  Community assembly is studied using individual-based multispecies models. The
models have stochastic population dynamics with mutation, migration, and
extinction of species. Mutants appear as a result of mutation of the resident
species, while migrants have no correlation with the resident species. It is
found that the dynamics of community assembly with mutations are quite
different from the case with migrations. In contrast to mutation models, which
show intermittent dynamics of quasi-steady states interrupted by sudden
reorganizations of the community, migration models show smooth and gradual
renewal of the community. As a consequence, instead of the $1/f$ diversity
fluctuations found for the mutation models, $1/f^2$, random-walk like
fluctuations are observed for the migration models. In addition, a
characteristic species-lifetime distribution is found: a power law that is cut
off by a "skewed" distribution in the long-lifetime regime. The latter has a
longer tail than a simple exponential function, which indicates an
age-dependent species-mortality function. Since this characteristic profile has
been observed, both in fossil data and in several other mathematical models, we
conclude that it is a universal feature of macroevolution.
