Relative Advantage and Fundamental Theorems of Natural Selection

According to the tenet of Darwinian selection, a phenotype will spread only if its fitness is greater than the mean fitness of the entire population. It is, therefore, natural to introduce the notion of relative advantage of a replicator, which is defined as the expected fitness of this replicator minus the average fitness of the entire replicator population. For the general replicator dynamics, it is shown that the relative advantage of an offspring population over its parent population is proportional to the variance in fitness. The relationship between the proposed and earlier versions of the fundamental theorem of natural selection is also discussed.