Non-equilibrium evolution of volatility in origination and extinction explains fat-tailed fluctuations in Phanerozoic biodiversity.

Fluctuations in biodiversity, large and small, are pervasive in the fossil record, yet we do not understand the processes generating them. Here we extend theory from non-equilibrium statistical physics to describe the previously unaccounted for fat-tailed form of fluctuations in marine invertebrate richness through the Phanerozoic. Using this theory, known as superstatistics, we show that the simple fact of heterogeneous origination and extinction rates between clades and conserved rates within clades is sufficient to account for this fat-tailed form. We identify orders and the families they subsume as the taxonomic level at which clades experience inter-clade heterogeneity and within clade homogeneity of rates. Following superstatistics we would posit that orders and families are subsystems in local statistical equilibrium while the entire system is not in equilibrium. The separation of timescales between background origination and extinction within clades compared to the origin of major ecological and evolutionary innovations leading to new clades allows within-clade dynamics to reach equilibrium, while between-clade diversification is non-equilibrial. This between clade non-equilibrium accounts for the fat-tailed nature of the system as a whole. The distribution of shifts in diversification dynamics across orders and families is consistent with niche conservatism and pulsed exploration of adaptive landscapes by higher taxa. Compared to other approaches that have used simple birth-death processes, simple equilibrial dynamics, or non-linear theories from complexity science, superstatistics is superior in its ability to account for both small and extreme fluctuations in the richness of fossil taxa. Its success opens up new research directions to better understand the evolutionary processes leading to stasis in an adaptive landscape interrupted by innovations that lead to novel forms.