in which cladistics outperformed stratocladistics, the closest topology was, on average, hidden among 227.5 topologies, compared with 1.4 for stratocladistics. Comparisons of average and minimum CFIs (Fig. 2, B and C) favor stratocladistics even more strongly. To examine the relation between the variables in our study and values of CFImax, we grouped the data in Fig. 2A by percent OTUloss and by F and B (Tables 1 and 2). Each group of results was subjected to a sign test to determine if CFImax was significantly higher for one method or the other (18). In most cases, mean CFImax is higher for stratocladistics and the sign tests are highly significant (P , 0.001) in favor of stratocladistics. In three cases, mean CFImax is higher for cladistics, but the differences from CFImax for stratocladistics are not significant. Of the remaining six sign tests that were not significant, only one (OTU-loss 5 80%) did not have more cases with higher stratocladistic CFImax than cladistic CFImax. Thus, stratocladistics generally outperforms cladistics to a statistically significant degree, and this outcome is largely independent of the evolutionary model and completeness of the fossil record assumed. Our results lay to rest the notion that an incomplete fossil record yields no clues for inferring phylogeny. The stratigraphic order of taxa preserved in the fossil record is a complex function of presence and absence controlled by many physical, chemical, and biological factors. To ignore this pattern or dismiss this class of data when it does not agree with a phylogenetic hypothesis makes an unwarranted “covering assumption” (5) that masks the real weightof-evidence and encourages less than evenhanded treatment of data. Stratocladistic hypotheses attempt to explain both the distribution of characters among taxa and the distribution of taxa through time. By doing this, stratocladistic hypotheses explain more features of the natural world and hence have greater explanatory power than purely cladistic hypotheses.