The Adaptation Front Equation Explains Innovation-Driven Taxonomic Turnovers and Living Fossilization

Evolutionary taxonomic turnovers are often associated with innovations beneficial in various ecological niches. Such innovations can repeatedly occur in species occupying optimum niches for a focal species group, resulting in their repeated diversifications and species flows from optimum to suboptimum niches, at the expense of less innovated ones. By combining species packing theory and adaptive dynamics theory, we develop an equation that allows analytical prediction for such innovation-driven species flows over a niche space of arbitrary dimension under a unimodal carrying capacity distribution. The developed equation and simulated evolution show that central niches (with the highest carrying capacities) tend to attain the fastest innovation speeds to become biodiversity sources. Species that diverge from the central niches outcompete the indigenous species in peripheral niches. The outcompeted species become extinct or evolve directionally toward far more peripheral niches. Because of this globally acting process over niches, species occupying the most peripheral niches are the least innovated and have deep divergence times from their closest relatives, and thus they correspond to living fossils. The extension of this analysis for multiple geographic regions shows that living fossils are also expected in geographically peripheral regions for the focal species group.