We study macroevolutionary dynamics by extending microevolutionary competition models to long timescales. It has been shown that for a general class of competition models, gradual evolutionary change in continuous phenotypes (evolutionary dynamics) can be nonstationary 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 nonequilibrium trajectories in phenotype space. We combine these lines of thinking by studying long-term coevolutionary dynamics of emerging lineages in multidimensional phenotype spaces. We use a statistical approach to investigate the evolutionary dynamics of many different systems. We find (1) that, for a given dimension of phenotype space, the coevolutionary dynamics tend to be fast and nonstationary for an intermediate number of coexisting lineages but tend to stabilize as the evolving communities reach a saturation level of diversity and (2) that 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.Regular 2015FONDECYTFONDECYT