Natural evolution and morality

Consider the following assumption: Darwinian evolution is the origin of our moral believes and of our moral semantics. In other words, suppose that our ordinary beliefs about what is good (e.g. compassion) and what is wrong (e.g. slavery) are the outcome of evolution, and that, in addition to that, even the concepts of good and evil themselves are the result of Darwinian evolution. Would it, under this particular assumption, follow that natural evolution is also the ontological ground of morality?

Perhaps this question needs further clarification. Being selected by natural evolution for believing the moral believes we have (e.g. that torture is wrong, etc.) would surely count as an explanation for why we have those believes, that is to say, it would explain the origin of those believes. But it would surely not explain why these believes are true, i.e. it would not reveal the truth-maker of these believes. Indeed, it is a fallacy, known as the genetic fallacy, to ignore the difference between explaining how it came to be that we believe some true proposition and providing a justification for, i.e. revealing the truth-maker of, its truth.

Yet, the assumption above is not only that are we are selected by natural evolution for holding the ordinary moral believes we hold, but that the whole conception of morality itself would be just a product of natural evolution, i.e. it is, under the assumption I consider, natural evolution that not just produced our moral believes, but also produced the notions of right and wrong themselves.

And the question is whether it would, under this more radical assumption, follow that evolution is "all there is" to morality, i.e. that evolution is the ultimate ontological ground of what we call moral values and duties.

Further, it is not so much that I am interested in a debate on the truth of the assumption itself. In fact I think it is false. My interest is whether this assumption, if true, would be sufficient to conclude that morality is ontologically grounded in natural evolution, thereby rejecting the theistic ontological account of morality.