The complex structure of hunter-gatherer social networks

Abstract

In nature, many different types of complex system form hierarchical, self-similar or fractal-like structures that have evolved to maximize internal efficiency. In this paper, we ask whether hunter-gatherer societies show similar structural properties. We use fractal network theory to analyse the statistical structure of 1189 social groups in 339 hunter-gatherer societies from a published compilation of ethnographies. We show that population structure is indeed self-similar or fractal-like with the number of individuals or groups belonging to each successively higher level of organization exhibiting a constant ratio close to 4. Further, despite the wide ecological, cultural and historical diversity of hunter-gatherer societies, this remarkable self-similarity holds both within and across cultures and continents. We show that the branching ratio is related to density-dependent reproduction in complex environments and hypothesize that the general pattern of hierarchical organization reflects the self-similar properties of the networks and the underlying cohesive and disruptive forces that govern the flow of material resources, genes and non-genetic information within and between social groups. Our results offer insight into the energetics of human sociality and suggest that human social networks self-organize in response to similar optimization principles found behind the formation of many complex systems in nature.

Figure 1

Boxplots of hunter-gatherer group sizes, g, as a function of Horton order, ω. The grey boxes encompass ±67% CIs, the single horizontal lines within the boxes are medians, the paired horizontal lines outside the boxes encompass the 95% CIs and open circles are outliers (outside the 95% CIs). All distributions are approximately lognormal. Note the considerable overlap in all group sizes.

Figure 2

Horton plots of mean number of groups per population for the entire data set and the data decomposed by continent. (a) All data, n=339; (b) Asia, n=29; (c) Africa, n=19; (d) North America, n=216; (e) Australia, n=56; (f) South America, n=19. All the distributions are well fit by linear functions as the 95% CIs around the slopes encompass all data points in all cases (error bars are 1 s.d.). Slopes vary from 1.19 to 1.33 reflecting variation in branching ratios across continents (table 2 and §5 for further details).

Figure 3

Distributions of (a) branching ratios (n=339) and (b) family sizes (n=114) over the entire data set. Both distributions are approximately lognormal and average values given are geometric means with 95% bootstrap confidence limits. Values for the data decomposed by continent are given in table 2.

Figure 4

Data collapse of cumulative probability distributions. (a) Probability distributions for the frequency of group sizes by Horton orders 1–5. Note that all distributions have a similar shape along the y-axis but are separated along the x-axis. (b) By rescaling each probability distribution by its respective mean collapses all the data onto a single curve. These data collapse demonstrates the striking self-similarity of the scaling relations within and across these populations.