Is this an adequate basis for morality?

So, I've been thinking for a while about a foundation for secular (atheistic) morality. I'd like your thoughts on the following summary of my view: Morality is not absolute nor is it God-given. The impulse to be moral is biological in nature and is not exclusive to humans; social animals ranging from... show more So, I've been thinking for a while about a foundation for secular (atheistic) morality. I'd like your thoughts on the following summary of my view:
Morality is not absolute nor is it God-given. The impulse to be moral is biological in nature and is not exclusive to humans; social animals ranging from chimpanzees to whales possess it in some form. There are two major "legs" upon which morality stands: empathy, the ability to share the pain/happiness of others, and our ability to reason. Empathy gives us the impetus to do good things for others and to prevent suffering, while reason allows us to analyze our actions in sticky situations.
My foundation for morality is Well-being (specifically Human Well-being). In very simple terms, suffering is evil and happiness (that which increases or maintains one's well-being) is good. It is similar to Epicurus' basis for morality, but avoids some of its pitfalls. That does not mean that a sociopath's joy in murder is good because it increases his happiness. Reason dictates that it is evil, because the twisted happiness harms someone else's well-being. There are many moral gray areas, but our reason can usually sort it out. A morality based on well-being can be applied anywhere. It is not restricted by culture or country. It is fairly universal, where as religious morality is not.

Any suggestions, please comment. If you don't agree, please explain why. Don't merely quote Bible verses. I'd love to hear from you guys.
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