Many social animals form linear dominance hierarchies, with a clear rank order among group members. Such hierarchies can profoundly influence health and access to resources, but the mechanisms underlying hierarchy formation and maintenance remain unclear. Do individual dominance ranks simply emerge from individual attributes – such as fighting ability? Or are linear hierarchies the product of social self-organization processes such as winner and loser effects – i.e. the phenomenon in which winners become more likely to win in subsequent encounters, and losers become more likely to lose? Here, we present the first evidence for social self-organization processes in a wild animal population. Specifically, we testedfor winner and loser effects in male hierarchy dynamics in the Amboseli baboons, using a novel statistical approach based on the Elo rating method. Elo ratings, used for everything from animal hierarchies to sports tournaments, enabled us to detect winner and loser effects in uncontrolled group settings, which had not been done before - all winner and loser effects to date had been demonstrated in captive experiments. Our results demonstrate (1) the presence of winner and loser effects and (2) that individual susceptibility to such effects may have a genetic basis. Specifically, we found that hybrid males were less influenced, in their future interactions, by past wins and losses than were yellow males.  Together, our results show that both social self-organization dynamics and prior attributes can combine to influence hierarchy dynamics even when agonistic interactions are strongly influenced by differences in individual attributes. We hypothesize that, despite variation in individual attributes, winner and loser effects exist (1) because these effects could be particularly beneficial when fighting abilities in other group members change over time, and (2) because the coevolution of prior attributes and winner and loser effects maintains a balance of both effects.