The recognition that past catastrophic events may have caused the simultaneous extinction of many taxa has prompted the development of statistical tests to determine the compatibility of the fossil record with such scenarios. Statistical tests necessitate simplifying assumptions, the most significant of which are continuous (as opposed to discrete) data in the sampling of the fossil record and random distribution of fossil occurrences because constant preservation potential and collecting intensity of fossils are assumed. The assumption of random distribution of fossil occurrences has been addressed quantitatively, but the continuity of data has not. The assumption of continuous data is not trivial, for although collecting may appear continuous, the resulting data are never strictly continuous because the stratigraphic positions of fossils are known with limited precision. For one test of simultaneous extinction, simulations demonstrate that the data behave in a less continuous manner as the occurrence rate increases, decreasing the reliability of the test at higher occurrence rates. Out of mathematical simplicity, nearly all tests use simultaneous extinction as the null hypothesis. However, even under ideal sampling circumstances, gradual extinctions that occurred over a sufficiently short stratigraphic interval are likely to be statistically indistinguishable from extinction occurring at a single horizon. Therefore, a range of gradual extinction scenarios will also be compatible with the fossil record even if the null hypothesis is not rejected. Because direct tests of gradual extinction scenarios have not yet been developed, simulations were used to determine the probability that an extinction occurring over a given stratigraphic distance with a given number of taxa will be statistically indistinguishable from extinction at a single horizon. The simulation results allow the test results to be used to define a range of extinction scenarios compatible with the fossil record. Finally, the simulation results were applied to two Late Cretaceous ammonite data sets. Although both data sets sufficiently approximate continuous sampling for the use of statistical tests, the method shows that the data are not always sufficient to rule out either stratigraphically simultaneous extinction or a literal reading of extinction rate as representing gradual or episodic extinction.
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