"Necessarily" is a standard that's too strict and binary. The relevant question is to what extent brain size facilitates and is correlated with intelligence.

"Necessarily" is a standard that's too strict and binary. The relevant question is to what extent brain size facilitates and is correlated with intelligence. It doesn't seem to be irrelevant. Large brains are correlated with higher IQ within humans. Also, humans' intelligence came about with an almost doubling in brain volume over two million years. Across very different species there is a weaker correlation but it still seems to be positive. Whales and dolphins are far smarter than ants. Octopuses seem to be an outlier in that respect. I think it's fair to say that the probability of an "Einstein" is positively correlated with body mass, and therefore negatively correlated with population density, at least up to a point (whether that correlation turns negative beyond a point can be debated).