Major discrepancies have been noted for some time between fossil ages and molecular divergence dates for a variety of taxa. Recently, systematic trends within avian clades have been uncovered. The trends show that the disparity is much larger for mitochondrial DNA than for nuclear DNA, also that it is larger for crown fossil dates than stem fossil dates. It has been argued that this pattern is largely inconsistent with incompleteness of the fossil record as the principal driver of the disparity. A case is presented that given the expected mutations from a fluctuating background of astrophysical radiation from such sources as supernovae, the rate of molecular clocks is variable and should increase back to a few Ma, before returning to the long-term average rate. This is a possible explanation for the disparity. One test of this hypothesis is to look for an acceleration of molecular clocks 2 to 2.5 Ma due to one or more moderately nearby supernovae known to have happened at that time. Another is to look for reduced disparity in benthic organisms of the deep ocean. In addition, due to the importance of highly penetrating muon irradiation, the disparity should be magnified for megafauna.