Endocranial volume is heritable and is associated with longevity and fitness in a wild mammal

Research on relative brain size in mammals suggests that increases in brain size may generate benefits to survival and costs to fecundity: comparative studies of mammals have shown that interspecific differences in relative brain size are positively correlated with longevity and negatively with fecundity. However, as yet, no studies of mammals have investigated whether similar relationships exist within species, nor whether individual differences in brain size within a wild population are heritable. Here we show that, in a wild population of red deer (Cervus elaphus), relative endocranial volume was heritable (h2 = 63%; 95% credible intervals (CI) = 50–76%). In females, it was positively correlated with longevity and lifetime reproductive success, though there was no evidence that it was associated with fecundity. In males, endocranial volume was not related to longevity, lifetime breeding success or fecundity.

. The relationships between selected variables: Pearson's productmoment correlations between endocranial volume, jaw length, skull length, back leg length, lifetime breeding success, lifetime reproductive success, and longevity (CI=confidence interval, a Bonferroni-Holm correction was applied to p-values to attempt to control for an increase in type 1 errors from conducting multiple tests on the same dataset). 'High' available investment categories were Summer and True Yelds because they either gave birth the year before but the offspring did not survive its first few months (died before 1 October in the previous year; summer yeld) or had given birth at some point, but not in the previous year (true yeld). (iii) High available investment but 'inexperienced' was the Naive status where it was a female's first time giving birth.

Birth year
The year in which the individual was born Mother's ID The ID of the subject's mother Animal ID The ID of the subject linked to the pedigree through the "ped" function in the model Supplementary Table S3. Fecundity and longevity models run with two variations of modeling relative endocranial volume (relEV: residuals of endocranial volume against jaw length) as fixed effects (either (a) relative endocranial volume or (b) relative endocranial volume + jaw length) show that, with two exceptions, conclusions do not differ from the models used in the text (fixed effects: endocranial volume + jaw length). The exceptions occur in the female LRS and female longevity models where, in both cases, the relative endocranial volume is not significant in the relative endocranial volume only model. This is in contrast with the other two methods of modeling relative endocranial volume, which both show this variable as significant (right side of the table below and in Tables 3 and 4). Random effects show variances and standard deviations (SD).

Dominance rank
We used dominance ranks from [32], which were calculated following [47] using data from 1974-1995. Dominance data only exist for females. Intra-cohort rank was controlled for age to distinguish among dominance and developmental effects and calculated as follows: the number of unrelated females of equal age or older that a focal individual threatened or displaced + 1 divided by the number of unrelated females of equal age or younger that a focal individual threatened or displaced + 1. Intra-cohort rank was then divided by the number of females in the cohort for a final score between 0 and 1 with higher numbers being more dominant. There was very little dominance rank data, therefore a separate model on this small dataset (n=51 all ages, n=49 adults) was run to determine whether dominance rank or mother's dominance rank should be included in the reduced model. The full model was the same as above except sex was removed because no males had rank data, and dominance rank and mother's dominance rank were added as fixed effects. Dominance rank and mother's dominance rank were not significant variables in this version of the full model, therefore they were not included in the reduced models (Supplementary Table S8).  Figure S1. The pedigree pruned to the deer whose endocranial volumes were measured (red lines = maternities, blue lines = paternities) and their relevant relatives. Each row represents one generation, from 0 through 7.

Further analyses of age-related variation in endocranial volume
We graphically compared endocranial volume vs age curves for individuals that died because they were shot outside the study area (n=129 females, n=178 males), which are a more random sample, with those that died of natural causes (n=493 females, n=489 males) in an initial analysis to ensure that the causes of natural deaths did not bias the results (R package: FlexParamCurve, function: pn.mod.compare [48]; R package: lattice, function: xyplot [49]). The curves for nonshot and shot deer were not different from each other (Supplementary Figure S2). Therefore, we can reliably determine adult status using all data (curves of best fit: female shot=richardsR31.lis, non-shot=richardsR12.lis; male shot=richardsR11.lis, non-shot=richardsR12.lis). Supplementary Figure S3. Adult female (3+ years) age at first reproduction was not associated with relative endocranial volume (A), whereas those females with larger relative endocranial volumes lived longer from age at first reproduction to death (B). Relative endocranial volume = residuals of endocranial volume against jaw length, shaded region = 95% Bayesian credible intervals, see Table 3 for analyses).

Supplementary
Supplementary Figure S4. Lifetime breeding (A, B) and reproductive success (C) for absolute endocranial volume in adults (3+ years) without accounting for jaw length.