The diversity of life on Earth is controlled by hierarchical processes that interact over wide ranges of timescales1. Here, we consider the megaclimate regime2 at scales ≥1 million years (Myr). We focus on determining the domains of 'wandering' stochastic Earth system processes ('Court Jester'3) and stabilizing biotic interactions that induce diversity dependence of fluctuations in macroevolutionary rates ('Red Queen'4). Using state-of-the-art multiscale Haar and cross-Haar fluctuation analyses,...