Did dawkins recant his selfish gene argument against group selection?

In 2007, David S. Wilson and Edward O. Wilson (27) pointed out that, Richard Dawkins had admitted that, contrary to what he had claimed in his book The Selfish Gene (1976) (7), the idea that only the gene is a fundamental unit of selection cannot be used as an argument against the notion of group selection. This elicited a sharp denial from Dawkins (30), which was followed by an explanatory reply by Wilson and Wilson (33) and another vehement denial by Dawkins (34). I analyse the prehistory of this surprisingly complex and convoluted dispute and subsequently disentangle it. My conclusion is that much of it is based on a series of misunderstandings. First, Wilson's and Wilson's (27) original interpretation of Dawkins' selfish gene argument was incorrect. Second, in their explanatory reply (33), they distinguished between two kinds of group selection: the idea that groups can be units of selection (theoretical group selection) and the idea that group selection plays a functional role in evolution (functional group selection). They clarified that their claim concerned theoretical group selection, not functional group selection. Third, that clarified claim was correct and not correct. It was incorrect because Dawkins has never explicitly acknowledged that he had erred by developing his selfish gene theory as an implicit argument against this kind of group selection. However, the distinction that he made, by 1978, between two kinds of unit of selection, replicators (genes) and vehicles (somas), does imply such an acknowledgment since it holds that groups can be units of selection (vehicles). In this important sense, Wilson's and Wilson's clarified claim (33) was correct. Fourth, Dawkins' second denial (34) concerned functional group selection, not theoretical group selection.