Abstract
Bounded estimates on divergence times between lineaes are crucial to the calculation of absolute rates of molecular evolution. Upper (minimum) bounds on divergence times are easily estimated based on earliest fossil finds. Lower (maximum) bounds are more difficult to estimate; the age of putative ancestors may be used, though in practice it is virtually impossible to distinguish ancestors from primitive sister groups, which do not, of logical necessit, consitute lower bounds on divergence times. Two relatively new approaches to estimating lower bounds directly assess the incompleteness of the fossil record. The first uses taphonomic control groups to distinguish real absences from nonpreservation, while the second, and probably more powerful, uses the quality of the fossil recored to estimate confidence intervals on the bases of stratigraphic ranges. For some groups, especially vertebrates, the inclusion or exclusion of problematic fossils can dramaticaly affect estimated lower bounds on divergence times, often swamping the uncertainties due to the incompleteness of the fossil record and/or corelation and dating errors. When datable paleogeographic events reflect ancient divisions of faunas, a lower bound on the divergence time of speices within a fauna can be established based on the geologic, rather than fossil, record. The fossil records of hominids, eutherianmammals, echinoids, and geese are used as examples.

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