Actually (presuming it holds up under testing and observation) the model of autonomous biological self-organizing complexity is itself a non-corporeal which drives the "variation". But then again it seems that physical reality is highly mathematical - as Wigner called it the "unreasonable effectiveness of math".
But also among the non-corporeals are "qualia" which contribute to behavior - likes, dislikes, pain, pleasure and other such phenomenon which can only be individually (or autonomously) experienced and cannot be expressed.
Decision making and awareness (properties of intelligence) are also non-corporeal per se as is successful communication (information) in biological systems - both in molecular machinery and among organisms.
Thus when a bird sees another with particularly fluffy red feathers and thinks "oh, baby!" and proceeds with a courtship - the decision of both selector and selectee contribute to the unique genes of their offspring who have likes and dislikes of their own.
Of a truth, the only metaphysical naturalist defense in the face of all these non-corporeals is the assertion that the mind is merely an epiphenomenon of the physical brain. Epiphenomenons are secondary phenomenons which can cause nothing to happen.
Thus, in that view, your thinking that you moved a finger to press a key was an illusion. It was actually the physical brain doing it.
The theory falls flat for many reasons, none the least of which is personal responsibility. If it were true, then the mass murderer is just doing what he must. There would be no such thing as free will at all. The universe would be highly determined, etc.
The concept is also refuted by decisions made among creatures which have no brain, swarm intelligence, etc.
There are those philosophers and scientists (naturalistic) who do believe strongly in determinism, that there is no such thing as free will. They will argue that all is just reaction to stimuli according to prescribed physical and/or biological law.
They really do consider the mind and the will to be epiphenomena of the brain. (And the "brain" an epiphenoma of biological/physical laws???)
On the other hand, there are those out there who believe: "I am real."
What's fascinating to me was God's revelation of his identity to Moses. He said --- "I AM."
That is nothing more than an argument from adverse consequences, a failure of reasoning. In light of the fact that the bulk properties of human behavior are thoroughly deterministic on a mathematical level (even though we cannot always make precise predictions ourselves), it is incumbent on others show that a mass murder is not on a deterministic path.
Choice is an illusion, an assertion supportable by the measurable determinism of human choices in practice. A system capable of supporting genuine free will would have very different behavioral characteristics.
Nevertheless, the stimuli do have to be transmitted in order to feed your "qualia." So there are at least three things here: the change itself, the means of transporting a stimulus (to the right place), and the qualia (qualium?) itself -- which in turn leads to a response of some sort.
That's a whole lot more than just a simple genetic change, which goes to point out that there are system-level things going on here that the debate (at least at FR) seems to leave out.