We suggest two extensions of the coalescent effective population size of Sjödin et al. (2005) and make a third, practical point. First, to bolster its relevance to data and allow comparisons between models, the coalescent effective size should be recast as a kind of mutation effective size. Second, the requirement that the coalescent effective population size must depend linearly on the actual population size should be lifted. Third, even if the coalescent effective population size does not exist in the mathematical sense, it may be difficult to reject Kingman's coalescent using genetic data.
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