Morality is not some intrinsic quality in living forms. It is a code of behavior that can be arrived at via group enforcement (which many mammal species practice, especially primates) or by reasoning out the benefits and consequences of certain behaviors and enforcing via societal structures (as humans almost always do). The former group does indeed arrive at its moral systems at least in part through evolution, since those species who enforce 'good' and punish 'bad' behaviors are more likely to survive in the long term.
As for the latter, if you can explain why an action is moral or immoral, then a deity is not a required component of a system of morality.