From
on page 44:
"What is more interesting, it is only in such small populations that natural selection would favour the spread of genes making for certain kinds of altruistic behaviour. Let us suppose that you carry a rare gene which affects your behaviour so that you jump into a river and save a child, but you have one chance in ten of being drowned, while I do not possess the gene, and stand on the bank and watch the child drown. If the child is your own child or your brother or sister, there is an even chance that the child will also have the gene, so five such genes will be saved in children for one lost in an adult. If you save a grandchild or nephew the advantage is only two and a half to one. If you only save a first cousin, the effect is very slight. If you try to save your first cousin once removed the population is more likely to lose this valuable gene than to gain it. But on the two occasions when I have pulled possibly drowning people out of the water (at an infinitesimal risk to myself) I had no time to make such calculations. Paleolithic men did not make them. It is clear that genes making for conduct of this kind would only have a chance of spreading in rather small populations where most of the children were fairly near relatives of the man who risked his life. It is not easy to see how, except in small populations, such genes could have been established. Of course the conditions are even better in a community such as a beehive or an ants' nest, whose members are all literally brothers and sisters."
I don't know whether anyone has noticed a subtle issue here. Haldane envisages a small population so that everyone is related; the benefit seems to accrue to a random member of the population. It therefore cannot raise the frequency of the altruism allele within that population -- in fact it decreases it by the risk to the altruist. But it could benefit the whole population (by benefiting a random member of it) and make it have a greater contribution to the weighted gene frequency in the whole species. Thus it seems that this is more a case of group selection than kin selection. In fact, as noted by Crow and Aoki (PNAS 1982) the Hamilton kin selection formula also works for group selection, so the distinction is in any case unclear. Haldane has the essential logic of the Hamilton argument, but in this case is applying it to group selection.