According to Wikipedia, “British anthropologist Robin Dunbar… proposed that humans can comfortably maintain only 150 stable relationships.” Malcolm Gladwell covers this well in his book “The Tipping Point.”
However, I first became aware of this fascinating basic concept long before in 1977 when reading “The Emergence of Society” by John E. Pfeiffer.
On page 33 when he is discussing the “mounting population pressure” of villages he says, “The magic number changed too. As the countryside became more thickly settled, conflict was more of a problem. The risk of fighting between tribes increased, so that a village had to be large enough to defend itself. On the other hand, its size was limited. The more people living closer together, the greater the number of conflicts between them, the greater the risks of dissension and falling apart. The first villages may have included 50 to 200 persons, but that magic number probably worked out to about 100 persons, with the tendency to split into two villages increasing sharply over that level.”
On page 55, Pfeiffer talks about “another magic number” when discussing how some hunter-gatherer tribal populations tended to “cluster at about 500 persons.” He says, that “500 may not be far from the number of individuals a person may be expected to recognize on a first-name basis. Beyond that the strain becomes greater on man’s powers of memory (one reason for an architect’s rule of thumb that an elementary school should not exceed 500 pupils if the principal expects to know them all by name and the decision of some churches to split into smaller groups when membership exceeds 500). When populations rise much above that level, people may need markers to identify themselves as friend or foe.”
Later in the book he goes on to relate all this to central place theory and to other things.
Of course, there’s also H. Russell Bernard and Peter Killworth’s “magic number” of 290, which differs from Dunbar’s. According to Wikipedia, “The Bernard–Killworth estimate of the maximum likelihood of the size of a person’s social network is based on a number of field studies using different methods in various populations. It is not an average of study averages but a repeated finding. Nevertheless, the Bernard–Killworth number has not been popularized as widely as Dunbar’s.”
https://en.wikipedia.org/wiki/Dunbar%27s_number#Alternative_numbers