Understanding how the traits, of lineages are related to diversification is key for elucidating the origin of variation in species richness. Here, we test whether traits are related to species richness among lineages of trees from all major biogeographical settings of the lowland wet tropics. We explore whether variation in mortality rate, breeding system and maximum diameter are related to species richness, either directly or via associations with range size, among 463 genera that contain wet tropical forest trees. For Amazonian genera, we also explore whether traits are related to species richness via variation in mean species-level range size within genera. Lineages with higher mortality rates - faster life-history strategies - have larger ranges in all biogeographic settings and have higher mean species-level range sizes in Amazonia. These lineages also have smaller maximum diameters and, in the Americas, contain dioecious species. In turn, lineages with greater overall range size have higher species richness. Our results show that fast life-history strategies influence species richness in all biogeographic settings because lineages with these strategies have greater range sizes. These links suggest that dispersal has been a key process in the evolution of the tropical forest flora.