Back to the fundamentals: a reply to Basener and Sanford 2018.

Fisher's fundamental theorem of natural selection has haunted theoretical population genetic literature since it was proposed in 1930, leading to numerous interpretations. Most of the confusion stemmed from Fisher's own obscure presentation. By the 1970s, a clearer view of Fisher's theorem had been achieved and it was found that, regardless of its utility or significance, it represents a general theorem of evolutionary biology. Basener and Sanford (J Math Biol 76:1589-1622, 2018) writing in JOMB, however, paint a different picture of the fundamental theorem as one hindered by its assumptions and incomplete due to its failure to explicitly incorporate mutational effects. They argue that Fisher saw his theorem as a "mathematical proof of Darwinian evolution". In this reply, we show that, contrary to Basener and Sanford, Fisher's theorem is a general theorem that applies to any evolving population, and that, far from their assertion that it needed to be expanded, the theorem already implicitly incorporates ancestor-descendant variation. We also show that their numerical simulations produce unrealistic results. Lastly, we argue that Basener and Sanford's motivations were in undermining not merely Fisher's theorem, but the concept of universal common descent itself.