Social genetic and social environment effects on parental and helper care in a cooperatively breeding bird

Phenotypes expressed in a social context are not only a function of the individual, but can also be shaped by the phenotypes of social partners. These social effects may play a major role in the evolution of cooperative breeding if social partners differ in the quality of care they provide and if individual carers adjust their effort in relation to that of other carers. When applying social effects models to wild study systems, it is also important to explore sources of individual plasticity that could masquerade as social effects. We studied offspring provisioning rates of parents and helpers in a wild population of long-tailed tits Aegithalos caudatus using a quantitative genetic framework to identify these social effects and partition them into genetic, permanent environment and current environment components. Controlling for other effects, individuals were consistent in their provisioning effort at a given nest, but adjusted their effort based on who was in their social group, indicating the presence of social effects. However, these social effects differed between years and social contexts, indicating a current environment effect, rather than indicating a genetic or permanent environment effect. While this study reveals the importance of examining environmental and genetic sources of social effects, the framework we present is entirely general, enabling a greater understanding of potentially important social effects within any ecological population.

feeding rate across its lifetime. Direct genetic effects !,! were modelled as additive genetic variance ( ! ) using the additive genetic relationship matrix derived from the pedigree. We fitted ID of the nest m that the bird was provisioning in year y ( !" ) to estimate shared environment variance ( ! ), which captures the similarity in feeding rates of birds provisioning the same nest. We included fixed effects to capture known sources of variability: sex, age of the focal bird (years), breeding role (coded parent = -1, helper = 1), whether helpers were related to the breeder [1] (coded as helper not related = -1, helper related = 1, parent = 0), brood size, number of helpers, hour of day observed, age of the brood (days), and interactions of sex with role, brood age, and number of helpers. The fixed effects thus contained the constant effects of having helpers and of changes in brood demand that have the same influence on all individuals.
All fixed effects were mean centred to handle missing random effects predictors from differing group sizes. The within-individual, daily fluctuations in feeding rate ( !"# ) not captured by other effects defined the residual variance ( ! ). We calculated heritability, repeatability, consistency, and other intraclass correlations in two ways [2]. The first, repeatability, was as a proportion of the observed phenotypic variance ! to understand the contribution of social effects relative to the phenotypic variance attributable to known fixed effects. Because our focus was on individual differences in provisioning rate, the second way, consistency, was in proportion to the within-year variance (after removing within-individual variability between observation days within a given year and variance from known fixed effects: Within-year consistency variance can be interpreted as variance in birds' mean effort over each year.
To compare results with a previous study of heritability in a subset of data in this sample [3] we also estimated direct effects only on parental provisioning rates. We calculated the variance attributable to fixed effects by multiplying each fixed effects coefficient by the relevant columns from the data, then calculating the variance of the resulting vector [4].
We next estimated social genetic and environment effects on feeding rate [5]. We conducted two sets of analysis: (1) using feeding rates of parents only to assess the social effects of helpers on parental performance and (2) using feeding rates of parents and helpers to assess the social effects of all members of a breeding group on each other. We first expanded the models to estimate the environment effects of helpers on parents to determine whether parents adjusted their feeding rates depending on who was helping in a given year: We fitted the social effects of each helper h ( !,! ) by specifying an overlay design matrix (i.e., the same random effect is attached to multiple columns in the data; because the maximum number of helpers was 5, the effect was associated with 5 random predictors; see Section 2) using the helpers' IDs, which estimates variance from individual social effects ( !"(!) ). Because groups differed in the number of helpers we used the 'include' option so that missing helper predictors became the reference level and we centred the fixedeffect inputs to match this parameterization. This model tests the average effect an individual has over its lifetime on the parents that it helps.
The next model split the helper social effects into effects that were consistent across all observations of a bird ( !,! ) from effects that differed across years ( !,!! ). Consistent social effects estimated the social permanent environment variance ( !"(!) ), though this parameter would include genetic effects as well, and social effects that varied between years made up the social current environment variance ( !"(!) )). This model tests whether the social effects of a helper are consistent across breeding seasons: The final model estimated the social genetic variance ( !(!) ) from social genetic effects ( !,! ). This model tests whether there is a genetic basis to the social effects of helpers that would increase the total heritability of provisioning behaviour [6]: We then repeated the model building procedure using data on both parent and helper phenotypes to test for social permanent environment, social current (within-year) environment, and social genetic effects of parents and helpers on the other carers provisioning the same nest. This also allowed us to test for correlations between direct and social effects. The models estimated separate contributions of social effects from each parent or helper j to estimate additional permanent environment ( !"(!) ), current environment ( !"(!) ), and genetic ( !(!) ) variance components for breeding group members' social effects.    Starting with the social effects model

MODEL SPECIFICATION FOR INDIRECT GENETIC EFFECTS
we fit a random regression with breeding role where role is coded ---1 for parents and 1 for helpers and FD,i is a random slope effect for each individual. Model 5.2 did not improve in terms of fit over We then fit individual slopes for number of helpers where 'ʹhelpers'ʹ is the number of helpers and GD,i is the individual slope coefficients. The group size plasticity model was also not significantly better (LR = 3.85, df = 1, p = .05) and the social current environment variance component was only slightly reduced (.0725, se = .0170) and the slope variance was not significant (component = .016, se = .011).

SEX DIFFERENCES IN REPEATABILITY
A study of house sparrows Passer domesticus [10] found that between---and within---year repeatabilities were higher in males than females, so we tested for sex differences in variance using data on parents.
A model that retained sex---specific residual variances and also fit separate permanent environment had convergence issues where the REML estimates of the permanent environment effects both went to zero.
Fitting sex---specific current environment variances did not improve model fit (LR = .49, df = 1, p = .48). We also did not find any evidence for sex differences in genetic variance in a model that also fit a genetic covariance term (LR = .41, df = 2, p = .81). The genetic covariance between male and female provisioning rates was rG = .98.

SEX DIFFERENCES IN SOCIAL EFFECTS
Because male long---tailed tits reduce effort more in response to helpers then females do [11], it is possible that there is a sex difference in sensitivities to social effects. To test this we fit a series of categorical random interaction models where an individual'ʹs social effect varied either as a function of its own sex or its partner'ʹs sex.
Starting from the basic social effects model, a focal individual i'ʹs phenotype ! is a result of its direct effect on itself, ! , and its J partners'ʹ social effects, !
In modelling social effects separately by sex, we can consider social effects being moderated either by the sex of the focal individual (i) or by the sex of its partner (individual j).
If social effects differ depending on the sex of the target then we are positing that individuals of one sex more extremely increase and decrease their feeding rate in response to their partners'ʹ presence.
where !,sex ! is individual j'ʹs effect on the phenotype of individual i depending on the sex of individual i. That is, individual j has one social effect on females and another social effect on males. Since in a cooperative breeding context where birds are interacting in groups rather than in pairs, this sex effect would have to be a difference in females'ʹ and males'ʹ behaviors in response to individual j rather than a difference in individual j'ʹs behavior when interacting with a female or male partner. In this model separate variance components are fit for a partner'ʹs effects on female focals !,female ! ~ Norm(0, !,female ! ) and on male focals !,female ! ~ Norm(0, !,male ! ). Given previous findings that males reduce effort in the presence of helpers more than females do [11], if there is a difference then we would expect that males would be the more responsive sex.
If instead social effects differ depending on the sex of the partner, then we are positing that males and females differ in how much they are responded to.
Because we are fitting effects to individuals, this is different from saying the mean response differs between male and female partners. Instead, if one sex varies more in the quality and quantity of provisioning behavior, then partners will respond more extremely to individuals of that sex. The model is where the only difference from equation S2 is that the social effect is now being indexed by the sex of individual j (the partner) rather than the sex of the focal individual i. Because a bird only has one sex, it is not possible to estimate the individual---level covariance between these components.
We built models to test sex differences in social effects. Given that in our main result we detected environmental but not genetic social effects, we fit models with sex---specific social environment effect variances. We started from the sex--specific repeatability model from section 7 (above). This model had single direct genetic, direct permanent environment, direct current environment, and nest effects. The model also had sex---specific residuals.
We tested for sex---specific social permanent environment effects and sex--specific social current environment effects using either the sex of the focal individual or its partners as the moderating variables. In each case we use the social permanent or social current effects as a base line, V(social), and compare models that fit separate V(social female) or V(social male) using the sex of the focal or the sex of the partners. We test for the significance of the sex × social variances against the baseline using the likelihood ratio test and compare all three sets of models using weighted AIC [12], which is the probability of the model given the data (among the models being compared). Variance components are listed with standard errors.  We found that permanent social effects did not differ based on the sex of the target (p = 0.055) or the partners (p = 0.37). The correlation between permanent social focal---sex effects was 0.49. Current social effects also did not differ based on the sex of the target (p = 0.080) or the partners (p = 0.54). The correlation between current social focal---sex effects was 0.68. Thus we found no evidence that social effects differ between males and females.

EFFECT OF RELATEDNESS ON SOCIAL EFFECTS
When kin and nonkin interact, it is also possible that the social effects between individuals differ depending on their relatedness [13]. We explored this possibility by fitting social effects moderated by the relatedness between target and partner individuals where kinij codes the relatedness between individuals i and j as either 'ʹkin'ʹ or 'ʹstrangers'ʹ. We fit separate variance components for the two relatedness categories as well as the covariance between them. We fit categorical random interaction models using both permanent and current social environment effects. Estimating separate variances components for the two relatedness categories did not improve model fit for either the permanent (LR = 2.8, df=2, p = .24) or current (LR = 2.6, df = 2, p = .28) social environment models, and thus the data did not support a difference in the size of social effects between kin and nonkin. The correlation between direct and indirect effects was r = .93 in the permanent social environment model and r = .78 in the temporary social environment model.

PHENOTYPIC PLASTICITY AS POSSIBLE CONFOUND
In our main analysis we separated out current and permanent environmental sources of social effects because group composition varies with a breeding season, with helpers joining breeding pairs and failed breeders becoming helpers at varying points in the breeding process. These changes over time create the possibility that individual differences in plasticity [14] to time--varying factors could create the appearance of social effects. In other words, a bird could vary its behaviour in response to a changing factor but this change coincides with the arrival of a helper and thus the change could appear to be a social effect of the helper.
Two such time varying factors that were measured and that change feeding rates are brood age and number of helpers. In the main analysis we fit these variables with constant slopes (that is, as fixed effects 12 GENOTYPING Genomic DNA was extracted from blood (stored in absolute ethanol) using ammonium acetate [15,16]. Nineteen published microsatellite loci were combined with two sex---typing markers and arranged into three multiplex (MP) sets using MULTIPLEX MANAGER v1.2 [17], each set containing between six and eight markers (Table  S1). The inclusion of two sex---typing markers enabled the confident assignment of sex and allowed us to identify  Table  S1]. Amplification was performed using a DNA

PEDIGREE CONSTRUCTION
We used FRANz [26] to reconstruct the whole pedigree using the molecular markers. We first ran FRANz using prior information about individual birth--death events and genetically---determined sex to identify all likely parents (LOD > 0) of each individual. For each individual we excluded their social mother if she had been genotyped and was not matched as one of the parents.
We output a pedigree of genetically---matched mother---offspring pairs and reran FRANz using this information to match fathers and to find full sibling groups among the founders and immigrants. The extra---pair paternity rate was 3% of nestlings. FRANz identified 20 likely full sibling groups out of the birds with unknown parentage. For these full sibling groups we entered dummy parent IDs into the pedigree. The full sibling test also identified 21 likely full sibling groups for whom only one parent was known from the social pedigree but the missing parent was not found among the genotyped candidates. For these groups we created a dummy ID for the missing parent in the pedigree.
For ungenotyped individuals we used parents assigned from the social pedigree.