A more precise speciation and extinction rate estimator
A new turnover rate metric is introduced that combines simplicity and precision. Like the related three-timer and gap-filler equations, it involves first identifying a cohort of taxa sampled in the time interval preceding the one of interest (call the intervals i 0 and i 1 ). Taxa sampled in i 0 and i 1 are two-timers (t 2 ); those sampled in i 0 and i 2 but not i 1 are part-timers (p); and taxa sampled only in either i 1 , i 2 , or i 3 are newly notated here as either s 1 , s 2 , or s 3 . The gap-filler extinction proportion can be reformulated as (s 1 −s 3 )/(t 2 +p). The method proposed here is to substitute s 3 with the second-highest of the three counts when the expected ordering s 1 ≥s 2 ≥s 3 is violated. In simulation, this new estimator yields values that are highly correlated with those produced by the gap-filler equation but more precise. In particular, it rarely produces highly negative values even when sample sizes are quite small. It is mildly upwards biased when sampling is extremely poor and turnover rates are extremely low, but it is otherwise highly accurate. Examples of Phanerozoic extinction rates for four major marine invertebrate groups are given to illustrate the method’s improved precision. Based on the results, the procedure is recommended for general use.