Aim Why are some species widespread and abundant while others are restricted and rare? Darwin (1859) and others have claimed that some species have become widespread because they are competitively dominant over related, geographically restricted species. An alternative hypothesis is that wide-ranging species are ecological generalists that have been able to opportunistically colonize many kinds of new, disturbed and/or marginal habitats, whereas related narrow-ranging species are ecological specialists that competitively dominate specific kinds of relatively stable habitats/resources. We tested these opposing hypotheses using small mammals, for which considerable data on competitive interactions and geographical range sizes are available.Location North America, Europe, Asia, Africa and Australia.Methods We analysed data for forty-three competitive interactions between congeneric species in twenty genera, seven families, and four orders of small mammals. Competitive dominance was identified from both field and laboratory experiments, which were lumped because they showed similar results.Results We found that (1) when all studies were analysed as individual data points, species with smaller geographical ranges tended to be dominant over congeneric species with larger geographical ranges, (2) lumping of interaction pairs sharing one or more of the same species yielded a similar result, (3) lumping all interactions involving the same genus also showed the same result, although it was not statistically significant, probably because of the small sample size resulting from this attempt to remove phylogenetic effects. Examination of the taxonomic relationships of the studied genera revealed no obvious phylogenetic effects on the relationship of competitive dominance with geographical range size. Furthermore, although body-size differences appeared to have played a role in the results observed, they cannot completely explain them.Main conclusions We tentatively conclude that Darwin's hypothesis is falsified for small mammals, while the alternative hypothesis that geographically restricted species are competitively dominant over related widespread species receives some support.