A UNIFIED QUANTITATIVE FRAMEWORK LINKING EXTINCTION MAGNITUDE, SELECTIVITY, AND EFFECT ON BIOTIC COMPOSITION

Mass extinctions are defined as times of unusually severe losses of taxonomic richness. However, richness recovered after even the biggest events, such that the longer-term effects of extinction relate to changes in the taxonomic/ecologic composition of a biota. The effects of an extinction event on composition depend on both magnitude and selectivity—that is, the intensity of the event and the variation in intensity among taxonomic/functional groups or with respect to some other parameter. An increase in either selectivity or magnitude will force greater changes in biotic composition. We present a new framework for quantifying the contributions of magnitude and selectivity in driving change in biotic composition, construed as the relative taxonomic richness of different clades or functional groups. The method is derived using Foote’s boundary-crosser metric, but should be applicable to rates that are measured on a similar scale. Extinction magnitude (M) is measured as the mean extinction rate of the clades under consideration. The change in taxonomic composition resulting from extinction (C) is measured as the standard deviation of the clade-level rates, which we show equals the Euclidean distance between the composition of pre- and post-extinction biotas in log space, after standardizing for total richness. Extinction selectivity (S) is defined as the coefficient of variation of the clade-level extinction rates (S = C / M). Thus, change in biotic composition is the product of magnitude and selectivity (C = M ∙ S). The multiplicative relationship means that an extinction event characterized by high magnitude and high selectivity will have immense effects on biotic composition, whereas a low value for either will blunt the effects of extinction on composition. We apply this method to the Phanerozoic record of extinction in marine animals. At the phylum level, mass extinctions are not more selective than background intervals. Among events of moderate to high magnitude, the end-Permian extinction and Early Triassic recovery interval stand out as unusually selective. The unique macroevolutionary importance of the Permian-Triassic transition derives from the coincidence of high magnitude and selectivity.