On the declining extinction and origination rates of fossil taxa

Abstract

The per-stage extinction rate is the product of the per-taxon extinction rate and stage length, and the per-stage origination rate is defined similarly. These rates decline from ancient to recent times because of the pull of the Recent, because there is more young than old fossiliferous rock, and because average stage length increases from the recent to the past. More specifically, the present model assumes that the graphs of ln(per-stage extinction rate) and ln(per-stage origination rate) versus geologic time have slope zero in the absence of sampling biases, and shows how sampling biases cause both these graphs to appear to have slope min(h,q) + s in the distant past, where h and q are the fossil loss and actual per-taxon extinction rates, and the stratigraphic constant, s, quantifies how stage length changes through time.Although the per-stage rates of bivalve families and marine invertebrate genera decline toward the recent, the magnitudes of these declines are entirely consistent with what the present model predicts sampling biases will produce. Hence there is no need to postulate a biological explanation for these patterns.