Fractal Structure of Human and Primate Social Networks Optimizes Information Flow

Abstract

Primate and human social groups exhibit a fractal structure that has a very limited range of preferred layer sizes, with groups of 5, 15, 50 and (in humans) 150 and 500 predominating. This same fractal distribution is also observed in the distribution of species mean group sizes in primates. Here we demonstrate that this preferential numbering arises because of the critical nature of dynamic self-organization within complex social networks. We calculate the size dependence of the scaling properties of complex social network models and argue that this aggregate behaviour exhibits a form of collective intelligence. Direct calculation establishes that the complexity of social networks as measured by their scaling behaviour is non-monotonic, peaking globally around 150 with a secondary peak at 500 and tertiary peaks centred on 15 and 50, thereby providing a theory-based rationale for the fractal layering of primate and human social groups.

Group-related phenomena in Wikipedia edits

“…This relationship is essentially information theoretic on a statistical level. In this respect, information is a cybernetic concept in the sense that it can involve the exchange of actual information about some aspect of the world or some token such as grooming that defines the quality of a relationship (see also West et al [2,3]). The link between intentions, promises, and trust points to this intentionality as the seed attractor in the explanation of process network dynamics [20].…”

“…Human social groups have a natural hierarchical structure whose layers have very specific values [1]. These layers represent a harmonic series of optima where information flow round the network is optimised [2,3]. The layers are an emergent property of the frequency with which individuals contact each other [4,5] and the way this creates a sense of trust through increasing familiarity, the evaluation of cues of community membership (otherwise known as the Seven Pillars of Friendship [6]) and the exchange of tokens [7,8].…”

Four errors and a fallacy: pitfalls for the unwary in comparative brain analyses

“…The result is a fractal structure to social groups, which, when seen from the individual's viewpoint, has a hierarchically inclusive layered structure with layers of very similar size across a wide variety of mammalian species including dolphins, elephants, cercopithecine monkeys, apes and humans (Hill & Dunbar, 2003; Wittemyer, Douglas‐Hamilton & Getz, 2005; Hamilton et al ., 2007; Hill, Bentley & Dunbar, 2008; Zhou et al ., 2005; Waller, 2011; Moss, Croze & Lee, 2011; Wakefield, 2013; MacCarron & Dunbar, 2016; Escribano et al ., 2022). These size regularities derive from the mathematical properties of networks and the way animals choose to allocate their limited social time (Tamarit et al ., 2018; Tamarit, Sánchez & Cuesta, 2022; West et al ., 2020, 2023). All that animals need do is maintain visual (or even auditory) contact with their one or two closest grooming partners, and the more casual (weak) links between sub‐networks are sufficient to maintain group cohesion (Castles et al ., 2014; Dunbar, 2023) – unless, of course, groups get very large and/or day journeys very long, in which case groups may fission down the fracture line created by the weak links between sub‐networks (Dunbar & Shultz, 2022).…”

Optimal Social Group Size in Spotted Hyaenas (Crocuta crocuta): Insights into a Multilevel Society

“…In Papio baboons, whose groups vary across a similar size range, analysis of the distribution of group sizes suggests that this is multimodal, forming two distinct optima whose size is determined by the habitat level of predation risk (Dunbar et al 2018b;Dunbar & MacCarron 2019). More importantly, mathematical analysis of the efficiency of information flow through networks suggests that only certain group sizes are optimal in this case, with these optima forming a distinct series (5,15,50,150,500) with a scaling ratio of ~3 (West et al 2020(West et al , 2023. In addition to defining the characteristic sizes of primate social groups (Dunbar et al 2018b), these values also form the template for the internal structuring of large social groups (Dunbar 2020;Escribano et al 2022).…”