Sex Deviations

Sex specific standard deviation scores (SDS) for height, weight and BMI were estimated using internally generated growth charts. The growth charts were constructed using the LMS (L = skewness; M = median; S = coefficient of variation) method (28 (link)). This is preferable to the use of an external reference, which can be misleading for historical cohorts (29 ).
In initial descriptive analyses, cross-sectional associations between each genotype and height, weight and BMI SD scores at each age were performed using linear regression assuming an additive genetic model, with adjustment for sex.
Longitudinal analyses were performed using hierarchical mixed models. These models take account of the correlation between repeated measures on the same individual and allow for incomplete outcome data on the assumption that data are missing at random. To initially test whether the association between genotype and each measure of body size (BMI, weight and height) changed with age, we first fitted linear age and genotype-by-age interaction terms, then added, in turn, quadratic and cubic ages and their interactions with genotype. For simplicity of presentation, and because the findings were very similar to those from the polynomial age models, we then fitted linear piecewise models with a knot at 20 years to allow different slopes for childhood (2–20 years) and adulthood (20–53 years) for BMI. The intercept was allowed to vary according to allele frequency in an additive genetic model. Genotype-by-linear age interaction terms (one for 2–20 years and another for 20–53 years) were then added to the model to assess whether the effect of genotype changed with increasing age. Likelihood ratio tests were used to assess the improvement in fit on addition of each new term in the model. We allowed for a random intercept and random slopes. For the weight trajectories, similar models were fitted except that baseline was taken as birth, due to the availability of birth weight data. For height, baseline was at age 2 years and change in height was modelled only to adulthood using a single slope. Because the first two measures of adult height (at age 20 and 26 years) were self-reported, height at 36 years was used as final attained adult height and was assumed to have been achieved by age 20 years.
Tests for sex interactions were not statistically significant, and therefore all models included both men and women and were adjusted for sex. Analyses were performed using Stata version 10.1.

The most precise measure of the reproductive success of individuals involves the genotyping of offspring and potential parents. In our study, this was not possible because the capture of small group members requires destruction of the shelters, which dissolves groups (14 , 22 (link), 97 ) and hence would have obstructed the collection of long-term life history data. Fortunately, several field studies of fish from the same population provided good estimates of the reproductive share within N. pulcher groups (14 , 96 (link), 97 ), revealing that reproductive success is greatly biased toward the dominants (15 , 36 ). Because of differences in the reproductive potential of the two sexes [the polygynous mating pattern renders a much higher maximum reproductive success for males than for females (67 )] and annual variation in colony-wide reproductive success, we standardized the reproductive success estimates of all marked individuals by transforming our counts of juveniles below helper size in each group into sex- and year-specific Z scores. Note that this estimates only the direct reproductive success of individuals, omitting any potential indirect fitness gains by helper effects on relatives. First, we calculated each individual’s expected share in its group’s reproduction based on the most recent parentage study in the same population (14 ): We assumed that dominant males sired 76% of offspring and that dominant females were the mothers of 82% of offspring. We further assumed that large (i.e., mature; >3.5-cm SL) subordinates in a group equally shared either 11% (males) or 5% (females) of their group’s reproductive success (assigning the remaining reproductive success to “unknown” individuals) (14 ). While it is possible that dispersal affects reproductive sharing in groups (54 (link)), these effects are unlikely to explain the patterns of reproductive success and dispersal behavior we report here (fig. S14B). Hence, we had information about an individual’s sex, social status, and reproductive success in a given year in 355 cases. On the basis of these, we calculated sex- and status-specific average annual reproductive success, i.e., average reproductive success in a given year of dominant females, dominant males, subordinate females, and subordinate males, respectively. For each individual, we then calculated its relative reproductive success throughout the observation period: sex- and status-specific Z scores were calculated for each individual and each year in which it was observed and then summed over the number of observation years [i.e., $Z=\frac{x_{ijk}-{\overline{x}}_{jk}}{S_{jk}}$ , where x_ijk is the reproductive success of individual i of sex j and status k, ${\overline{x}}_{jk}$ is the average annual reproductive success of individuals of sex j and status k, and S_jk is the standard deviation of annual reproductive success of individuals of sex j and status k (98 (link))]. We calculated Z scores for each individual throughout the observation period as a measure of its relative reproductive success compared to other individuals of the same sex and status (dominant or subordinate) observed at the same time.