What does this equation mean?

The prediction itself has a precise origin and it is much narrower than its reputation. Robin Dunbar’s 1992 paper in the Journal of Human Evolution ran a comparative regression across primate genera and found that group size tracked one variable with real predictive power — the ratio of neocortex volume to the volume of the rest of the brain — while the ecological variables he tested alongside it, tied to diet and ranging behavior, did not [ 1 ] . Stated as a model, the claim was this: $\log(N_{\text{group}}) = \alpha + \beta \cdot \log\left(\frac{V_{\text{neocortex}}}{V_{\text{rest of brain}}}\right)$. Group size as a function of relative neocortex volume, nothing else in the model earning its keep. Dunbar’s interpretation was mechanistic rather than merely statistical: neocortical processing capacity limits how many relationships an individual can track simultaneously, groups that exceed the limit fragment, and large stable groups in nature are typically built by welding together smaller grooming cliques rather than by everyone bonding with everyone [ 1 ] . A year later, in Behavioral and Brain Sciences , Dunbar ran the human neocortex ratio through the same regression and extrapolated that people should live in stable social groups of roughly 150, a figure he supported by pointing to census data collected from a range of tribal and traditional societies in which groups of about that size recurred as a structural unit [ 2 , 4 ] . That 1993 paper is doing more work in the popular imagination than any single subsequent study, because it is the paper that actually says “150” about humans. Everything since has either supported it, refined it, or tried to take it apart.