A species may overlap with a mosaic of species across its geographic range. Many types of species interaction cause selection on mating traits, but their role in generating within-species divergence has been neglected. The pattern of reproductive character displacement (RCD) has been classically attributed to reinforcement, a process driven by selection against hybridisation. Recent reinforcement research shows that sexual isolation can result between displaced and non-displaced populations. We argue that RCD (and hence potentially speciation) among populations can be generated by a variety of fundamental species interactions beyond reinforcement. We unify these interactions under one process of mating trait divergence and speciation ('RCD speciation'). This process can occur in many geographic settings. Because selection is acting directly on mating traits, rapid speciation can result involving little differentiation in other traits. This pattern of diversification is seen in many groups and regions, and has previously been attributed to sexual selection alone.