Direct and indirect phenotypic effects on sociability indicate potential to evolve

The decision to leave or join a group is important as group size influences many aspects of organisms' lives and their fitness. This tendency to socialise with others, sociability, should be influenced by genes carried by focal individuals (direct genetic effects) and by genes in partner individuals (indirect genetic effects), indicating the trait's evolution could be slower or faster than expected. However, estimating these genetic parameters is difficult. Here, in a laboratory population of the cockroach Blaptica dubia, I estimate phenotypic parameters for sociability: repeatability (R) and repeatable influence (RI), that indicate whether direct and indirect genetic effects respectively are likely. I also estimate the interaction coefficient (Ψ), which quantifies how strongly a partner's trait influences the phenotype of the focal individual and is key in models for the evolution of interacting phenotypes. Focal individuals were somewhat repeatable for sociability across a 3‐week period (R = 0.080), and partners also had marginally consistent effects on focal sociability (RI = 0.053). The interaction coefficient was non‐zero, although in opposite sign for the sexes; males preferred to associate with larger individuals (Ψ (male) = −0.129), while females preferred to associate with smaller individuals (Ψ (female) = 0.071). Individual sociability was consistent between dyadic trials and in social networks of groups. These results provide phenotypic evidence that direct and indirect genetic effects have limited influence on sociability, with perhaps most evolutionary potential stemming from heritable effects of the body mass of partners. Sex‐specific interaction coefficients may produce sexual conflict and the evolution of sexual dimorphism in social behaviour.