spectral analysis. Somewhat surprisingly, the results show that the two techniques are equivalent. JAMES L. CORNETTE Iowa State University 1521-9615/07/$25.00 © 2007 IEEE Copublished by the IEEE CS and the AIP