Group & kin selection

I promised I'd go over the recent PNAS paper, Group selection and kin selection: Two concepts but one process. This is one of those articles where most of the heavy lifting is in the technical appendix. I've decided that it isn't worth the effort to restate this verbally in detail, I looked over the algebra and I didn't catch anything glaring (though I could have looked more closely), and would have felt ridiculous pointing out where they used "the chain rule here." The main point that I gathered from this paper is that Martin Nowak's model used groups which did not split very often, but persisted for long periods only subject to within group dynamics. Operationally by the time that splitting did occur Nowak's groups would be inbred as all the individuals exhibited identity by descent from a common genetic ancestor for the locus in question (which would be fixed).¹ This means that the coefficient of relatedness within these groups is on average about ~1. In other words, the demes that compete within Nowak's model are actually simply extended families for whom inclusive fitness applies as well.

1 - In small groups most alleles go extinct either through drift or selection over the long term so that one allele at a given generation, t, eventually fixes to 100% at t + n generations. Mutation-selection balance and balancing selection can maintain polymorphism isolated populations.