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On balance, it is most parsimonious to infer that, although turnover may or may not be pulsed, interval boundaries do not coincide consistently with pulses, so continuous-time rates are more realistic than turnover proportions. These rates also have the advantage of removing the upper bound present in proportions, which can cause analytical artifacts. The continuous rates are not standardized for bin length in subsequent analyses because of the timescale’s relative homogeneity and the suggestion that doing so would bias them. For the current dataset, this technical problem is most likely moot, because there is no trend through time in bin length (ρ = 0.168, n.s.), and the standard deviation of logged bin lengths is modest (0.348).

Phanerozoic Decline in Extinction Rates

Again based largely on Sepkoski’s data, it has long been believed that there has been a decline through the Phanerozoic in both extinction rates (Raup and Sepkoski, 1982) and origination rates (Gilinsky and Bambach, 1987). These observed declines are robust to the choice of rate metrics (Foote, 1994b). Indeed, the new data clearly support a decline in both kinds of rates (extinction vs. time: ρ = 0.547, P < 0.001; origination vs. time: ρ = 0.533, P < 0.001). The patterns are influenced by extremely high values at the beginning of the time series that represent the Cambrian and earliest Ordovician (Fig. 11.1). However, removing these points does not greatly weaken the trends (extinction: ρ = 0.446, P = 0.003; origination: ρ = 0.465, P = 0.002). It is noteworthy that the correlations still appear even though the earlier studies (Raup and Sepkoski, 1982; Gilinsky and Bambach, 1987; Gilinsky, 1994) used finer timescales and therefore had greater statistical power. They also did not correct for sampling biases that would favor finding such a pattern.

To quantify the steepness of the declines, it is appropriate to perform a linear regression after log-transforming the turnover rates (Quinn, 1983; Foote, 1994), which is necessary because they are skewed and bounded by zero. For extinction and origination after the earliest Ordovician, the respective regression slopes are 0.201% and 0.158% per Myr, and the intercepts at 0 Ma are 0.218 and 0.282. Sepkoski’s data imply much steeper slopes and predict much lower extinction rates for the Neogene (Peters, 2006), which is expected because the data are influenced by the Pull of the Recent.

The drop in rates could be explained in at least four ways. First, a trend might be created by sampling biases or an increase through the Phanerozoic in the average durations of sampling bins (Pease, 1992). The former problem has been fully resolved by sampling standardization of the data and by the use of rate equations that are robust to edge effects



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