Extinction and the temporal distribution of macroevolutionary bursts.

Phenotypic evolution through deep time is slower than expected from microevolutionary rates. This is the paradox of stasis. Previous models suggest stasis occurs because populations track adaptive peaks that remain relatively stable on million-year intervals, raising the equally perplexing question of why these large changes are so rare. Here, we consider the possibility that peaks can move more rapidly than populations can adapt, resulting in extinction. We model peak movement with explicit population dynamics, parameterized with published microevolutionary estimates. Allowing extinction greatly increases the parameter space of peak movements that yield the appearance of stasis observed in real data through deep time. Extreme peak displacements, regardless of their frequency, will rarely result in an equivalent degree of trait evolution because of extinction. Thus, larger peak displacements will rarely be inferred using trait data from extant species or observed in fossil records. Our work highlights population ecology as an important contributor to macroevolutionary dynamics, presenting an alternative perspective on the paradox of stasis, where apparent constraint on phenotypic evolution in deep time reflects our restricted view of the subset of earth's lineages that were fortunate enough to reside on relatively stable peaks.