Analysis of "group selection and inclusive fitness are not equivalent"

I briefly analyzed the paper:

Group selection and inclusive fitness are not equivalent; the Price equation vs. models and statistics by Matthijs van Veelen, Julian Garcia, Maurice W. Sabelis, Martijn Egas.

This is one of the papers mentioned on my equivalence naysayers page.

The paper claims that group selection and kin selection are not equivalent. It argues that inclusive fitness requires fitnesses to be "additive". Additive fitness is a common assumption when deriving Hamilton's rule - and is indeed associated with inclusive fitness. However, inclusive fitness is a simplified model of kin selection. Kin selection enthusiasts are not too impressed with such critiques - the limitations of inclusive fitness are well known. The paper uses "kin selection" and "inclusive fitness" as though these concepts are interchangeable. I think this is not all that useful an approach.

Kin selection doesn't depend on fitness being additive. That idea is associated with inclusive fitness and Hamilton's rule. These are concepts associated with simplified models of kin selection.

Hamilton advocated using "inclusive fitness" instead of "kin selection". Hamilton (1975) "Innate social aptitudes of man" says:

The usefulness of the ‘inclusive fitness’ approach to social behaviour (i.e. an approach using criteria like (b K-k) > 0) is more general than the ‘group selection’, ‘kin selection’, or ‘reciprocal altruism’ approaches.

However, I think the pendulum has swung away from "inclusive fitness" and back towards "kin selection" as the term of choice. That's what Gardner and West use tend to use, for example. I'm with them.