Variation in colonization ability (comprising the dispersal and successful establishment of lineages in new regions) and its connection to species diversification may be one of the major reasons why clades vary widely in standing diversity. Diversity variation driven by colonization ability can be generated under two scenarios. Under a neutral model, high colonization ability enables some clades to colonize unoccupied areas and over time diversify into more species. Under a nonneutral model, some competitively superior clades are able to rapidly diversify into already occupied niches, both on continents they already occupy and on continents they are invading. Because entire lineages occasionally become extinct, including those that have colonized other landmasses, it can be difficult to distinguish between these models based on extant species. Here, we test these two alternatives using a species-level phylogeny of all extant and extinct species of the mammalian order Carnivora and related extinct groups. We find that species that colonize new continents leave more descendant species than noncolonizers and that colonizing species belong to clades that were diversifying faster than noncolonizers at the time of colonization. Our results suggest that variation in diversification may be partly driven by nonneutral processes with variable competitive ability between lineages. Our study highlights the importance of including extinct species in phylogenies when trying to understand evolutionary and biogeographic patterns.