RANDOM WALKS IN THE HISTORY OF LIFE

The simplest null hypothesis for evolutionary time series is that the observed data form a random walk. We examined whether aspects of Sepkoski's compilation of marine generic diversity depart from a random walk using statistical tests from econometrics. Throughout most of the Phanerozoic, the random walk null hypothesis is not rejected for marine diversity, accumulated origination or accumulated extinction. The pervasive overall result is perhaps surprising because the analysis of Phanerozoic diversity, origination, and extinction has revealed a variety of interesting events, patterns and trends. Although our result may not obviate the need to invoke complex mechanisms to explain these apparent trends, it at least suggests that caution needs to be exercised when looking for trends in these time series. One interpretation of our results could be that apparent trends in the history of life might be random fluctuations; however, this is not the sole interpretation. Notably, a significant correlation between marine fractional origination rate and estimates of Phanerozoic atmospheric carbon dioxide levels was described in [Proc. Natl. Acad. Sci. USA. 99:7832-7835 ]. The carbon dioxide time series also exhibits random walk character similar to that of marine diversity, but with only 58 data points this result requires further investigation. Thus, the failure to reject a random walk does not require that causality is absent, but instead could mean aspects of marine diversity and macroevolution are themselves correlated with environmental variables that follow a random walk. The only departure from the general random walk pattern involves the diversity and accumulated origination time series which do not conform to a random walk for roughly the last 50-75 million years. These deviations are probably not related to sampling issues or the pull of the recent. Instead they may reflect real changes in the biota that occurred in the Cenozoic.