The megafaunal rodent Amblyrhiza inundatafrom Anguilla and St. Martin is often cited in lists of late Quaternary human-induced extinctions, but its date of disappearance has never been established. Here, we present a suite of uranium-series disequilibrium dates from three independent Amblyrhizasites in Anguilla, all of which cluster in marine isotope Stage 5. Thus, there is no indication that Amblyrhizasurvived into the late Holocene, when islands of the northern Lesser Antilles were first invaded by humans. We argue that the most probable cause of the extinction of Amblyrhizawas a failure of island populations to adjust to catastrophic reductions in available range which accompanied last interglacial sea-level maxima. We support this argument with quantitative extinction probability estimates drawn from persistence time models. Amblyrhizaexhibits body-size hypervariability, a common but underemphasized feature of island megafaunal species. We argue that hypervariability is a record of morphological response to oscillating natural selection, which in turn is driven by asymmetries in the relationship of population size, body mass, and persistence time. The fate of Amblyrhizastands in marked contrast to that of most other West Indian land mammals, whose losses increasingly appear to have been anthropogenically mediated.