how does evolution explain altruism that's not reciprocated?
This has been explained using game theory - surprisingly enough. The prisoner's dilemma is the tool to use. The prisoner's dilemma is a non-zero-sum game, and I'll be so bold as to hash it out here in case you are unfamiliar with it.
Two guys are arrested, but the evidence is thin on the ground. The police decide to offer both guys a deal: Testify against the other to avoid a harsh penalty. There are three possibilities: Both men will agree to testify against each other, they both stay silent and one testifies and one remains silent. The prisoners cannot collude.
For each of these outcomes there is a consequence for the prisoners:
If both testify, they both go to prison - but they are given only a 5 year sentence for essentially cooperating with the police.
If both stay silent, they both got to prison for 6 months for a lesser charge.
If one testifies and the other remains silent, the silent one goes to prison for ten years and the testifier goes free.
What is the best strategy for the prisoners? If you were prisoner A you don't know what your cohort is going to do. If he stays silent your best strategy is to betray him. If he betrays you your best strategy is to betray him to to avoid the harsh sentence. Thus, whatever he chooses to do - betraying him is the best option.
This is the situation that most people think about when they think in terms of morality in a godless world...there is no reward for nice guys so why bother being nice?
However, our social interactions are rarely so straightforward. So we imagine a more complex game in which the two prisoners face a similar dilemma 100 times. This time they get half a day added to their sentence if they both stay silent, they get 5 days added to their sentence if they both betray and if one betrays and the other doesn't, the silent one has 10 days added to his sentence and the betrayer gets 0 days added.
Is it possible that cooperating with one another can emerge as a successful strategy in this environment? It is possible, yes. A successful strategy can be nice (is not inclined betray), retaliatory (punishes those that betray them by betraying them in the next round), forgiving (will become nice again if the other player stops betraying them) and non-envious (doesn't try and beat their opponent, just tries to do as good as they can).
Things get even more interesting if we take the iterated prisoner's dilemma to its next level: A population of prisoners rather than just two, and they come all to play against one another. Then we see that several strategies can be successful and an equilibrium forms. If any one prisoners changes their strategy they will automatically do worse. They might not be 'winning', but given the strategies everyone else is employing it could still be the best strategy to employ.
Now altruistic tendencies are based on 'rules of thumb', which is our strategy for dealing with our iterated dilemmas (ie social interactions). And we have another rule in play: advertisement.
It is easier to lie than it is to detect a lie - but consistently lying and you will be found out and it could become public knowledge. So it is no good just pretending we are nice as a way to advertise we are worth being nice to - we'll generally end up getting caught. A much better strategy is to actually be nice, so evolution will tend us towards making us actually nice rather than just appearing to be nice.
This has the knock on effect of making us be nice, even when technically there is no good reason to be: our action will go unnoticed or we will die (advertisement is useless), and the people we are nice to contain genetic rivals (genetic madness). Reproductive pressures to fit in to the group are much stronger than the reproductive disadvantage to occasionally being selfless without getting noticed.
It is much easier to do nice things for non-relatives nowadays so it all seems paradoxical, but a mere 10,000 years ago it all makes a great deal of sense.
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