Network reaction norms: taking account of network position and plasticity in response to environmental change

Consistent inter-individual differences in behaviour are thought to be related to consistency in social network position. There is also evidence that network structures can show predictable temporal dynamics, suggesting that consistency in social network position across time does not preclude some form of plasticity in response to environmental variation. To better consider variation in network position and plasticity simultaneously, we investigate the extension of the behavioural reaction norm (BRN) to dynamic social networks. Our aim is to estimate both an individual's position and plasticity within a network across an environmental gradient (i.e. to generate a network reaction norm (NRN)). We show that it is possible to account for the non-independence of network measures using covariance structures but that, in cases where the independent variables are group-level environmental measures, a standard multilevel model is sufficient. We therefore outline when a standard multilevel model is appropriate for NRNs and highlight the benefits and limitations to this approach. As an illustrative example, we used an NRN approach on 7 years of behavioural data on chacma baboons to quantify both the consistency with which individuals maintained social behaviour (node strength) and central positions (eigenvector centrality) within the social network. We found evidence for individual plasticity for node strength but little evidence for eigenvector centrality. Conversely, we found evidence of consistent individual differences in eigenvector centrality but not strength. These results suggest that individual node strengths are influenced by environmental changes, but the social structure of the group remains remarkably stable nevertheless. We suggest that expanding from measures of repeatability in social networks to network reaction norms will provide a more contextually nuanced way to investigate social phenotypes, leading to a better understanding of the development and maintenance of social structures in changing environments.Significance statementAn individual's position within a social network can have consequences for its fitness, resulting in great interest into how individuals develop and maintain particular network positions. Here, we extend the notion of behavioural reaction norms to include social network data. Given the non-independence of network data, however, the application of BRNs is not straightforward. Consequently, we have developed an alternative statistical extension that uses covariance structures to account for non-independence. Although we find that under one specific set of assumptions, it is possible to apply the standard BRN to network data. Applying this approach to data from a social group of chacma baboons, we found individual social behaviours shifted in response to environmental variables, yet the social structure of the group remained remarkably stable.