Social transmission in networks: global efficiency peaks with intermediate levels of modularity

Abstract

In myriad biological systems, multiple lines of evidence indicate that modularity, wherein parts of a network are organized into modules such as subgroups in animal networks, may affect social transmission processes. In animal societies, there is increased interest in understanding variation in the effects of modularity on transmission as it may provide important insight into a given network’s performance, in addition to the evolutionary consequences the structure of the network may have for individual fitness. Yet, to our knowledge, the degree to which network efficiency is modularity dependent has not yet been investigated in great detail in behavioral and evolutionary ecology. Here, we investigated to what degree network efficiency, as a proxy for social transmission, is modularity dependent. We created 2798 networks varying in group size and density, and tested whether network structure (density, Newman’s modularity, eigenvector centralization) and group size shape network efficiency. We also used published data from 41 primate social networks to test whether the predictions generated in our simulations were supported by empirical observations. Our results show a non-linear relationship between modularity and global efficiency, with the latter peaking at intermediate values of modularity in both theoretical and empirical networks. This phenomenon may have relevance for observed variation in social structure and its link with network performance. Our results may thus provide a basis from which to discuss the evolution of complex systems such as animal societies. Networks may maximize performance and minimize transmission costs, as demonstrated in neural networks, but to what degree network efficiency is modularity dependent has not yet been investigated in behavioral ecology. We provide evidence that modularity, such as subgrouping in animal networks, can have non-linear effects on transmission processes, with low values of modularity tending to positively influence social transmission and high values tending to negatively influence transmission. This pattern was consistent across small, medium, and large social groups from theoretical networks, and was corroborated by our empirical networks which were derived from 41 small- to medium-sized groups of 15 primate species. These results have potential implications for the understanding of social flexibility and its link with network performance, in addition informing many interdisciplinary fields, such as communication and computer science.