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Figure 7.2 Kill curves resulting from impacting bolides of varying diameters. Source: Adapted from Raup (1990).

shows the proportional gain or loss in the number of genera during each stage or substage interval. Manifestly, the 'big five' extinctions are the only extinction events with more than a 20 per cent proportional loss of genus diversity. Richard Bambach and his colleagues used two tests to detect continuity or discontinuity in the magnitude of extinction. First, they tested the smoothness of extinction magnitude intensity (1) for the whole Phanerozoic and (2) for the time since the Cambrian diversity plateau of low diversity and high turnover. Second, they compared the extinction magnitude for each interval with the distribution of extinction magnitudes for each segment of the timescale, based on the average high or low extinction rates to which the interval belongs. Only if extinctions in an interval satisfied both these criteria (that is, the interval is not part of a continuous and smooth distribution of extinction magnitudes and if the interval appears as an 'outlier' in magnitude compared with the other intervals in its particular segment - or 'stratigraphic neighbourhood' - of the time-scale) were they regarded as a truly global mass extinction.

Placing the mid-Ordovician to Recent extinction intensities in rank order showed a continuous and smooth curve broken only by six intervals at the upper end. These six intervals encompass four of the 'big five' (the end-Ordovician, the end-Permian, the end-Triassic, and end-Cretaceous), plus two intervals that bracket the terminal Permian interval. Further statistical tests, which involved calculating residuals from a nonlinear lowess (smoothing function) regression of the 88 post-Arenig intervals, showed that the end-Ordovician, end-Permian, and end-Cretaceous intervals have extinction magnitudes that lie outside the magnitudes expected if they were part of a continuum of extinction magnitudes. Figure 7.3(a) shows the proportion of extinction in each interval plotted against time. In general, the extinction intensity declines from high values in the Early and Mid Palaeozoic to lower values in the Jurassic through to the Cenozoic. However, the decline is not monotonic (indeed, with the Cambrian and Early Ordovician data excluded, a decline in extinction intensity is not evident). Rather, there are six stratigraphically coherent intervals of lower and higher proportions of extinctions, each of which constitutes a 'stratigraphic neighbourhood' (Figure 7.3(b)) (Bambach et al. 2004). Judging origination and extinction within these longer time slices, just three intervals stand out as distinct outliers - the end-Ordovician (late Ashgillian), the end-Permian (Guadalupian and Djhulfian), and the end-Cretaceous (late Maastrichtian). However, the late Frasnian (Late Devonian) and the late Norian/Rhaetian (at the close of the Triassic) are not out of line with the extinction intensities in the larger time slice to which they belong. A foremost conclusion of this detailed analysis is that there have been three, and not five, global mass extinctions. That is not to say that the end-Frasnian and end-Triassic lacked high extinction intensities, but extinction itself does not fully explain the strong drop of diversity at these times (Bambach et al. 2004).

The interplay between origination and extinction casts a revealing light on the nature of the three confirmed and two rejected mass extinctions. Extinction rates taken in isolation can be misleading. In 90 per cent of the intervals during the Phanerozoic, genus extinction rates ran at 8 per cent or more. When origination rates matched these loss rates, diversity stayed the same and the high extinction rates seem unremarkable. Likewise, when extinction rates ran at background levels but origination rates fell uncharacteristically low, diversity decreased without extinction rates having changed intensity. Figure 7.3(c) shows the actual interplay of origination and extinction rates based on Sepkoski's data set. Notice that for the end-Ordovician, end-Permian, and end-Cretaceous intervals, origination rates were a little to a lot higher than the average rates for their 'stratigraphic neighbourhoods', but the extinction rates were exceptionally high. This evidence supports the view that the three intervals are true global mass extinctions. Interestingly, had origination rates for these intervals been more typical of their stratigraphic neighbourhoods, diversity losses would have been even higher. However, for the late Frasnian and end-Triassic intervals, the imbalance between origination and extinction displays a more complicated pattern. During both intervals, origination rates were below the norm for their stratigraphic neighbourhoods and extinction rates were a little elevated. Overall, some 66 per cent of the late Frasnian diversity loss and 60 per cent of the end-Triassic diversity loss results from origination failure rather than raised extinction rates.

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