Survivorship Analysis of Fossil Taxa When Real-Time Extinction Rates Vary: The Paleogene Planktonic Foraminifera

Abstract

For a survivorship curve to show a meaningful pattern, it is essential that a suitably homogeneous group is selected for analysis. If taxa have originated at different times in the geological record and have consequently experienced different extinction probabilities during the times that they existed, they do not constitute such a homogeneous group. A correction factor for variations in real-time extinction rates must be employed, as is described here. By application of the “corrected survivorship score,” it is shown that the Paleogene planktonic foraminifera exhibit a very strong survivorship pattern, namely an extinction probability that progressively increases with taxonomic longevity. That is to say, when extinction occurred, it was preferentially selective of older taxa. This is manifested as convexity in the survivorship curves. However, the pattern is degraded by variations in the real-time extinction rate, which causes straightening of the survivorship curves if they are calculated in the usual uncorrected way. If the law of constant extinction is to be tested for a given group, it is necessary either that stochastically constant real-time extinction rates are demonstrated or that variations in the extinction rate are corrected for in the manner described. As a separate issue, it is also essential that biologically meaningful taxa are analyzed. The convexity of planktonic foraminiferal survivorship curves is probably an artifact of the way evolving lineages have been subdivided in the application of typological taxonomy. Consequently, we are still a long way from being able to use survivorship analysis of planktonic foraminiferal data for adequately testing evolutionary models such as the Red Queen's hypothesis.