Computational studies of an evolutionary model on a rugged phenotype landscape suggest the existence of a phase transition as the maximum mutation size is varied. I will discuss more recent results that show phase transition behavior in on a neutral phenotype landscape, in which all organisms have equal fitness (i.e., equal numbers of offspring). This behavior occurs for organisms that undergo assortative mating and also in a model where organisms reproduce by bacterial "fission". In contrast, the phase transition does not occur when the organisms mate randomly. The transition takes the system from a state of survival to a state of extinction, and is thus an absorbing, non-equilibrium transition. The system can be characterized by critical exponents that coincide with those of the directed percolation (DP) universality class. Finally, I will present evidence that an ordinary percolation transition occurs in the system as well, for slightly different values of the critical parameter than those at which the DP transition is observed, and I will discuss the implications of the model for the problem of multi-level selection.