Statistical analyses of extinction in the marine fossil record

Abstract

Several questions regarding the nature of extinction in the fossil record of marine invertebrates were investigated using statistical methods and familial diversity data. First, a series of analyses were performed to determine whether the magnitudes of mass extinctions were statistically distinguishable from the magnitudes of background extinctions. The expected proportions of familial extinction for each order in a stage (based on an estimate of the ordinal probability of familial extinction for each of 134 orders) were compared to the observed proportions of familial extinction in the stage using a simple X2 goodness-of-fit test. The results indicate that eight stages in the Phanerozoic had a statistically significant excess of extinction. A second set of X2 analyses was done using estimates of per taxon familial extinction rates for the orders, rather than familial extinction probabilities. The X2 tests resulted in four additional stages that contained a statistically significant surplus of familial extinction. To test the results further, a set of bootstrapping analyses was done for each of five different extinction metrics. Two stages, the Ashgillian and the Dzhulfian, had a statistically significant excess of extinction in both Xl analyses and in four out of five of the bootstrapping analyses. Two additional stages, the Guadelupian and the Maestrichtian, had a statistically significant magnitude of extinction in every analysis. Thus, the results provide strong support for the argument that mass extinctions comprise a distinct group of evolutionary phenomena. <p>Familial extinction rates have declined from the early Phanerozoic to the Recent. Some have suggested that familial extinction rates have been constant through time within most major taxonomic groups and that the decline in familial extinction rates is the result of the successive elimination of groups with relatively high familial extinction rates (a process referred to as taxon sorting). A model of total familial extinction rates through time based on stationary probabilities of familial extinction within orders closely mimics the observed decline in total familial extinction rates supporting the taxon sorting hypothesis. Linear regressions of the familial extinction probabilities of orders versus the geologic time of both their first and their last occurrences suggest that the observed decline in extinction rates resulted from the early elimination of orders with characteristically high probabilities of extinction, and the later origination of orders with relatively low probabilities of extinction. In addition, a statistical analysis comparing the evolutionary volatility of extinct versus extant taxa suggests that extinct orders had greater volatility in their diversity histories which may have contributed to their early demise. <p>The taxonomic selectivity of both background and mass extinctions was investigated using simple X2 analyses. The results suggest that familial extinction during mass extinctions was taxonomically more selective than extinction during background extinctions. In addition, the magnitude of familial extinction experienced by an order in a stage was compared to the familial extinction probability estimated for the order using the binomial theorem. Then, those orders that suffered an unusual excess of familial extinction during particular stratigraphic stages were separated from the remaining orders in the stage. The results suggest that sessile filter feeders (particularly those groups important in ancient reefs) and pelagic groups suffered the greatest during intervals of mass extinction. <p>Finally, the potential relationship of familial diversity to both sea level and I7Sr/86Sr ratios was statistically examined using linear regression techniques. No statistically significant correlation was found between sea level and familial diversity. However, a significant correlation was discovered between diversity and I7Sr /86Sr ratios. Strontium ratios are believed to be an indirect measure of the aerial extent of exposed continental crust. Thus, the relationship between 17 Sr/86Sr ratios and diversity suggests that familial diversity has been a function of 1) the aerial extent of epeiric seas and 2) the amount of clastic material being supplied to these seas. The last factor could have affected familial diversity by restricting normally diverse, shallow carbonate environments.