Nonequilibrium evolution of volatility in origination and extinction explains fat-tailed fluctuations in Phanerozoic biodiversity

Fluctuations in biodiversity, large and small, pervade the fossil record, yet we do not understand the processes generating them. Here, we extend theory from nonequilibrium statistical physics to describe the fat-tailed form of fluctuations in Phanerozoic marine invertebrate richness. Using this theory, known as superstatistics, we show that heterogeneous rates of origination and extinction between clades and conserved rates within clades account for this fat-tailed form. We identify orders and families as the taxonomic levels at which clades experience interclade heterogeneity and within-clade homogeneity of rates, indicating that families are subsystems in local statistical equilibrium, while the entire system is not. The separation of timescales between within-clade background rates and the origin of major innovations producing new orders and families allows within-clade dynamics to reach equilibrium, while between-clade dynamics do not. The distribution of different dynamics across clades is consistent with niche conservatism and pulsed exploration of adaptive landscapes.