This argument is somewhat long-winded, and I believe some of my points may have already been touched on elsewhere. So please bare with me. I am numbering the paragraphs for ease of reference.
1. In "The God Delusion", Dawkins briefly discussed "absolute" foundations for morality, his two instances being religion and patriotism (and the hybrid). I would argue that we can find another in physics. I could swear that he was making this argument in "The Selfish Gene", with the concept of altruism being a selected genetic trait. We may not need to go on from here, but please indulge me.
2. Being RC most of my life, I have always known the core of morality as "love thy neighbour". But all the great religions basically espouse the minimization of selfishness/greed, and the maximization of selflessness - the well-being of the other or the collective - sometimes including non-human entities. So, for this argument, let us boil morality down to the kernel of the selfless-selfish distinction. (If you do not agree, please respond.)
3. I like the concept of symbiosis at a biological level, and it definitely plays a role. But I am not convinced/satisfied that it is a fundamental enough explanation. I am a reductionist, so I believe all higher tiers of science & explanation ultimately boil down to the laws of physics that run the Universe. So the synergistic "sum of the parts" is not greater than the whole. But rather we assign emergent abstract models/patterns to the interactions of self-organizing systems. (Unfortunately, many people only just stand in awe of complexity.) I prefer to invoke the concept of self-organizing systems over "life", since the boundary of the latter is not generally well-defined, or agreed upon. As such, entities can be seen as self-organizing systems or "organisms" at different levels of a scale.
4. I would argue that the selfless-selfish distinction can be derived from the concept of "self-healing" (in which I conveniently include facets like homeostasis and stability). We can see "self-healing" at all levels of the entity scale.
5. Members of the biological taxonomy (humans included) are self-healing, in that their constituent parts/cells work together to heal the organism's tissues via proteins (symbiosis does come into play as well). The cells are in effect behaving "selflessly", and hence "morally". But in the act of using up energy and resources to heal oneself, an organism is effectively acting "selfishly", and hence "amorally".
6. Kin selection causes organisms to assist close relatives, and reciprocal altruism causes organisms to help each other. The human species as a whole can be seen as the humanity organism, which heals itself whenever humans reach out to help other humans (the traditional definition of selflessness). But this can selfishly damage the environment. Humans can symbiotically help other beings, say animals or the rain-forests, via "environmentalism". But I believe that is merely the self-healing action of the Gaia superorganism of Earth, of which we are a part. (Some of our less-helpful actions could be considered carcinogenic to Gaia.)
7. Gaia is likely not alone in the Universe, and I would like to think that she is just another "cell" in a higher order of life organism. Not entirely far-fetched, considering hypotheses like panspermia. The great distances involved could be overcome given enough time, of which the Universe has plenty. So perhaps the solar systems, galaxies, clusters, and even the universes (plural intended :-)) are all self-healing.
8. Moving down a level from us in the entity scale, basic cells can heal themselves using polymers from the environment. DNA can be "healed" by the rebuilding of its chemical structure, similar to the process of self-replication. At the molecular level, collections of atoms survive because they are in stable configurations sharing electrons, (as Dawkins discusses in "The Selfish Gene"), and can restablize if perturbed - another sense of "self-healing".
9. Most of the atoms of the Periodic Table of Elements are formed from stable configurations of particles, energy, and forces. When perturbed, an atom can also endeavour to restablize. For example, if photon excites the electrons of an atom, the atom will (at some point) decay to a lower energy state and hence may release a photon. I suppose quarks could have "good charm" for their hadrons, and strings could have "good vibrations" (sorry!).
10. In the religious argument for morality, one could argue (though the religious do not) that selflessness is ultimately selfish, since one's kind actions towards others are motivated by self-gain. Conversely too, the church argues that selfishness (in the form of hoarding money, real estate, etc.) actually enables selflessness. In my physical argument for morality, the natural "self-healing" processes are simultaneously both selfish and selfless!
11. In summary, I believe physical stabilization combines with self-organizing systems and evolution to enable the behaviours of self-healing entities, which forms a fundamental basis for the selfless-selfish distinction, hence morality.
Clarifications, corrections, additions, and details to help fill in gaps, are all welcome!