The adaptive nature of sociality has long been a central question in ecology and evolution. However, the relative importance of social behavior for fitness, compared to morphology and environment, remains largely unknown. We assessed the importance of sociality for fitness (lamb production and survival) in a population of mark6d bighorn sheep (Ovis canadensis) over 16 years (n = 1022 sheep-years). We constructed social networks from observations (n = 38,350) of group membership (n = 3150 groups). We then tested whether consistent individual differences in social behavior (centrality) exist and evaluated their relative importance compared to factors known to affect fitness: mass, age, parental effects, and population density. Sheep exhibited consistent individual differences in social centrality. Controlling for maternal carryover effects and age, the positive effect of centrality in a social network on adult female lamb production and survival was equal or greater than the effect of body mass or population density. Social centrality had less effect on male survival and no effect on adult male lamb production or lamb survival. Through its effect on lamb production and survival, sociality in fission-fusion animal societies may ultimately influence population dynamics equally or more than morphological or environmental effects.