Confidence intervals on stratigraphic ranges: partial relaxation of the assumption of randomly distributed fossil horizons

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Abstract
The equations for calculating classical confidence intervals on the end points of stratigraphic ranges are based on the restrictive assumption of randomly distributed fossil finds. Herein, a method is presented for calculating confidence intervals on the end-points of stratigraphic ranges that partially relaxes this assumption: the method will work for any continuous distribution of gap sizes, not just those generated by random processes. The price paid for the generality of the new approach is twofold: (1) there are uncertainties associated with the sizes of the confidence intervals, and (2) for large confidence values (e.g., 95%) a rich fossil record is required to place upper bounds on the corresponding confidence intervals. This new method is not universal; like the method for calculating classical confidence intervals it is based on the assumption that there is no correlation between gap size and stratigraphic position. The fossil record of the Neogene Caribbean bryozoan Metrarabdotos is analyzed with the new approach. The equations developed here, like those for classical confidence intervals, should not be applied to stratigraphic ranges based on discrete sampling regimes, such as those typically established from deep-sea drilling cores, though there are exceptions to this rule.