The change in a mean measurement that is invariant under reshuffling of genes

Fisher's fundamental theorem of natural selection continues to be widely cited in the literature but there is still misunderstanding about its interpretation and significance. Even though it is now recognized that the additive genetic variance in its statement captures only a partial rate of change in mean fitness, the original terms and arguments used to present it remain unclear, not to mention its real meaning. Here, we revisit the interpretation of this partial rate of change. Applying the properties of the additive genetic values and residual addends of a quantitative trait to the relative growth rate of genotype frequency in a diploid population, and comparing two reproductive systems, clonal reproduction and sexual reproduction with either random union of gametes or random mating with additive fecundities of mating types, we argue that this additive genetic rate of change corresponds to the change that is invariant under reshuffling of genes. We show that this is actually the case for the partial rate of change in the mean of any measurement given by the additive genetic covariance with fitness. We focus on the one-locus multiallele setting in continuous time without age effects for simplicity, but the conclusion can be extended to multilocus settings with age effects in continuous time as well as discrete time.