  We analyze with hydrodynamical simulations the evolution of galaxy clusters
in a cosmological environment. Power ratios (Buote \& Tsai 1995) are used to
quantitatively relate cluster morphologies to their dynamical states. The
simulated clusters follow the same ``evolutionary track'' obeyed by a sample of
low-redshift $(z<0.2)$ ROSAT PSPC clusters (Buote \& Tsai 1996) indicating that
the detailed evolution of individual simulated clusters is consistent with
observed clusters. However, the distribution of simulated clusters (for
$\Omega=1$ standard Cold Dark Matter) along the evolutionary track at the
present epoch, which indicates a measure of the present balance of cluster
formation and relaxation rates, suggests that there are too many simulated
clusters with significant amounts of substructure to be consistent with the
observations, thus favoring a lower value of $\Omega$. Perpendicular to the
evolutionary track the distributions of observed and simulated clusters are
consistent which may indicate a success of the cosmological model (e.g., power
spectrum). Analysis of high-redshift simulated clusters suggests that the
distribution of clusters both along and perpendicular to the evolutionary track
is effectively constant from $z\sim 0.6$ to the present but changes
significantly for $z > 0.6$.
