Comparing Methods for Confidence Intervals on Stratigraphic Ranges Under Non-Uniform Recovery Potential

A variety of methods have been developed for estimating the true stratigraphic range of a fossil taxon. Some of these methods require the assumption of uniform fossil recovery potential, but may not perform well if this restrictive assumption is violated. Other methods are intended to work even if recovery potential is not uniform, but as a tradeoff such methods often give imprecise estimates. Here we compare a variety of methods using data simulated from uniform and non-uniform recovery functions. We find that existing methods are either highly sensitive to the assumption of uniform recovery, or else yield wide intervals that do not strongly constrain the true range. In fact, some existing methods do not even possess the minimal statistical property of consistency — i.e., the methods do not perform better as more data are collected. We introduce a new method, which simultaneously estimates both recovery potential and the true range. Our new method thus requires neither the assumption of uniform recovery, nor a priori knowledge of the recovery function. We demonstrate that the new method is able to estimate true ranges with relatively high precision under a variety of recovery functions.