OPTIMAL METHODS FOR ESTIMATING THE STRATIGRAPHIC POSITION OF A MASS EXTINCTION BOUNDARY

Even when a collection of taxa experiences mass (simultaneous) extinction, the distribution of last appearances in the fossil record may seem gradual due to the Signor-Lipps effect, making it difficult to estimate the stratigraphic position corresponding to the mass extinction boundary. Here we describe methods that account for the incompleteness of the fossil record in order to estimate the stratigraphic position of a mass extinction boundary, and describe conditions under which each is optimal.

First, assuming uniform preservation and recovery potential, we generalize the method of Strauss and Sadler (1989) and show that estimates based on the highest fossil horizon are optimal, having the smallest variance of all possible estimates. Next, when uniform preservation and recovery cannot be assumed, we provide a general methodology for calculating optimal estimates. Our approach takes a weighted average of estimates calculated from individual taxa, and uses constrained optimization to find weights that yield the smallest possible variance among unbiased linear estimators. We also propose a framework for studying hypothesized mass extinctions that does not assume simultaneous extinction. Instead, we aim to estimate the "shape" of the series of extinction events. In particular, we are interested in the distance between the first and last taxon extinctions; if this distance is sufficiently small (smaller than stratigraphic resolution), then the hypothesis of a mass extinction is supported. Examples are given from Macellari's (1986) ammonite data from Seymour Island, Antarctica.