As discussed above, dominance relations are not necessarily fixed but can be modified and may even evolve. Fisher's basic argument was the following. At mutation-selection balance, deleterious alleles are kept at low frequency in a population but, nevertheless, reduce its mean fitness. Therefore, genes that protect the population from the effects of recurrent deleterious mutations should be selectively favored and increase in frequency. Since most rare alleles occur in heterozygotes, modification of the heterozygous phenotype would increase mean fitness. Wright introduced a model that formalized Fisher's proposition and has become the archetype for the evolutionary modification of dominance. It assumes a primary locus at which a wild-type allele, A, and a deleterious mutant allele, a, occur. In addition, it assumes a so-called modifier locus, with alleles M and m, where M modifies the fitness effects of heterozygous genotypes as follows:
Here, the intensity of selection against a is s >0, and the dominance coefficients satisfy 0 < k < h < 1 and h ^ 0. Mutation is assumed to occur from allele A to allele a at rate u, and recombination between the two loci occurs with frequency r, with 0 < r < xh. Fisher, and in order to refute him, also Wright, assumed that evolution commences at mutation-selection balance between A and a when a new allele M is introduced at the modifier locus at low frequency. At this initial state, with fitnesses given by the last line of , the mean fitness of the population is approximately 1 — 2u. If M became fixed, which was not proved by Fisher or Wright but only much later, the first line in  applies, and the mean fitness increased to about 1 — u. This model is in line with the graphical representation in Figure 1a. Several more elaborate analyses in the 1960s and 1970s corroborated and extended Wright's analysis. Given that per-locus mutation rates are very small, typically of the order of 10—6 to 10—5, this is a very small fitness increase. Whereas Fisher considered this to be sufficient, Wright argued for the contrary because, in his opinion, genetic drift could easily overcome this tiny fitness advantage and probably cause the loss of the modifier. In addition, the slightest disadvantage of the modifier would nullify its favorable effect. However, Fisher adhered to his proposition because he considered population sizes to be very large, of the order of 109 or higher. Hence, in contrast to Wright, genetic drift was only of minor relevance to him. Today, we know that so-called effective population sizes (this is what matters for the effects of genetic drift) are much lower than actual population size, and for most higher organisms (even species of Drosophila) less than 106. For these and other reasons, Fisher's proposition is now generally considered to be untenable.
Several other hypotheses, usually also formalized in terms of modifier models, and mostly in line with one of the mechanisms depicted in Figure 1b or 1c, have been advanced to explain various cases of dominance evolution. If, for instance, as in Figure 1b, a homozygous phenotype is changed to resemble the advantageous heterozygote, then the potential fitness increase is substantial and there are no theoretical obstacles to such an occurrence. Several cases of mimicry fall into this category. Similarly, if, as in several cases of pesticide resistance, underdominance is maintained by spatially heterogeneous selection, heterozygotes are frequent and their fitness disadvantage can be reduced by modifiers. In general, whenever there is a balanced polymorphism, as in Figure 1b or 1c, there are many heterozygotes present and evolution of dominance can readily occur.
An interesting hypothesis, in line with the formal model , was considered by Haldane in 1956. He suggested that when a gene was sweeping through a population as a result of natural selection, heterozygotes would be very frequent, and this would provide an opportunity for intense selection for modification of the heterozygote. A case in point seems to be industrial melanism in moths and butterflies. Apparently, selection of the modifier has occurred during the spread of a favorable mutant. This requires that, when the favorable mutant arises, or a rare mutant becomes favorable through a change in the environment, modifiers are already present in the population. During such a process, heterozygotes become very frequent, and a modifier can rise to high frequency and become fixed. It was proved by Burger and Wagner in the early 1980s that this mechanism indeed works. It also helps to explain several obstacles raised by backcrossing experiments in various cases of industrial melanism. Another interpretation of this process, put forward by G. S. Mani in 1980, maintains that heterozygotes have been kept at high frequency by migration-selection balance, a scenario studied in more detail by S. Otto and D. Bourguet in 1998.
Despite many well-established cases of evolution of dominance and despite several mathematical analyses that have demonstrated that dominance evolution can occur under a number of scenarios (but not under Fisher's original one), evolutionary explanations have been largely dismissed and are ignored by most textbooks.
There are several reasons why evolutionary explanations of dominance are considered to be irrelevant or even wrong. One is that Fisher's original proposition is untenable and many seem to believe that this applies to any evolutionary explanation of dominance without realizing how different they can be. A second and related reason is, as first pointed out by Charlesworth, the strong inverse correlation between the deleteriousness of a mutant and its degree of dominance. Such a correlation cannot, and was not, predicted from Fisher's theory. If, however, evolution occurs as in Haldane's model and the population is finite, the situation changes. A third, very important reason, is that Kacser and Burns' metabolic theory has been widely accepted, and thus an evolutionary explanation of dominance had seemed unnecessary. Finally, Orr showed that in 'artificial' diploids of the normally haploid alga Chlamydomonas, wild types are about as often dominant as in diploid species. He claimed that this finding falsifies Fisher's theory. It, however, only shows that dominance can occur without evolution. Moreover, as discussed by Saved and Mayo, a similar observation has already been made in 1947 by D. Lewis.
What is clear by now is that, even if the theory of Kacser and Burns is eventually replaced by a more general or different theory, molecular pathways can often generate dominance. Therefore, a priori, dominance does not necessarily require an evolutionary explanation. However, it should also be noted that molecular pathways can allow for dominance modification, and hence dominance evolution. Furthermore, and this must not be ignored, many instances of evolution of dominance have been demonstrated, noteworthily in well-understood ecological settings, and these require an evolutionary explanation.
We close this discussion by pointing out that evolution ofdominance, by whatever mechanism, is a special case of evolution of robustness, and modifier models are conceptually the simplest, and oldest, models to study it. More generally, epistatic interactions among loci can lead to the evolution of robustness and of genetic architecture, for instance, because new mutants can change the effects of current as well as future (mutant) alleles at other loci. In recent times, this has become an active field of research, and due to the complexity of the problems involved, is likely to remain so in the coming years.
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