The predictability of genetic structure from social structure and differential mating success was tested in wild baboons. Baboon populations are subdivided into cohesive social groups that include multiple adults of both sexes. As in many mammals, males are the dispersing sex. Social structure and behavior successfully predicted molecular genetic measures of relatedness and variance in reproductive success. In the first quantitative test of the priority-of-access model among wild primates, the reproductive priority of dominant males was confirmed by molecular genetic analysis. However, the resultant high short-term variance in reproductive success did not translate into equally high long-term variance because male dominance status was unstable. An important consequence of high but unstable short-term variance is that age cohorts will tend to be paternal sibships and social groups will be genetically substructured by age.