Data on volumes of different brain structures were gathered from the literature [43,58]. The major structures of the brain included in the analyses were the pons, medulla oblongata (including the reticular formation), cerebellum (including the brachium and the nuclei pontis), mesencephalon (excluding the reticular nucleus), diencephalon and telencephalon (cerebrum). To further investigate hypotheses regarding different substructures of the telencephalon, we also used volume information for the septum, striatum, amygdala, schizocortex (entorhinal, perirhinal and presubicular cortices), hippocampus, and neocortex (isocortical grey and underlying white matter). As noted above, information was unavailable for the sexes of the animals for the brain measurements.
We also gathered data on body mass  and group size  for the species with brain data. Female group size served as a proxy for social complexity , whereas sexual size dimorphism was used to measure sexual selection . The number of data points limited our choice for alternative variables indicating strength of sexual selection. Instead, we repeated some of the analyses using canine dimorphism as a proxy for sexual selection, and these analyses produced results similar to those for body mass. The fact that more data were available on primate body masses than canine dimensions led us to prefer the former to the latter; thus, body mass dimorphism results are presented here. Although data exist for strepsirhine primates, these were not included in the analyses because there is very little variation in both sociality and sexual size dimorphism in the species for which data on the volumes of different brain structures is also available [61-63]. All variables were log10-transformed prior to analysis.
Haplorhine (Old World) primates are generally larger, more dimorphic and live in larger groups than platyrrhine (New World) primates. That is, the causal factors we use in this study are similar within taxonomic groups, because of their shared evolutionary history. For this reason, we employed phylogenetically independent contrasts that use differences between species and taxonomic groups instead of the species' values themselves . This approach produces statistics untainted by problems caused by similarity due to common descent. We used Purvis'  estimate of primate phylogeny, which was created using a super-tree technique to combine a large number of source phylogenies. This phylogeny uses information published to the date of its construction and unites knowledge gathered from both molecular and morphological data. It is therefore based on more information, and covers more species, than any alternative phylogeny. Hypothesis testing was performed using the aforementioned phylogenetically independent contrasts , as implemented in the computer program PDAP . Diagnostic tests showed that branch lengths given in Purvis  needed no adjustment .
Because we were interested in investigating the effects of multiple independent variables on different brain components, we analyzed the influence of these variables using stepwise multiple regression. To investigate which variables were significantly correlated with the dependent variables, we used a backwards-removal procedure with all variables initially included in the model, and then sequentially removed variables with significance levels > 0.1. Because correlations exist between female body mass and total brain volumes, between female body mass and dimorphism, and between male and female group sizes, we tested whether collinearity rendered our multiple regression models unstable by calculating Variance Inflation Factors (VIFs) . With only one exception, the VIFs were [68,69]. The exception involved female body mass and "remaining brain volumes," which had VIFs> 10, but these analyses were restricted to secondary analyses (Additional files 3 and 4).
To control for allometric effects, we subtracted the volume of the brain component under scrutiny from the total brain volume and used this "remaining brain volume" as a covariate in all regression models. Including total brain volume instead of the "remaining brain volume" as a covariate produced results similar to those presented here, but we feel that the measure we used better corrects for part-whole correlation problems. The volumes of all examined brain parts were closely correlated to our "remaining brain volume" measure (p 1). We chose "remaining brain volume" rather than body mass when controlling for allometric effects primarily because including female body mass and "remaining brain volume" together in the regression models almost always gave non-significant partial regression coefficients for female body mass. In addition, brain volume is both statistically and conceptually closer to the brain components under scrutiny than is body mass. To make sure that our results were not due to indirect effects of body mass, we double-checked our regression models by forcing female body mass into the equations (Additional files 3 and 4). Because the effect of sexual selection on male size has been shown to be a main cause of sexual size dimorphism in haplorhine primates , inclusion of male body mass has the unwanted effect of including effects of sexual selection in the body mass measure. For this reason, inclusion of male body mass, or the mixed body masses of Stephan et al. , produced results that were difficult to interpret. Although sexual selection also affects female body mass, these effects are smaller than those on males .
The telencephalon (cerebrum) is by far the largest substructure in the haplorhine primate brain (65–85% of the total brain volume) and the largest substructure within the telencephalon is by far the neocortex (40–80% of the total brain volume). Selection pressures affecting the relative size of the neocortex could therefore also affect the relative sizes of all other brain components (e.g. if the neocortex becomes comparatively larger, the other brain components automatically become comparatively smaller). For this reason, we checked our results by repeating the analyses while excluding the neocortex from the "remaining brain volume" variable. Results that were statistically significant in the first round of analyses but non-significant when excluding the neocortex volumes (or vice versa) have to be judged carefully (Additional files 5 and 6).