Many atheists draw upon moral relativity to some degree, or at least the idea that morals evolved over time with species. For example, murder is counter productive to species development, if a community of prehumans stop killing each other, they thrive. Such morals, or at least something suggestive of such, is probably in our DNA.
Some primates, I believe chimpanzees (at least), show genuine empathy towards others, even ones not of their own kind. They have also been shown to help others with no reward to themselves. They had a chimp and a man in a room together, and the man was reaching for a stick (a tool), but in a position unable to grab it. The chimp walked up, grabbed the stick and gave it to the man. With absolutely no reward for itself, other than gratification. They have no bible to tell them to do this.
We get our morals not only from evolution and genetics, but from society, which is influenced by human behavior. We don't need a universal source for morals, we just use ones that make sense based on our history.
Bassoon, n. A brazen instrument into which a fool blows out his brains.