Richard Dawkins says no. “We don’t need to get morals from our religions … We don’t want to find morals from the holy books. We can have our own enlightened secular values.”
We do need God, however, to account for the existence of morals. Evolution - no natural process - can do that. Morals are immaterial, universal values. They aren't physical things so science can't study them and natural processes can't explain them. There's no mechanism in nature or evolutionionary theory to explain the nature or existence of morality.
The only alternative for a committed naturalist as Dawkins is is moral relativism. But then naturalists have to give up their claim that morality has any obligation on us because relativism gives up any universal claim. Yet naturalists such as Dawkins and Michael Shermer want to maintain that they do believe in objective morality. This was illustrated in Greg Koukl's debate with Shermer a couple of years ago. But they have no adequate explanation for morality in their materialist worldview.
Morality has to be explained and fit in a worldview. And theism is the only one that has explnatory resources for the source and nature of morality. It's called the "grounding problem." Religions and holy books may or may not reveal specifics of morality, but it's God that is the explanation for why morality exists.
At the end of the article, Dawkins blunders by claiming that if God created the universe then His existence needs an explanation, so it explains nothing. Dawkins obviously has never attempted to consider the arguments he disagrees with.
We know from observation, and it's a fundamental fact of science, that events need causes. No event occurs without a cause. There are two kinds of causes - other events and persons. Persons can be independent actors, causes without a need for further explanation. God is a person, and as an immaterial being wthout a beginning, He has no need of a cause and is an adequate explanation in Himself. So God as the first cause of the universe needs no further explanation for His existence.
Now Dawkins may not accept that this God exists. But the cosmological explanation is logically sound and doesn't beg the question of God's existence. In that way at least, it is explanatorily superior to evolution for the origin of the universe.