Social buffering as an indirect effect: mixed-effects modeling approaches

O_LIThe potential for an individuals social partners to buffer--or otherwise modify-- how individuals respond to their environment has been demonstrated to be important in many contexts. This buffering has the potential to affect responses to human modifications of environments. Unfortunately, statistical tools for identifying buffering effects have not been well developed. C_LIO_LIHere, we demonstrate how social buffering fits into the context of a phenotypic equation conceptual approach and then connects to mixed-effects modeling for estimating buffering and other modifying effects of social behavior. C_LIO_LIWe explore the power and accuracy for buffering in response to known environments, providing a guide for empirical investigation. We found that increasing the sampling of social interactions decreases bias and increases precision and power to a greater extent than increasing sampling of focal individuals. C_LIO_LIWe also introduce how buffering in response to unknown environmental variation can be statistically modeled and tested. If environments are unknown, social buffering can be statistically tested for using double hierarchical generalized linear models by including social partner identity as a random effect that influences residual variation. C_LIO_LIFinally, we discuss how these approaches fit into the broader literature on indirect effects and indirect genetic effects. Placing social buffering in the context of indirect effects reveals that the evolution of social buffering is affected by both variation in an individuals behavior and variation in how individuals affect each other. This has important implications for social and evolutionary organismal responses to changing environments. C_LI