4.3.2 A biological exam ple
One type of mediocrity gene alters reproductive capacity. All sexual organisms have their reproductive capacity limited in some way, either through senescence (Hamilton
1966) or through a fixed number of germ cells (Hodgkin and Barnes 1991). Limited capacity evolves because additional capacity is seldom used (Hamilton 1966) and is costly to create (Chapman et al. 1995). An organism with a given genotype has an
optimal capacity which reflects a trade-off between increased capacity and fecundity in adverse conditions. The optimal capacity for an individual with many mutations is likely to be lower than the optimal capacity for an individual with few. Therefore, the trade-off between high eapacity and high fecundity in adverse conditions is likely to lead to a trade-off between fitness on a good genetic background and fitness on a poor genetic background.
A gene which specifies the optimal capacity for an individual with n deleterious
mutations is necessarily a mediocrity gene. An individual which has the gene, but which has no deleterious mutations, will have lower than optimal capacity for the genotype, and, as a result, may not significantly outperform genotypes with many
more mutations. An individual with the gene and many more than n mutations will
attempt to create a higher than optimal reproductive capacity. This genotype may not be capable of surviving until reproductive maturity. In this case, the genotype will have zero fitness.
This example shows that mediocrity genes may occur as a result of commonplace and observable trade-offs.
4.3.3 Selection on m ediocrity genes
At mutation/selection balance, the mutation number per individual is approximately normally distributed (Charlesworth 1990). In the absence of epistasis, the variance in mutation number is equal to the mean. Therefore, most individuals have between
n - 2^ln and n + z Æ mutations. Individuals with few mutations contribute
disproportionately to the next generation. Nevertheless, most of the next generation
will be produced by individuals with between n - z Æ and n -f- zV« mutations.
Consider a mediocrity gene which increases the fitness of individuals with between 1 - 3 -
—n and —n mutations but decreases the fitness of other individuals. Provided n is
Z Z
large, a gene with this effect will increase in frequency in the short term. However, the gene also reduces the additive genetic variance in fitness by reducing the number of
1 - 3 -
offspring with less than —n mutations or more than —n mutations. The reduction in
2 Z
additive genetic variance may cause a reduction in frequency of the gene in future generations. Recall from Section 1.6 that a gene which reduces recombination under synergistic epistasis has a similar effect, increasing mean fitness, but reducing the additive genetic variance in fitness. Thus, the conditions for the spread of a mediocrity
gene are analogous to the conditions for the spread of a modifier reducing
recombination. Reduced recombination is more likely to evolve if the recombination rate between the modifier and its background is loose (Barton 1995). So mediocrity genes are more likely to spread when the recombination rate is high. In fact, mediocrity genes cannot spread in an entirely asexual population. In an asexual population, the only genotypes which contribute to the gene pool in the long run are those which have very few mutations. Mediocrity genes reduce the fitness of these individuals.
Mediocrity genes are more likely to spread if n is large. Increasing n reduces the
standard deviation of mutation number compared to the mean. Therefore, mediocrity genes are more likely to spread if the mutation rate is high, or if each mutation has a small fitness effect.
4.3.4 M ediocrity is self-rein forcin g
The spread of mediocrity genes causes synergistic epistasis. Once synergistic epistasis has evolved, selection causes negative linkage disequilibria to build up (Section 1.1.1). The build up of disequilibria may make the fixation of further mediocrity genes more likely for two reasons. First, the reduction of the variance in mutation number ensures that a mediocrity gene increases the fitness of a larger proportion of the population (Figure 4.1). This increases the advantage of mediocrity genes. Secondly, synergism may cause the evolution of increased recombination (Chapter 1). This will dissipate some of the linkage disequilibria, but will reduce the selection against mediocrity genes that results from their effect on the additive genetic variance (Section 4.3.3).
Therefore, mediocrity and recombination may co-evolve. The fixation of mediocrity genes leads to selection for higher recombination rates, which in turn causes the fixation of further mediocrity genes.
4.4 C on clu sion s
The level of epistasis may depend on the mutation rate. Species with low mutation rates tend to have low recombination rates, and, in these species, little or no mediocrity is likely to evolve. Above a certain threshold, which depends on both the mutation and recombination rates, selection for mediocrity may become significant. Organisms which lie above this threshold evolve higher recombination rates because of selection on deleterious mutations. Higher recombination rates in turn cause stronger selection for synergistic epistasis. Thus, there may be a "mediocrity threshold", above which synergism becomes important. This threshold may coincide with the evolution of obligate sexuality.
The only convincing estimates of epistasis to date were made by Elena and Lenski (1997) and de Visser et al. (1997). Both authors used a direct approach, constructing genotypes with known numbers of mutations and measuring their fitness. However, the approach may not be feasible for obligately sexual organisms, because the measurement of fitness of individual genotypes is more difficult.
Of the indirect approaches, the best is the comparison of the fitness of progeny from crosses between genotypes with very different numbers of mutations with the fitness of their parents. However, if these experiments are performed in organisms with low mutation rates, then they would not provide a good indication of the level of epistasis in organisms with high mutation rates. An alternative approach is to measure the capacity for mediocrity to evolve. The persistence of mediocrity genes is dependent on a trade-off between fitness on a genetic background with many mutations and fitness on a genetic background with few mutations. This trade-off may exist in every
organism, regardless of its natural mutation rate. The existence of the trade-off may be testable as follows:
Two selection lines are created. The first is maintained on a mutagenised genetic background, the second is maintained on an unmutagenised background. It is
necessary to renew the genetic backgrounds frequently in order to ensure that the first selected line becomes adapted to mutagenised backgrounds in general, rather than to mutations in a specific mutagenised genotypes. After several generations of selection, the fitness of the two lines are compared on mutatagenised and unmutagenised backgrounds. Provided the trade-off exists and there is suitable genetic variation, the fitness of the first line should be higher than the second on a mutagenised background, but lower on an unmutagenised background. It is necessary to devise an experiment which ensures that, while the lines undergo selection on a mutagenised or
unmutagenised background, they do not recombine with that background. This is possible, at least in principle. Rice (1996) cycled chromosomes from females of a non responding stock out of the population every generation. A similar design could ensure that mutagenised and unmutagenised chromosomes were cycled out of the population each generation.