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1 Department of Statistics, Harvard University, Cambridge, Massachusetts 02138
2 Present address: Department of Mathematics and Statistics, Swarthmore College, Swarthmore, Pennsylvania 19081. scwang{at}swarthmore.edu
3 Museum of Comparative Zoology, Harvard University, Cambridge, Massachusetts 02138. cmarshall{at}oeb.harvard.edu
Marshall (1995) used the distribution of the endpoints of 50% range extensions added to the stratigraphic ranges of individual taxa to bracket the position of an extinction boundary. Here we describe two improvements to Marshall's method. First, we show that more precise estimates of the position of such a boundary may be obtained using range extensions with confidence levels of less than 50% (e.g., 20%). Second, we introduce a new method of calculating confidence intervals that explicitly takes into account the position of the highest fossil find. Incorporating these improvements leads to confidence intervals for simulated data sets that are approximately four times more precise than those obtained by using Marshall's (1995) original method and approximately twice as precise as those using other published methods. We provide a look-up table that shows for different numbers of taxa the confidence level that should be used to maximize the precision of the estimated position of the extinction boundary, while ensuring that the boundary still lies within the stratigraphic interval bounded by at least one range extension. Unlike some other methods, our method is nonparametric and does not make the restrictive assumption of uniform preservation and recovery potential. We apply the method to Macellari's (1986) ammonite data from the late Cretaceous of Seymour Island, Antarctica.
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