Long-term cycles in the history of life: Periodic biodiversity in the Paleobiology Database

📝 Abstract

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.

💡 Analysis

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.

📄 Content

Long-Term Cycles in the History of Life: Periodic Biodiversity in the Paleobiology Database Adrian L. Melott* Department of Physics & Astronomy, University of Kansas, Lawrence, Kansas, United States of America Abstract 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. Citation: Melott AL (2008) Long-Term Cycles in the History of Life: Periodic Biodiversity in the Paleobiology Database. PLoS ONE 3(12): e4044. doi:10.1371/ journal.pone.0004044 Editor: Robert DeSalle, American Museum of Natural History, United States of America Received October 3, 2008; Accepted November 24, 2008; Published December 24, 2008 Copyright:
2008 Melott. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: The University of Kansas had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The author has declared that no competing interests exist.

• E-mail: melott@ku.edu Introduction The first high significance detection of long-term periodicity in the fossil record is fairly recent [1], based on marine fossil biodiversity over ,500 My. A significant 6263 My periodicity was superimposed on the long-term trend, confirmed by a variety of re-analyses of the same data [2–3]. No particular causal mechanism was proposed, but the result was initially published based on its relatively high statistical significance (p = 0.01) and potentially strong implications. However, these studies were all based on a large compendium [4] which was not controlled for systematic errors such as sampling rate. However, such systematic errors may compromise quantita- tive study [5,6]. For this reason, an intensive effort (the Paleobiology database: http://paleodb.org ) has resulted in a new data set [7,8], constructed, weighted, and subsampled with the intention of minimizing such errors. A statistical study of this dataset concluded with the statement that evidence for autocor- relation did not exist, which result is inconsistent with periodicity [8]. I have extended the analysis around these questions, and found evidence of autocorrelation. I have also found a specific periodic signal consistent with reports based on older data [1–3]. 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 [3,9]. A few comments are in order: biodiversity periodicity does not depend solely on precise timing for mass extinctions. Any time series can be decomposed into a sum of sinusoids; the question is whether any particular frequencies stand out above the rest. If so, they imply at least a partially repeating pattern. Standard methods are derived from Fourier analysis. Methods 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 [7,8]. This is the sample-standardized number of marine invertebrate genera, as published in [7] Figure 1. I have not made any cuts in the data. The cubic is the best-fit of the various simple alternatives, highlighting the general increase over time, with a pause centered around 300 Ma. Fits tested were linear, quadratic, cubic, exponential, logarithmic, power, and hyperbolic. Cubic has the highest Coefficient of Determination, either in an absolute sense or adjusted for the number of degrees of freedom. My interest is in whether any repeating patterns of fluctuation about the

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