We present a formal framework for modeling evolutionary dynamics with special emphasis on the generation of diversity through branching of the evolutionary tree. Fitness is defined as the long term growth rate which is influenced by the biotic environment leading to frequency-dependent selection. Evolution can be described as a dynamics in space with variable number of dimensions corresponding to the number of different types present. The dynamics within a subspace is governed by the local fitness gradient. Entering a higher dimensional subspace is possible only at a particular type of attractors where the population undergoes evolutionary branching.