Sorting unsigned permutations by reversals is an NP-hard optimization problem with applications in computational molecular biology. Several approximation and metaheuristic algorithms were proposed, among them, in a previous work, a competitive genetic algorithm and its parallel version using island models were proposed. In this paper, focusing on improving accuracy, new island models are proposed by diversifying the distribution of genetic material between islands through static and dynamic communication topologies. In static topologies, communication between islands is predefined and maintained during the computation, while in dynamic topologies the communication is continuously modified. The proposed island models use parallelism in a global and a local level, in which respectively, the exchange of individuals between islands and the fitness computation occurs. Results from the experiments performed with randomly generated synthetic permutations show that parallel island models using both dynamic and static communication topologies outperform parallel approaches found in the literature in terms of run-time as well as accuracy.