A fundamental challenge to our understanding of biodiversity is to explain why some groups of species undergo adaptive radiations, diversifying extensively into many and varied species, whereas others do not(1,2). Both extrinsic environmental factors (for example, resource availability, climate) and intrinsic lineage-specific traits (for example, behavioural or morphological traits, genetic architecture) influence diversification, but few studies have addressed how such factors interact. Radiations of cichlid fishes in the African Great Lakes provide some of the most dramatic cases of species diversification. However, most cichlid lineages in African lakes have not undergone adaptive radiations. Here we compile data on cichlid colonization and diversification in 46 African lakes, along with lake environmental features and information about the traits of colonizing cichlid lineages, to investigate why adaptive radiation does and does not occur. We find that extrinsic environmental factors related to ecological opportunity and intrinsic lineage-specific traits related to sexual selection both strongly influence whether cichlids radiate. Cichlids are more likely to radiate in deep lakes, in regions with more incident solar radiation and in lakes where there has been more time for diversification. Weak or negative associations between diversification and lake surface area indicate that cichlid speciation is not constrained by area, in contrast to diversification in many terrestrial taxa(3). Among the suite of intrinsic traits that we investigate, sexual dichromatism, a surrogate for the intensity of sexual selection, is consistently positively associated with diversification. Thus, for cichlids, it is the coincidence between ecological opportunity and sexual selection that best predicts whether adaptive radiation will occur. These findings suggest that adaptive radiation is predictable, but only when species traits and environmental factors are jointly considered.