Explaining the diversity in geographic range sizes among species is a central goal of ecological and evolutionary studies. We tested species age as an explanation of range size variation within a group of understory shrubs in the Neotropics (Psychotria subgenus Psychotria, Rubiaceae). We distinguish between range occupancy (filling an occupied area) and range extent (maximum distances dispersed). We used Bayesian relaxed-clock dating of molecular sequence data to estimate the relative age of species, and we used species distribution modeling to predict species' potential ranges. If the range sizes of species are limited by time for dispersal, we hypothesize that older species should have (1) larger realized range occupancies and realized range extents than younger species, (2) filled a greater proportion of their potential range occupancies, and (3) colonized a greater proportion of their potential range extents. We found (1) a significant but weak positive relationship between species age versus both realized range occupancy and realized range extent, (2) no relationship between species age and filling of potential range occupancies, but (3) that older species had colonized a significantly greater proportion of their potential range extents than younger species. Our results indicate that a time-for-dispersal effect can limit the extent of ranges of species but not necessarily their occupancies.