Genius emerges from individualism - the genius just is an individual who is significantly and personally responsible for some major human accomplishment.
So the seedbed of genius is a society, or a kind of person, who is individualistic - and such societies and persons have been absent for much of human history. When the individual feels himself to be immersed in the group - genius is not possible; only when persons are self-aware, at least somewhat differentiated from their social group is genius possible.
This is presumably partly a matter of genetic change - but it is surely a matter of historical and cultural change: to all appearance, there has been evolution (in the sense of change) of consciousness. Socrates would not have been possible in most of the human world up to that time - perhaps in no other part of the human world until some parts of Ancient Greece?
But the genius is Altruistic as well as individualistic - and I mean, here, altruistic in terms of differential reproductive success (or 'fitness'). The average genius seems, as a matter of measurement, to have lower than average reproductive success - especially when we consider that throughout most of human history it was necessary to produce more than four children for the minimum replacement number of two of them to survive to adulthood in a sufficiently healthy state to reproduce. Not many geniuses had five children; many had none.
And aside from the estimated numbers; it is clear that the genius has less than usual interest in social and sexual success - and that this is intrinsic to genius, since the genius must have (at least during the years of his greatest accomplishment) a focus on his work that is intense and often obsessive - and such an investment of time, energy and resources entails a major shift in priorities away from those of normal (non genius) people.
Consider the sheer impact of a genius - of that one single person. The impact of a genius on the reproductive success of his group may orders of magnitude faster and greater than that of any possible person operating via natural selection. Some high status men may have had hundreds of children; but some geniuses have affected the survival and reproduction of millions of people.
As a recent example, Alan Turing (presumably) had no children and made zero genetic impact on the species; but without him the German Enigma code would not have been solved and the 1939-45 World war would have lasted longer and the casualties on the Allied side would have been significantly greater - without Turing the development of the computer would also have been delayed or impaired, with large and widespread effects.
My point is that (when his work is beneficial) a genius has an effect on a broad population of genetically unrelated and mostly unknown people which far outstrips the genetic level of impact. So the genius is both an individual yet, in effect, he is 'working for' other people (in the sense that any personal gains he may make from his work are likewise utterly dwarfed by his contributions to the larger group).
The situation therefore seems to be that when there occurs an increase in the incidence of genius, this arises from a human population in which individualism has been intensified; but that the genius does not pursue individualistic goals for individual benefit - it is as if the genius had been called-forth or created by the group in order to serve the group (not just his kin, not just those in the group who have a relationship - but a much wider group).
It is as if the genius is set up so that as an individualistic-individual, he willingly and by choice and effort, sacrifices his own (relatively modest) chance of genetic success in altruistically attempting to generate a much greater success in terms of survival and reproduction of his group.
Since altruism in biology is defined as acting to increase the reproductive success of other at cost to oneself, this makes the genius the ultimate altruist.