The role of social attraction and social avoidance in shaping modular networks

Abstract

How interactions between individuals contribute to the emergence of complex societies is a major question in behavioural ecology. Nonetheless, little remains known about the type of immediate social structure (i.e. social network) that emerges from relationships that maximize beneficial interactions (e.g. social attraction towards informed individuals) and minimize costly relationships (e.g. social avoidance of infected group mates). We developed an agent-based model where individuals vary in the degree to which individuals signal benefits versus costs to others and, on this basis, choose with whom to interact depending on simple rules of social attraction (e.g. access to the highest benefits) and social avoidance (e.g. avoiding the highest costs). Our main findings demonstrate that the accumulation of individual decisions to avoid interactions with highly costly individuals, but that are to some extent homogeneously beneficial, leads to more modular networks. On the contrary, individuals favouring interactions with highly beneficial individuals, but that are to some extent homogeneously costly, lead to less modular networks. Interestingly, statistical models also indicate that when individuals have multiple potentially beneficial partners to interact with, and no interaction cost exists, this also leads to more modular networks. Yet, the degree of modularity is contingent upon the variability in benefit levels held by individuals. We discuss the emergence of modularity in the systems and their consequences for understanding social trade-offs.

Keywords: agent-based model; behavioural variation; complex system; group-living; interaction costs and benefits; social trade-off.

Figure 1.

Schematic of the theoretical conditions under study (a) and the emergent social networks after 2000 interactions per individual (b). Networks are examples of model outputs with a group size = 10. In (a), the distribution of values assigned to benefits (purple dashed lines) and costs (red continuous lines) vary from 0 to 1 (y-axis) across individuals (x-axis: individuals' ID number, N = 10). The functions determining the values of benefits/costs were either linear (Y = 0; Y = 0.5; Y = (1/N) × ID; Y = 1 − (1/N) × ID − 1), where ID is the ID of the individual) or power-law distributed (γ = 10), and calculated using the unique ID number of individuals ranging from 1 to N. In (b), nodes (circles) represent individuals in the model (for N = 10 here) with their sizes directly related to the individual degree centrality coefficient (the higher the centrality, the larger is the size of the node). Network edges are undirected and weighted, such that pairs with higher association indices have thicker edges. Networks were built using the ‘igraph’ package in R [31].

Figure 2.

Schematic of the interaction rules occurring at each time step.

Figure 3.

The relationship between modularity, group size and the estimated inequality of costs and benefits in the system (i.e. ‘global index’). (a) The negative effect of the global index on the emergence of modular networks. Values in the global index vary from −1 (few individuals monopolizing high values of costs) to 1 (few individuals monopolizing high values of benefits), with values equal to 0 indicating perfect equality (My-benefits = My-costs). The regression line and its surrounding shaded area show linear model (LM) fit and standard error over replicates. (b) The positive relationship between Newman's modularity and group size. Statistical analyses were performed on conditions where individuals hold both benefits and costs in the system (conditions 6–8, 10–12, 14–20).