Jos Gibbons, of course you do what? Do you mean that all characteristics must be copied? But what has such an overly stringent definition to do with evolution?

Obviously a bacteria doesn't copy itself molecule for molecule. But so what? It can still make a genetically identical copy of itself, and that is what should matter. I'm not exactly the same individual I was a year ago if we look at all characteristics, and molecule for molecule, but how is that relevant for evolution?

I don't really understand what you are saying about r, but it does not seem to answer my request for empirical evidence for the 1/2 and 1/4 numbers.

It seems to me that it's only "the conditional probability that the recipient of altruism contains an altruism-causing gene given that the altruist does", if the altruist is the only source of that gene. But I just pointed out that in real life we have no reason to assume that the altruist is the only source.

So when a successful gene spreads through the population, the 1/2 and 1/4 stuff should no longer be relevant. It only holds for a newly introduced gene, right ...?