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Extensive empirical evidence suggests that there is a maximal number of people with whom an individual can maintain stable social relationships (the Dunbar number). We argue that this arises as a consequence of a natural phase transition in the dynamic self-organization among N individuals within a social system. We present the calculated size dependence of the scaling properties of complex social network models to argue that this collective behavior is an enhanced form of collective intelligence. Direct calculation establishes that the complexity of social networks as measured by their scaling behavior is nonmonotonic, peaking around 150, thereby providing a theoretical basis for the value of the Dunbar number. Thus, we establish a theory-based bridge spanning the gap between sociology and psychology., Competing Interests: The authors declare no competing interest., (Copyright © 2020 the Author(s). Published by PNAS.)

The typical human personal social network contains about 150 relationships including kin, friends, and acquaintances, organized into a set of hierarchically inclusive layers of increasing size but decreasing emotional intensity. Data from a number of different sources reveal that these inclusive layers exhibit a constant scaling ratio of [Formula: see text] While the overall size of the networks has been connected to our cognitive capacity, no mechanism explaining why the networks present a layered structure with a consistent scaling has been proposed. Here we show that the existence of a heterogeneous cost to relationships (in terms of time or cognitive investment), together with a limitation in the total capacity an individual has to invest in them, can naturally explain the existence of layers and, when the cost function is linear, explain the scaling between them. We develop a one-parameter Bayesian model that fits the empirical data remarkably well. In addition, the model predicts the existence of a contrasting regime in the case of small communities, such that the layers have an inverted structure (increasing size with increasing emotional intensity). We test the model with five communities and provide clear evidence of the existence of the two predicted regimes. Our model explains, based on first principles, the emergence of structure in the organization of personal networks and allows us to predict a rare phenomenon whose existence we confirm empirically., Competing Interests: The authors declare no conflict of interest., (Copyright © 2018 the Author(s). Published by PNAS.)

There is growing evidence that the number and quality of social relationships have substantial impacts on health, well-being, and longevity, and, at least in animals, on reproductive fitness. Although it is widely recognized that these outcomes are mediated by a number of neuropeptides, the roles these play remain debated. We suggest that an overemphasis on one neuropeptide (oxytocin), combined with a failure to distinguish between different social domains, has obscured the complexity involved. We use variation in 33 SNPs for the receptor genes for six well-known social neuropeptides in relation to three separate domains of sociality (social disposition, dyadic relationships, and social networks) to show that three neuropeptides (β-endorphin, oxytocin, and dopamine) play particularly important roles, with each being associated predominantly with a different social domain. However, endorphins and dopamine have a much wider compass than oxytocin (whose effects are confined to romantic/reproductive relationships and often do not survive control for other neuropeptides). In contrast, vasopressin, serotonin, and testosterone play only limited roles., Competing Interests: The authors declare no conflict of interest.