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Dominance rank in female chimpanzees correlates positively with reproductive success. Although a high rank obviously has an advantage for females, clear (linear) hierarchies in female chimpanzees have not been detected. Following the predictions of the socio-ecological model, the type of food competition should affect the dominance relationships among females. We investigated food competition and relationships among 11 adult female chimpanzees in the Taï National Park, Côte d'Ivoire (West Africa). We detected a formal linear dominance hierarchy among the females based on greeting behaviour directed from the subordinate to the dominant female. Females faced contest competition over food, and it increased when either the food was monopolizable or the number of competitors increased. Winning contests over food, but not age, was related to the dominance rank. Affiliative relationships among the females did not help to explain the absence of greetings in some dyads. However comparison post hoc among chimpanzee study sites made differences in the dominance relationships apparent. We discuss them based on social relationships among females, contest competition and predation. The cross-site comparison indicates that the differences in female dominance hierarchies among the chimpanzee study sites are affected by food competition, predation risk and observation time.