The futility of attempts to rehabilitate fisher’s fundamental theorem of natural selection

Fisher's "Fundamental Theorem of Natural Selection" purports to relate the rate of change of the mean fitness of a diploid sexual population to the additive genetic variance in fitness. On one interpretation, the "theorem" concerns the total change in fitness and is false under general conditions. According to another interpretation, Fisher's claim relates to only one component of the change in fitness, which corresponds to the change attributable to selection or to changes in allele frequencies. However, this correspondence is the subject of debate. I argue, based on illustrative scenarios, that the quantity in question has neither of these meanings, nor any other meaning related to the effect of selection on fitness. First, I show that this quantity can differ dramatically from the effect of selection on fitness and from the effect of changing allele frequencies. Second, I demonstrate that this quantity is sensitive to the presence of selectively neutral genetic differences, which do not alter the effects of selection on fitness. Thus, interpreting it as a measure of such effects leads to incoherent conclusions. Such interpretations must therefore be rejected, along with the claim that the Fundamental Theorem represents an important biological truth.