Ecological factors such as changing climate on land and interspecific competition have been debated as possible causes of postglacial Caribbean extinction. These hypotheses, however, have not been tested against a null model of climate‐driven postglacial area loss. Here, we use a new Quaternary mammal database and deep‐sea bathymetry to estimate species–area relationships (SARs) at present and during the Last Glacial Maximum (LGM) for bats of the Caribbean, and to model species loss as a function of area loss from rising sea level. Island area was a significant predictor of species richness in the Bahamas, Greater Antilles, and Lesser Antilles at all time periods, except for the Lesser Antilles during the LGM. Parameters of LGM and current SARs were similar in the Bahamas and Greater Antilles, but not the Lesser Antilles, which had fewer estimated species during the LGM than expected given their size. Estimated postglacial species losses in the Bahamas and Greater Antilles were largely explained by inferred area loss from rising sea level in the Holocene. However, there were more species in the Bahamas at present, and fewer species in the smaller Greater Antilles, than expected given island size and the end‐Pleistocene/early Holocene SARs. Poor fossil sampling and ecological factors may explain these departures from the null. Our analyses illustrate the importance of changes in area in explaining patterns of species richness through time and emphasize the role of the SAR as a null hypothesis in explorations of the impact of novel ecological interactions on extinction.