  The terrestrial fossil record shows a significant variation in the extinction
and origination rates of species during the past half billion years. Numerous
studies have claimed an association between this variation and the motion of
the Sun around the Galaxy, invoking the modulation of cosmic rays, gamma rays
and comet impact frequency as a cause of this biodiversity variation. However,
some of these studies exhibit methodological problems, or were based on coarse
assumptions (such as a strict periodicity of the solar orbit). Here we
investigate this link in more detail, using a model of the Galaxy to
reconstruct the solar orbit and thus a predictive model of the temporal
variation of the extinction rate due to astronomical mechanisms. We compare
these predictions as well as those of various reference models with
paleontological data. Our approach involves Bayesian model comparison, which
takes into account the uncertainties in the paleontological data as well as the
distribution of solar orbits consistent with the uncertainties in the
astronomical data. We find that various versions of the orbital model are not
favored beyond simpler reference models. In particular, the distribution of
mass extinction events can be explained just as well by a uniform random
distribution as by any other model tested. Although our negative results on the
orbital model are robust to changes in the Galaxy model, the Sun's coordinates
and the errors in the data, we also find that it would be very difficult to
positively identify the orbital model even if it were the true one. (In
contrast, we do find evidence against simpler periodic models.) Thus while we
cannot rule out there being some connection between solar motion and
biodiversity variations on the Earth, we conclude that it is difficult to give
convincing positive conclusions of such a connection using current data.
