Some spotty thoughts (I haven’t read the whole thread):
I think it has been assumed that “free will” is some known (or knowable) quantity, and that this known quantity is always present in human beings (implied here by there being a physical form of it in a gene), while the truth is that it is almost always absent. It only appears upon reflection, and most people do not reflect on most of what they choose or do, they simply choose and do. Free will seems only to come up when a problem arises - that is, we don’t seem to notice freedom until we lack it for some reason. Otherwise, at other times, free will is not an issue. (I think that the whole question is backwards: it ought to be answering what the nature of restraint is. It is interesting that the exercise of free will usually seems to be posited in connection to ethics, which is to say in terms of using one’s freedom, and reason, to limit one’s choices, i.e., the proper use of freedom is to limit freedom.)
The evolutionary aspect might be found in what allows for reflection, and the development of the habits of mind (psychology if you prefer) that lead to our questioning our lack of ability to do anything we want whenever we want. Habits of mind depend not only on the physical, material brain, but the evolution of culture that allows the kind of thought that ends up being self-contemplating, that can create a self, in the mind, to contemplate. That capacity is not innate, but arises from interaction of minds, and the interaction that produces self-reflection depends on culture to exist. I say that self-reflection appears only with interaction on the evidence of what becomes of people who do not interact, especially in the case of “feral” children, but also of other people denied human interaction - even established self-conception appears to be eroded by a lack of interaction.
Put differently, free will depends on my realizing that I have free will, which in turn depends on my realizing that I am an “I”. In turn, I recognize that I am an “I” because I interact with others who appear to recognize “I"s of their own, and me as another “I”. In explaining why they do what they do, and why I do what I do, I have recourse to this idea of free will, which is at first a recognition that you can do otherwise than you do, and that I can do otherwise than I do, at least in principle. This, in turn, leads to the idea of responsibility - that you must answer for what you do, because I presume you choose to do it freely (of course, in your response, you can educate me as to what the actual choice was, and that perhaps your freedom was limited in some way I was not aware of).
As for other species, if you ask whether a dog has free will, you can answer that he does, because he can choose where to lie down, whether to drink some water or not, and so on, so that to the extent that a dog makes choices that are free that the dog has free will. But we usually attach some kind of awareness of the free will as a part of the definition. That seems like a bit of a dodge to me. A dog that is used to some kind of freedom - an open gate, or lack of a leash, e..g - which is then denied that freedom might be agitated, and give use evidence that it is aware of it’s former freedom. But who could know what’s really on a dog’s mind?
I suppose I am falling back on the pragmatist definition of what a concept of something “is” - “Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have. Then, your conception of those effects is the whole of your conception of the object.” That is, when we think of “free will”, what we mean by it is defined by the practical effects that our idea of “free will” has in the world. So considered, I don’t think anyone can really deny that there is some freedom to the will of anything that we consider as having any will at all.