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Analyzed the data: ALM. Wrote the paper: ALM.

The author has declared that no competing interests exist.

Time series analysis of fossil biodiversity of marine invertebrates in the Paleobiology Database (PBDB) shows a significant periodicity at approximately 63 My, in agreement with previous analyses based on the Sepkoski database. I discuss how this result did not appear in a previous analysis of the PBDB. The existence of the 63 My periodicity, despite very different treatment of systematic error in both PBDB and Sepkoski databases strongly argues for consideration of its reality in the fossil record. Cross-spectral analysis of the two datasets finds that a 62 My periodicity coincides in phase by 1.6 My, equivalent to better than the errors in either measurement. Consequently, the two data sets not only contain the same strong periodicity, but its peaks and valleys closely correspond in time. Two other spectral peaks appear in the PBDB analysis, but appear to be artifacts associated with detrending and with the increased interval length. Sampling-standardization procedures implemented by the PBDB collaboration suggest that the signal is not an artifact of sampling bias. Further work should focus on finding the cause of the 62 My periodicity.

The first high significance detection of long-term periodicity in the fossil record is fairly recent

However, these studies were all based on a large compendium

The question of periodicities in fossil biodiversity, or sometimes only in the timings of mass extinction has generated considerable past interest, debate, and discussion. Review of this history is outside the scope of this paper, and can be found elsewhere

In order to do Fourier analysis, long-term trends should be removed: in this case it would be the overall patterns of growth in biodiversity over the last half-billion years. My methods begin by least-squares fit to a cubic of the new, controlled data kindly provided by J. Alroy

Note that there is an alternating pattern of peaks and troughs with a period of about 150 My, and extending with declining amplitude to the entire sample interval. The question of periodicity will be treated more quantitatively using power spectra.

My analysis has been done two ways: 1.) based on the data taken as a function of the intervals (and their midpoints), and 2.) on a file constructed by assigning those values to the time of the mid-point of the interval, and then linearly interpolating between them to assign values every 1 My. A time series running 5–520

Reanalysis of the power spectrum of the data using alternate methods based on the Lomb-Scargle

The autocorrelation function can be used to investigate long-term behavior when plotted as a function of time. The time series was extended with zeroes, as needed to prevent a spurious “wraparound” effect

Correlation analysis is not the best technique to detect periodicities because the value at any particular lag is a sum over all the oscillations in the data, at different frequencies. In this case a particular frequency signal can be detected clearly because it dominates. Power spectral analysis is to be preferred, since it separates out various frequencies present

In order to demonstrate its robustness, I computed power spectrum in two ways. The first is based on the interpolated data as described above, and uses conventional Fast Fourier Transform methods on interpolated data. The spectrum shown on log-log axes in

Higher frequency fluctuations are not shown due to sampling limitations (too close to the interval timescale). The total power is dominated by the area under a few high peaks which exceed confidence limits. These peaks are, from left to right period T = 1/f 157 My, 63 My, and 46 My. Fluctuations outside the plotted frequency range are not shown due to sample limitations (interval length and overall time range). The parallel lines indicate significance at levels p = 0.05, 0.01, and 0.001 against the probability of any such peak arising against the spectral background. Equivalent peaks appear in an analysis based on Lomb-Scargle methods, which do not require binning and interpolation.

The same analysis was repeated with Lomb-Scargle, with no binning or interpolation, on the data as provided

The frequency (f) range shown was restricted in _{N}

The biggest peak is at the lowest frequency, corresponding to a period of 157 (+24 −20)

The peak at

Another peak at

Two peaks close to the first two of the above actually appear in

The appearance of long-period spectral peaks in a completely different sample from their original appearance, prepared under controlled conditions, lends support to the reality of the biodiversity variation. This increases the probability that periodicities in biodiversity have existed which are not fossil sampling artifacts, further motivating the search for causal agents which have strongly contributed to the rise and fall of biodiversity on Earth. For this reason additional statistical tests should be applied, if possible across the two data sets.

A combined analysis, additionally using the Sepkoski database as downloaded from Supplementary Information in _{i}*A_{i}_{i}_{i}*C_{i}

I show Real(C_{sp}) the real part of the cross-spectrum, as a function of frequency (_{sp} has substantial imaginary component. Even if a given frequency is not a peak in both data sets, it is present and the phase angle can be compared also. This coefficient in the two data sets is out of phase by 1.34 radian at 156 My and by 0.68 radian at 47 My (these correspond to 33 My and 5 My, respectively). Consequently the objective origin of these frequencies are questionable, because although both periodicities appear in the cross-spectrum, the maxima and minima of the cyles do not happen at the same times in the two data sets. Any conclusions about these must be regarded as very tentative, because of this mismatch. If they originated in actual changes in biodiversity, the phases should have good agreement. They may be affected by boundary conditions in one case and temporal resolution in the other.

This is a measure of the combined significance of the same frequency in both datasets, with the same phase angles, so that the peaks coincide. The inset numbers give the period corresponding to the shown frequency peak. The number in parentheses is the mismatch, in My, between the peaks in one set versus the other. The 62 My cycle dominates the figure and has excellent phase agreement between the two compendia.

If I detrend using a linear function, the minimum necessary for detrending, the 157 My signal drops far below the level of significance in both datasets, while the 62 My signal does not. In general the 157 My signal greatly changes its level with various choices of detrending function, while the 62 My does not. Possibly the cubic has in some sense generated the 157 My signal, perhaps interacting with data corrections. The shape of a cubic has non-negligible low frequency power. More tests of this conjecture will appear elsewhere.

Contrarily, the cross-spectral peak at 61.7 (+4 −3, FWHM) My is completely robust. Its phase displacement is only 0.16 radian between the two sets, corresponding to a 1.6 My difference in the placement of peaks and valleys of a much longer cycle. The two data sets do share some common data, but there is also substantial additional data in PBDB, and the treatment of the data has been completely differerent

I have shown that a periodicity at 62±3 My with essentially identical period and phase which was uncovered

While the point of this paper is not to demonstrate any causal mechanism, I summarize those suggested to date that either (a) have a theoretical reason which has been argued to produce such a periodicity, or (b) have empirically demonstrated some closely related periodicity.

One possibility is that there is simply a long delay for recovery from extinction events

One causal clue is an observed strong correlation between the 62 My biodiversity cycle and ^{87}Sr/^{86}Sr isotope ratio

A second independent result at low significance is a periodic signal at 61

Thirdly, biodiversity declines correspond in timing with excursions of the Solar System to Galactic north, and they are possibly caused by the effects of a resulting increased exposure high-energy cosmic rays (

Sea level changes are strongly correlated with fossil biodiversity changes from the late Triassic to the Pliocene

I know of no other mechanisms which would be expected to produce a 62 My periodicity, or other coincident data which are in phase with the biodiversity fluctuations. This, of course, does not mean that they may not exist.

I thank J. Alroy for providing the data, and R. Bambach, M. Benton, B. Lieberman, B. Thomas, and referee J. Lipps for useful comments which improved the manuscript.