  We study macroevolutionary dynamics by extending microevolutionary
competition models to long time scales. It has been shown that for a general
class of competition models, gradual evolutionary change in continuous
phenotypes (evolutionary dynamics) can be non-stationary and even chaotic when
the dimension of the phenotype space in which the evolutionary dynamics unfold
is high. It has also been shown that evolutionary diversification can occur
along non-equilibrium trajectories in phenotype space. We combine these lines
of thinking by studying long-term coevolutionary dynamics of emerging lineages
in multi-dimensional phenotype spaces. We use a statistical approach to
investigate the evolutionary dynamics of many different systems. We find: 1)
for a given dimension of phenotype space, the coevolutionary dynamics tends to
be fast and non-stationary for an intermediate number of coexisting lineages,
but tends to stabilize as the evolving communities reach a saturation level of
diversity; and 2) the amount of diversity at the saturation level increases
rapidly (exponentially) with the dimension of phenotype space. These results
have implications for theoretical perspectives on major macroevolutionary
patterns such as adaptive radiation, long-term temporal patterns of phenotypic
changes, and the evolution of diversity.
