The replicator equation, originally used in evolutionary game theory, has been widely applied in evolutionary biology and ecology to model the complex dynamics of multi-type interacting species, such as multi-species ecological ensembles or multi-strain microbial pathogens. In this seminar we explore aspects of the competitive dynamics encoded in the replicator equation, paying special attention to invader-driven systems, in which all species are proactive. We focus on relating properties of the fitness matrix to the quality of species dynamics and to the diversity of these systems at equilibrium, and we find a mechanism for the selection of the final set of surviving species.