The Ash Twins Blog

Hamilton et al (2007) use an ethnographic dataset with information for over a thousand hunter-gatherer groups to show that all primitive human societies are organized according to a branching, fractal-like system in which individuals are subsumed into successively larger hierarchies. Groups of approximately 3.7 individuals form one unit in the next level of the hierarchy (e.g., 4 individuals in a family, 14 individuals in an extended family, 51 individuals in a village, etc.). Following I excerpt part of the discussion section:

The hierarchical fractal-like organization of hunter-gatherer social systems is similar to the self-organized structures of other complex systems in nature (Arenas et al. 2001, 2004; Oltvai & Barabasi 2002; Sole & Bascompte 2006). We suggest that these complex social systems have been shaped by similar optimization processes operating to maximize whole-system performance. In the present case, these human social systems are hypothesized to reflect optimized networks of flows of essential commodities: food, other material resources, genes and culturally transmitted information. . . .

Yet, how do we account quantitatively for the branching ratio? We offer the following hypothesis. Recall . . . that the branching ratio is simply the ratio of the frequency of group sizes between successive levels, . This can be rearranged to be or more generally , and as , we have Further, as N(g₁) = population size, g_Ω, we then have g_Ω=B^Ω−1 or g_Ω=B⁵ in this case as Ω=6. [I]t follows that the number of families in a population scales with the branching ratio as N(g₂)=B^Ω−2. As N(g₂)=g_Ω/g₂, we can write the branching ratio as B=(g_Ω/g₂)^1/Ω−2 where family size, g₂, can be expressed in terms of the net reproductive rate, R, thus g₂=2(R+1). Substituting this expression into the preceding equation, we then have

and rearranging, the net reproductive rate is then

Hence, as population size, g_Ω, approaches B^Ω−1, the net reproductive rate goes to 1 (i.e. reproductive replacement rates) as this equation reduces to R=B/2−1=1. Therefore, at replacement rates, independent of population size or the number of levels in the network, the branching ratio reaches an equilibrium of 4 and follows the replacement family size of 4 (two parents and two offspring). It follows that in growing populations where the net reproductive rate R>1, the branching ratio should be less than the mean family size, and family size will be greater than 4. Our results show that the mean branching ratio in our sample is approximately 3.8, suggesting that hunter-gatherer populations are, on average, growing, predicting that mean family size should be greater than 4. Indeed, mean family size is significantly greater than 4, F=4.48 (4.30–4.67), giving a mean net reproductive rate R=1.28 (1.15–1.33), and a mean population growth rate r=0.011 (0.007–0.015) or approximately 1%, where r=ln R/τ, and τ is generation time, approximately 20 years for traditional human populations under natural fertility conditions (Walker et al. 2006). . . .

[G]roup dynamics are governed by two basic kinds of forces: (i) cohesive forces that tend to draw and hold individuals together and (ii) disruptive forces that tend to pull individuals apart and to create barriers to exchanges between them (see Chagnon 1975). Cohesive forces in hunter-gatherer groups include kin selection due to genetic relatedness, sharing of non-genetic information and exchange of material resources. There are clear cohesive forces within families and wider kin relations, but there are also cohesive forces that extend to larger groups at higher levels of the societal hierarchy. These include exchange of marriage partners so as to avoid inbreeding, communication of information about social and environmental conditions, and exchange of material resources through trade and commerce. Disruptive or antagonistic forces include competition for material resources and for mates, inter-personal conflict and disease epidemics. The intensity of competition, the balance between mutualistic and antagonistic interactions, and the probability of disease outbreak all increase with increasing group size, with the result that individuals aggregate into successively larger groups with successively decreasing frequencies and only for specific purposes, such as exchange of marriage partners, trade in goods that are not available locally, and defence against or competitive aggression (e.g. warfare) towards other higher-level groups.