The concept of species-level heritability is widely contested. Because it is most likely to apply to emergent, species-level traits, one of the central discussions has focused on the potential heritability of geographic range size. However, a central argument against range-size heritability has been that it is not compatible with the observed shape of present-day species range-size distributions (SRDs), a claim that has never been tested. To assess this claim, we used forward simulation of range-size evolution in clades with varying degrees of range-size heritability, and compared the output of three different models to the range-size distribution of the South American avifauna. Although there were differences among the models, a moderate-to-high degree of range-size heritability consistently leads to SRDs that were similar to empirical data. These results suggest that range-size heritability can generate realistic SRDs, and may play an important role in shaping observed patterns of range sizes.