In this paper, we design distributed spectrum access mechanisms with both complete and incomplete network information. We propose an evolutionary spectrum access mechanism with complete network information, and show that the mechanism achieves an equilibrium that is globally evolutionarily stable. With incomplete network information, we propose a distributed learning mechanism, where each user utilizes local observations to estimate the expected throughput and learns to adjust its spectrum access strategy adaptively over time. We show that the learning mechanism converges to the same evolutionary equilibrium on the time average. Numerical results show that the proposed mechanisms achieve up to 35 percent performance improvement over the distributed reinforcement learning mechanism in the literature, and are robust to the perturbations of users' channel selections.