Cost of natural selection
The selective death that must occur for a gene to be substituted was called the cost of selection by the biologist J.B.S. Haldane.
The higher the intensity of natural selection, the higher the amount of selective death (or infertility) there must be. A population cannot tolerate an indefinitely large amount of selective death: if selection is too strong it will drive the population extinct.
The cost of selection places an upper limit on the rate of evolution:
Suppose there are two alleles in a population, A and A' with fitnesses 1 and (1-s) and frequencies p and q (=1-p) respectively.
In any generation, of the q A' -bearers, s will die without reproducing and (1-s) will survive likeA -bearers. A proportion, sq, of the population dies without reproducing because of selection at this locus.
We can now define a ratio of the proportion of individuals in the population that survive to the proportion that die: sq die, and p+q(1-s) = 1-sq survive. The ratio in one generation is sq/(1-sq). The ratio is the same every generation until A' is eliminated. As selection operates each generation, more and more selective death accumulates.
We can now define the total cost of natural selection as:
C = S [sq /(1 - sq)]
(The summation is over all the generations it takes to fix the A gene.)
If a population is to maintain itself, the individuals that survive have to produce sufficient extra offspring to make up for those that die before reproduction. Because of this there will be an upper limit to the possible cost of natural selection. If the ratio was 0.999/0.001, each survivor would have to leave 1000 surviving offspring, which would be much more difficult.
The upper limit suggested by Haldane for a diploid population was one gene substitution per 300 generations. Haldane’s cost of selection was used to argue that the rates of molecular evolution are too fast to be explained by natural selection.
The geneticist Linda Partridge defines the cost of selection.
The image is of J.B.S. Haldane, photographed in 1914.