Organisms typically inhabit environments that are not entirely homogeneous, owing to local variation in habitat quality or environmental conditions. Some regions of a population can then consistently produce more offspring than others, resulting in a net flux of individuals from these regions into less productive parts of the population. However, the potential impacts of such source-sink dynamics are rarely incorporated into population genetic models. Here we show that even a small source with a modest net outflux into an otherwise large, stable population can dramatically reduce coalescence times and overall levels of genetic diversity. By contrast, variance and inbreeding effective population sizes may remain close to the census size. When demographic inference methods are applied to such populations, the inferred history often resembles a strong recent population expansion. Nonetheless, source-sink dynamics leave distinctive signatures of tree imbalance in coalescent genealogies that allow us to distinguish them from true population expansions. We further extend these analyses to scenarios involving multiple sources and to nonstationary settings in which sources emerge only transiently. Our results provide a potentially widespread mechanism for confounding demographic inference and reducing a species’ effective population size without requiring selection, high reproductive variance, or changes in census size over time.