The Dunbar number (Dunbar’s Number, n.d.), proposed by British anthropologist Robin Dunbar, posits that humans have a cognitive limit to the number of stable social relationships they can maintain, estimated to be around 150 individuals. This theory is based on the size of the neocortex, the part of the brain associated with social and cognitive processing, and the average size of social groups observed in many primate species.
While the Dunbar number has been subject to critiques and alternative proposals, its plausibility is supported by empirical observations and studies. However, there is no one definitive derivation of the Dunbar number from first principles.
In an attempt to derive the Dunbar number, I will assume that the most important cohesive group in prehistoric societies was the family, or more precisely, the extended family. Hunter-gatherer societies relied mostly on their relatives while competing with other families. Therefore, the maximum group size was not determined by the capacity of the neocortex. Instead, the neocortex evolved to track the maximum number of extended families living in proximity to the group.
By using maximum birth rates and child mortality rates from research on modern isolated hunter-gatherer societies, the sizes of immediate (adolescent children and parents) and extended (from grand-grand-children to grand-grand-parents) family groups can be estimated. The birth rate for prehistoric societies is estimated to be 4-6 children per mother, and a maximum child birth rate of 6 children per mother will be assumed (Kramer, 2005, 224-237). The mortality rate for prehistoric hunter-gatherer populations was estimated to be around 30-40% for individuals who survived childhood and reached reproductive age, and a maximum survival rate of 70% or 0.7 factor will be used (Walker et al., 1988, 183-8).
My main proposition here is that the maximum size of a socially cohesive group is a result of the natural selection process of getting used to your extended family size.
With the maximum rate of 6 and survival rate of 0.7. The first generation will have 0.7 6 = 4.2 children + 1 father, which amounts to 1+ (0.7 × 6 )²=5 family members in the first generation, (1+ (0.7 × 6 ))² = 27 in the second generation and (1+ (0.7 6 ))³ = 140 in the third. With the average life expectancy of about 33 to 37 years, as an example, a study of the !Kung San people of southern Africa found that their average life expectancy at birth was around 37 years (Howell, N. (1979). Demography of the Dobe !Kung. New York, NY: Academic Press.) There will be at most 3 generations for the extended family to form from grandchildren to grandparents. The maximum size for the 3 generations of the family will be 1+ (0.7 × 6 ))³ = 140.
The calculations are also consistent with the Dunbar number of the first generation of 5.
I am also is fully aware that my calculations are based on several assumptions and simplified models of prehistoric societies. The actual social structures and dynamics of prehistoric societies were likely much more complex and varied than our current understanding. Moreover, the Dunbar number is not an absolute cognitive limit, but rather an estimate of the maximum number of stable social relationships that humans can maintain on average. Individuals’ actual social networks can vary widely based on various factors, including cultural and individual differences. Nonetheless, my calculations are close to the Dunbar number, derived from first principles and come from the simple assumptions.
This proposal sheds light on the potential evolutionary origins of the Dunbar number and highlights the importance of extended family and kinship ties in the formation of social groups. It also suggests that the cognitive capacity for social relationships may have evolved in response to the demands and opportunities of prehistoric societies, where social cooperation and coordination were crucial for survival and reproduction.