Paleobiologists have used many different methods for estimating rates of origination and extinction. Unfortunately, all equations that consider entire age ranges are distorted by the Pull of the Recent, the Signor-Lipps effect, and simple edge effects. Attention has been paid recently to an equation of Foote's that considers counts of taxa either crossing the bottom and top of an interval or crossing one boundary but not the other. This generalized boundary-crosser (BC) method has important advantages but is still potentially subject to the major biases. The only published equation that circumvents all of them is the three-timer (3T) log ratio, which does so by focusing on a four-interval moving window. Although it is highly accurate it is noisy when turnover rates are very high or sampling is very poor. More precise values are yielded by a newly derived equation that uses the same counts. However, it also considers taxa sampled in a window's first and fourth intervals but missing from the third (i.e., gap-fillers). Simulations show that the 3T, gap-filler (GF), and BC equations yield identical values when sampling and turnover are uniform through time. When applied to Phanerozoic-scale marine animal data, 3T and GF agree well but the BC rates are systematically lower. The apparent reason is that (1) long-ranging but infrequently sampled genera are less likely to be split up by taxonomists and (2) the BC equation overweights taxa with long ranges. Thus, BC rates pertain more to rare genera that are likely to represent large clades whereas GF rates pertain more to actual species-level patterns. Given these results, all published turnover rates based either on genus-level data or on age ranges must be reconsidered because they may reflect taxonomic practices more strongly than the species-level dynamics of interest to biologists.
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