There are many layers to genius - although typically only those nearest the surface are considered.Some of the main layers are:
1. Sociological - Impact on history
2. Biological - differential - Reproductive Success
3. Biological - ideal - Fitness
4. Philosophical - Fitness for what?
5. Theological - in relation to Ultimate Purpose
1. Sociological - this is the usual level of analysis, the usual definition of a genius.
A genius is seen as a person who has made a disproportionately large impact on human history. This can be measured more-or-less objectively.
2. Biological - Differential. A genius is seen in biological terms as one who makes an disproportionately large impact on human reproduction.This is measured in terms of reproductive success, which is measured in terms of the number of descendants of a genius and/or the group to which he he belongs.
By this measure, a genius is one who causes a measurable increase in the number or proportion of his society (by some measure) - such geniuses would be those who created the technical breakthroughs leading to the agrarian and industrial revolutions.
(And an anti-genius would be one who did the opposite: caused a decline in the number or proportion of descendants. These would include those who invented or promoted liberal Christianity, atheism, socialism, feminism and the sexual revolution.)
3. Biological - Ideal. This takes account of the objective, not differential, effect of fitness (as best this may be estimated) by estimating organismal functionality.
For example, a lineage may increase in its numbers or proportion of the population; even though there is an accumulation of deleterious mutations which damage basic functionality.
So reproductive success(absolute or relative) can increase even as the underlying functionality or fitness declines.
This can happen when the environment is less harsh, inflicts a lower mortality rate (as with animals in a zoo, or human in modern society).
4. Philosophical - Fitness for what? If an ideal, not actual, concept of fitness is to be used, then it is not clear what is the environment against which fitness/ functionality should be measured.
This creates a need for, opens space for, a philosophical discourse about what Man's fitness ought to be.
By this account, a genius is one who enhances his group's fitness for (or functionality-in) the kind of environment which Man is aiming-for, or wants to have. One version of this would be a genius tending to create Men fitted for utopia.
This definition would include philosophers in the broad sense of the word; artists, painters, poets, literary authors etc.
5. Theological. Finally, and ultimately, this relates to the idea of a genius being one who promotes the ultimate purpose of Life, of divinity.
This definition would include prophets and saints; and also some artists, poets, and thinkers.
It can be seen that these various definitions of genius dissociate. For example, a genius who promotes theological ultimate purpose may damage reproductive success (if a good new religious group is exterminated). A genius who promotes reproductive success, may damage ideal fitness (i.e. population increases but so does the deleterious mutation load).