  We analytically study the dynamics of evolving populations that exhibit
metastability on the level of phenotype or fitness. In constant selective
environments, such metastable behavior is caused by two qualitatively different
mechanisms. One the one hand, populations may become pinned at a local fitness
optimum, being separated from higher-fitness genotypes by a {\em fitness
barrier} of low-fitness genotypes. On the other hand, the population may only
be metastable on the level of phenotype or fitness while, at the same time,
diffusing over {\em neutral networks} of selectively neutral genotypes.
Metastability occurs in this case because the population is separated from
higher-fitness genotypes by an {\em entropy barrier}: The population must
explore large portions of these neutral networks before it discovers a rare
connection to fitter phenotypes.
  We derive analytical expressions for the barrier crossing times in both the
fitness barrier and entropy barrier regime. In contrast with ``landscape''
evolutionary models, we show that the waiting times to reach higher fitness
depend strongly on the width of a fitness barrier and much less on its height.
The analysis further shows that crossing entropy barriers is faster by orders
of magnitude than fitness barrier crossing. Thus, when populations are trapped
in a metastable phenotypic state, they are most likely to escape by crossing an
entropy barrier, along a neutral path in genotype space. If no such escape
route along a neutral path exists, a population is most likely to cross a
fitness barrier where the barrier is {\em narrowest}, rather than where the
barrier is shallowest.
