In polygynous mammals, fitness differences may reflect differences in phenotypic quality as well as experience. This study determines dominance hierarchy among female reindeer Rangifer tarandus from two experimental herds (consisting of c. 45 animals in each) during 2 consecutive years. The influence of body mass, antler size and age on social rank in the herds was investigated, first using simple regression analysis. The combined effect of body mass, age and antler size on female rank was further assessed using principal component analysis, as these three parameters were significantly correlated. The improved Laundau linearity index of c. 0.5 (P r < 0.001) in both herds indicated that a substantial part of the hierarchies was explained by their linearity properties. Consistently, body mass, female age and antler size, as well as their combined effect (measured by the scores on the main axis, PC1), influenced social rank in all four groups. It was concluded that both body mass and age are good predictors of social rank in female reindeer, whereas antler size in comparison plays a less important role in herds with a 'normal' female age structure. This suggests that female antlers may have evolved in intersexual rather than intrasexual competition. The temporal variations in the importance of body mass and age, probably owing to variation in female age structure between the 2 years, calls for conservative interpretations of whether body mass or age is more important in determining social rank among female reindeer. This is confirmed by the PCA analyses, where all three variables contributed more or less equally to the first component, the size variable, which on average explained more of the variation in female rank than body mass and age, suggesting that phenotypic quality expressed as the combination of the three variables is a better predictor of social rank than the variables per se. Hence, general conclusions about social rank based on single studies including few animals may not be credible.