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Temporal variation in extinction risk and temporal scaling of extinction metrics

Many areas of paleobiological research require reliable extinction metrics. Branching-and-extinction simulations and data on Phanerozoic marine families and genera are used to investigate the relationship between interval length and commonly used extinction metrics. Normalization of extinction metrics for interval length is problematic, even when interval length is known without error, because normalization implicitly assumes some model of variation in extinction risk within an interval. If extinction risk within an interval were constant, or if it varied but played no role in the definition of stratigraphic intervals, then Van Valen's time-normalized extinction metric would provide a measure of average extinction risk that is effectively unbiased by interval length. When extinction risk varies greatly within an interval and interval boundaries are drawn at times of heavy extinction, extinction metrics that normalize for interval length are negatively correlated with interval length. Despite its intuitive appeal, the per-taxon extinction rate (proportional extinction per million years) is biased by interval length under a wide range of extinction models. Empirically, time-normalized extinction metrics for Phanerozoic families and genera are negatively correlated with interval length. This is consistent with an extinction model in which many times of very low risk are punctuated by a few times of very high risk which in turn determine stage boundaries. Origination and extinction patterns are similar, but origination intensity varies less among stages than extinction intensity. This observation has at least two plausible explanations: that origination episodes are more protracted than extinction episodes, and that biologic groups do not respond in unison to origination opportunities the way they seem to respond during extinction events. For families and genera, there is enough variation in extinction intensity among stages that stage length can be ignored when studying certain extinction patterns over the entire Phanerozoic.