Richard Dawkins, in a fine bit of rhetoric in his book the selfish gene, asserts that from one perspective, that our bodies are merely the means by which genes reproduce themselves. We are mortal, but genes are immortal.
Selfishness, however requires intentionality, a conscious will to that purpose. Genes are neither conscious nor will-full subjects. They are not subjects at all.
Being thus not a subject, then they lack any notion of the self, one could say in all truthfulness - the self-less gene.
But are genes altruistic, are they giving? We would certainly not exist if genes did not exist. Are we then the gift of genes? But why stop at genes, we certianly wouldn't exist without matter, nor space, nor time. Are we then the gift of space and time and matter?