Per-capita change rates of the Phanerozoic Earth-life system exhibited Zipf distributions

The Zipf distribution is widespread in physical and biological systems on the modern Earth; whether such distributions existed in the ancient Earth-life system, however, remains understudied. Here I demonstrate that per-capita change rates (PCCRs) of the atmospheric CO₂ level, global average temperature, genus richness, and body size during the Phanerozoic exhibited Zipf distributions. Statistical analyses, including the goodness-of-fit test, likelihood-ratio test, and complementary cumulative distribution function (CCDF), support these Zipf distributions. Moreover, correlation analyses show that these environmental variables and biological metrics are correlated while their PCCRs are not, suggesting that Zipf distributions in PCCRs are unlikely to directly connect to each other; instead, there probably existed a set of common but unknown factors responsible for these systematic Zipf distributions in PCCRs. The results in this study offer new perspectives on the evolutionary patterns of the ancient Earth-life system.