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The issue on female ranks was still in suspense owing to a series of social factors.Until recently,female social ranks and hierarchical steepness which was not just used as the main characteristic of groups structure but it also represent the degree of discrepancy of apply and demand were achieved in a quantitative level.Moreover,according to female hierarchical steepness biological market theory gave us some testable models to explain pattems of grooming exchange.During mating season (from September to December 2011),we used focal animal sampling and all occurrences sampling to observe female grooming and aggressive behaviors in two provisioned free-ranging Tibetan macaques (Macaca thibetana) groups (Yulingken A1 and Yulingken A2),respectively.The purpose was to discuss the influence of the steepness of dominance hierarchies on grooming investment based on female dyadic aggressive relationships.Our data showed that the steepness of female dominance hierarchies (0.66 based on Dij) in YAI was steeper than hierarchical steepness (0.56 based on Dij) in YA2.Females groomed more frequency and duration in YAI than in YA2 in group level (P < 0.05),especially for middle-ranking animals (P<0.05).However,we did not find this pattern both in high- and low-ranking individuals (P>0.05).The results suggested that the steepness of donunance hierarchies influenced female grooming investment pattems,and females could adjust their grooming investment flexibly and swiftly to adapt the domination pattems.