Distributed coevolutionary Generative Adversarial Network (GAN) training has empirically shown success in overcoming GAN training pathologies. This is mainly due to diversity maintenance in the populations of generators and discriminators during the training process. The method studied here coevolves sub-populations on each cell of a spatial grid organized into overlapping Moore neighborhoods. We investigate the impact on the performance of two algorithm components that influence the diversity during coevolution: the performance-based selection/replacement inside each sub-population and the communication through migration of solutions (networks) among overlapping neighborhoods. In experiments on MNIST dataset, we find that the combination of these two components provides the best generative models. In addition, migrating solutions without applying selection in the sub-populations achieves competitive results, while selection without communication between cells reduces performance.