Our first set of analyses concerned the major subdivisions of the brain. These tests showed that body mass dimorphism was significantly positively correlated with the relative volumes of the medulla oblongata, mesencephalon and diencephalon, and negatively correlated with the relative volumes of the pons and telencephalon (Table 1). The telencephalon may also have been the target of social selection differing between the sexes, as indicated by a negative correlation between relative telencephalon volume and male group size, but a positive correlation with female group size, whereas correlations in the opposite direction were found in analyses of the diencephalon (Table 1). These analyses controlled for total brain volume (see Methods).
To further assess how functional differences between males and females operate on different brain structures, we analyzed specific structures of the telencephalon. The results concerning social selection showed that sociality for both males and females was correlated with different components of the telencephalon. Whereas male group size was significantly negatively correlated with the relative volumes of the septum, schizocortex and perhaps the neocortex (partial regression p = 0.064), female group size was positively correlated with relative neocortex volume  and negatively correlated with relative hippocampus volume (Table 2). Body mass dimorphism also correlated negatively with the relative sizes of the septum, striatum and schizocortex, but positively with the relative size of the amygdala (Table 2). As in the case of the brain components, these analyses also controlled for total brain volume.
For methodological reasons involving a possibly confounding effect of body mass (see Methods), we re-ran all analyses with female body mass forced into the regression models (Additional files 3 and 4). These results support the same patterns as those presented above, except that the relative volume of the pons in this scenario was not significantly correlated with sexual size dimorphism (Additional file 3). Although these results are similar to those presented, Variance Inflation Factors (VIFs) indicate that these regression models were unstable (see Methods).
To ensure that our results were not due to undue influences of results concerning the large volume of the neocortex, we repeated our analyses after removing the neocortex volumes from the "remaining brain volume" variable used to correct for allometric effects (Additional files 5 and 6). These results also support the general patterns presented above, except that the diencephalon was no longer significantly correlated with male and female group sizes, and female group size was positively correlated with the relative volumes of the septum and striatum but not significantly correlated with that of the hippocampus.
Variation in female group sizes is larger than variation in male group sizes, which could unduly influence our model choice in the stepwise regression analyses. The larger variance of female group size could tend to include female group size in the model first, thereby possibly forcing the correlated measure of male group size out of the models. For this reason, we checked all results by including the group sizes of the two sexes independently in all models. This produced qualitatively similar results to those presented above; for example, whenever male group size was non-significant when female group size was also included, it was also non-significant when female group size was not included. Thus, with only the few exceptions outlined in the previous two paragraphs, the results presented in Tables 1 and 2 remained consistent when running the analyses with alternative assumptions.