Title: "Decomposing social interactions: a statisti- cal method for estimating social impact and social responsiveness".

Social interactions mediate the phenotypic expression of fitness-relevant traits. The expression of such labile social traits includes three distinct components: an individual's mean trait value (direct effect), its social responsiveness, and its social impact (indirect effects). Traditional methods, such as variance-partitioning or trait-based models, usually only partition individual variation into direct and indirect effects. However, individual variation in social responsiveness and its covariation with direct effects and social impact will affect responses to selection. To date, no studies have explored the performance of models that allow the decomposition of responsiveness from impact. Here, we describe a model for studying variation in phenotypic expression caused by social interactions, and we use simulations to explore its performance under various experimental designs. Our analyses show that with adequate total sample sizes (≥3200), variance components are estimated accurately across all study designs. In contrast, covariance estimation would benefit most from including more unique individuals, followed by more unique social partners per individual, whereas repeated interactions with the same partners added the least improvement to the covariance estimation. We also found that failing to model individual variation in responsiveness, and neglecting measurement error, increases bias and imprecision in trait-based approaches. Hence, disregarding individual variation in responsiveness would ignore a key component of social behaviour, and hamper our ability to acquire unbiased estimates of indirect genetic or social effects.