Monday, 1 August 2011

Filling in Dunbar's Number

Robin Dunbar has argued that -- based on brain size, grooming time, and the size of existing human societies -- humans evolved in groups of around 150 individuals. There are many ways to take this figure, but here I want to take it at face value and think about the people who would have filled up that number. Let's keep it simple, and see where we get.

If everyone died when they were 60 years old, we would expect 50 kids (0-19), 50 adults (20-39), and 50 post-reproductive 'seniors' (40+). But of course, there is much more wastage under natural fertility conditions, and the population is much more 'pyramidal'; so let's say 75 kids, 50 adults, and 25 seniors. We can also say that there would have been about 75 males and 75 females; although because males die off earlier, there would have been slightly more male kids, and slightly fewer male seniors. We would end up with a society that looked something like this:

What else can we say?

Well, let's suppose that the juveniles start getting interested in the opposite sex in their late teens. And let's say that two of the males and two of the females leave the group to seek mates elsewhere (to avoid mating with their brothers and sisters), and are replaced with new arrivals. This leaves about 8 single guys competing for the affections of about 8 single girls -- not much to choose from! About four of these guys would settle down with a cousin (or a more distant relative); and two would settle down with a newcomer.

The 50 adults have already been through this process, leading to about 25 parenting couples, forming the nucleus of 25 families. On average, these families would have consisted of three kids, and one grandparent. Drawing the family tree of this society has so far defeated me (perhaps I'll have another go in a future post), but it should be possible to construct one, and from there calculate typical degrees of relatedness.

(Polygamy and 'extra pair copulations', would have complicated the picture a little. If one in ten adult males has two wives, and if one in ten children is the product of an extra-pair copulation, then we would have about two or three single guys, and two or three cuckolded husbands. But let's not go there just now.)

Adult males would have competed for status with around 24 of their peers. Individuals can augment their power by recruiting allies and forming coalitions, and to the extent that disputes are won by the minimally-larger coalition, we should expect the internal politics of the group to consist of one coalition of 11 and another of 13. These coalitions may have divided along family lines, by age cohort, marital status, around some prominent individual, or no doubt some ever-changing, dynamic combination.

If the males of the group went to war with their neighbours -- with the youngest seniors commanding both the adults and the oldest juveniles -- we would expect to see around 37 males on each side.

Of course, I am just making up these numbers (and trying to keep it all straight with the help of a spreadsheet). The point is that, even with minimal information and starting assumptions, it is possible to make rich inferences about the structure of the social lives of our ancestors.

What other inferences can be drawn? What happens if there is a baby boom? What if we put in a more realistic level of infant mortality? What if all the warring males get wiped out? What proportion of the couples might prove to be infertile? What if the society is exclusively matri-local (all the young males leave and are replaced) or patri-local (all the young females leave and are replaced) as opposed to both? What does that family tree look like? What happens when societies combine? When do they split?

Have a play with the model, and let me know how you get. 

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