Materials and methods
I gathered species mean data from previously published sources for diurnal, group-living
anthropoids (1-4). Data were analyzed using a series of phylogenetically informed multiple
regressions (see below) with facial nucleus volume as the dependent variable and medulla
volume as an independent variable to control for allometric effects (5). The following
variables were also used as predictors: time spent grooming, group size, and neocortex
ratio. Neocortex ratio was calculated as neocortex volume/(total brain volume –
neocortex). I used neocortex ratio as a measure of relative neocortex size because it
exhibits the strongest correlation with social group size of any relative brain size measure
(6). Neocortex ratio is also highly correlated with various measures of socio-cognitive skill,
including tactical deception rate and executive brain functioning (7, 8). The grooming data
were derived from the same groups as the group size data (4). The group size data depicted
in figure 4 were taken from the website of Charles Nunn1. All data were natural-log
transformed prior to analysis.
Regressions were performed using a phylogenetic generalized least-square (PGLS)
approach (9-11) implemented in the program BayesTraits. This approach incorporates
phylogenetic information directly into the regression model by representing the error term
as a variance-covariance matrix scaled by the parameter λ, which is a measure of
phylogenetic signal (12). The λ parameter is estimated from the data via maximum
likelihood and ranges from 0 to 1. When λ = 0, the results are equivalent to nonphylogenetic regression because the internal branches of the tree are collapsed to zero,
resulting in a star phylogeny. Values of λ > 1 represent increasing degrees of phylogenetic
1
http://www.people.fas.harvard.edu/~nunn/archive/Nunn_vSchaik_II.htm
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dependence among the regression residuals, with λ = 1 indicating no transformation of the
branch lengths were used because the error term is perfectly dependent on phylogeny. To
take into account phylogenetic uncertainty, I downloaded a sample 100 chronometric trees
from the 10kTrees website, which provides access to a Bayesian posterior probability
distribution of primate phylogenies (13). I ran each analysis across the entire tree block so
that the results would not be dependent on any one tree or set of branch lengths. The
statistical significance of regression coefficients was assessed with reference to the
conventional p-value thresholds.
The λ parameter was estimated to be zero in all regressions, suggesting that the
degree of phylogenetic dependence among regression residuals was negligible for the data
and taxa used in this study. For this reason ordinary least-squares (OLS) residuals are
plotted in figures 2-4. Moreover, the regression results were identical for all 100 trees
downloaded from 10kTrees, due to the absence of residual phylogenetic signal.
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