Although available paleobiological data indicate that the geographic ranges of marine species are maintained throughout their entire observable durations, other evidence suggests, by contrast, that the ranges of higher taxa expand as they age, perhaps in association with increased species richness. Here, I utilize a database of Ordovician genus occurrences collected from the literature for several paleocontinents to demonstrate that a significant aging of the global biota during the Ordovician Radiation was accompanied by a geographic and environmental expansion of genus ranges. The proportion of genera occurring in two or more paleocontinents in the database, and two or more environmental zones within a six-zone onshore-offshore framework, increased significantly in the Caradocian and Ashgillian. Moreover, widespread genera tended to be significantly older than their endemic counterparts, suggesting a direct link between their ages and their environmental and geographic extents. Expansion in association with aging was corroborated further by demonstrating this pattern directly among genera that ranged from the Tremadocian through the Ashgillian. Taken together, these results are significant not only for what they reveal about the kinetics of a major, global-scale diversification, but also for what they suggest about the interpretation of relationships between diversity trends at the alpha (within-community) and beta (between-community) levels.