On fitness and the cost of natural selection
Authors: Feller William 
Published: September 2009

A Mendelian population without artificial external constraints does in general not increase at a constant rate. Formulas neglecting the changes in population size introduce an error which is negligible under ordinary circumstances but whose cumulative effect over long periods may be disastrous. Questions relating to the cost of natural selection, the nature of an unstable equilibrium, the survival of genes, etc. cannot be treated without regard to absolute population sizes. The limitation of the notion of relative fitnesses is illustrated by the fact that in some typical situations the survival of the a-gene depends only on the absolute fitness of the Aa-heterozygote, but not on the fitnesses of the homozygotes. Furthermore, a decrease of the (absolute or relative) fitness of one genotype may actually increase the viability of the population and its ultimate size.

Even when the relative frequency qn of the a-gene tends to zero the absolute number of such genes may increase from generation to generation at a geometric rate. Therefore the circumstance that qn → 0 may be insignificant as compared to the fact that the earth cannot sustain an infinitely increasing population. Ultimately the population size is bound to influence the environment and so the fitnesses will change. Thus we must consider density-dependent fitnesses and then observed fitnesses cannot be used to predict the ultimate fate of a population. It is now known (Dobzhansky, 1965) that relative fitnesses are sometimes very sensitive to small changes in environment and that the same species may occupy a great variety of environmental niches. It is therefore quite likely that at least part of a population will find itself in a modified environment before too many generations have passed. For the evolution of a species and the development of new forms it is then not important that under fixed conditions the relative frequency qn of the a-gene would tend to zero. The problem is whether the actual number of such genes will increase for a period sufficiently long to encounter changed conditions or to establish itself in new combinations. This question is significant because the convergence of the frequencies qn to zero may be extremely slow. Thus even in a population of fixed size a disappearing gene could exist long enough to contribute to evolutionary processes.

Speaking generally, the thinking in terms of an assumed steady state and relative fitnesses seems to aggravate the problem of applying the wonderful results of modern genetics to the theory of evolution. For example, various mechanisms which are often considered as eliminating genetic variability may sometimes produce the opposite effect. The theory of evolution should distinguish between what the physicist would call macroscopic and microscopic equilibrium. Even if the world as we see it were in a perfect equilibrium this would not imply an approximate steady state for individual species, not to speak of genes. It is clear that an evolution to higher forms depends on a frequent decrease in fertility rates. If one considers slow changes rather than an unattainable steady state then a loss of fitness may be beneficial in the long run and contribute to genetic variety.