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An individual's reproductive success will depend on traits that increase access to mates, as well as the number of mates available. In most well-studied mammals, males are the larger sex, and body size often increases success in intra-sexual contests and thus paternity. In comparison, the determinants of male success in species with reversed sexual size dimorphism (RSD) are less well understood. Greater horseshoe bats (Rhinolophus ferrumequinum) exhibit RSD and females appear to exert mate choice when they visit and copulate with males in their underground territories. Here we assessed putative determinants of reproductive success in a colony of greater horseshoe bats during a 19-year period of rapid population growth. We genotyped 1080 bats with up to 40 microsatellite loci and assigned maternity to 99.5% of pups, and paternity to 76.8% of pups. We found that in spite of RSD, paternity success correlated positively with male size, and, consistent with our previous findings, also with age. Female reproductive success, which has not previously been studied in this population, was also age-related and correlated positively with individual heterozygosity, but not with body size. Remarkable male reproductive skew was detected that initially increased steadily with population size, possibly coinciding with the saturation of suitable territories, but then levelled off suggesting an upper limit to a male's number of partners. Our results illustrate that RSD can occur alongside intense male sexual competition, that male breeding success is density-dependent, and that male and female greater horseshoe bats are subject to different selective pressures.