Genetic loads under fitness‐dependent mutation rates

Abstract Although much theory depends on the genome‐wide rate of deleterious mutations, good estimates of the mutation rate are scarce and remain controversial. Furthermore, mutation rate may not be constant, and a recent study suggests that mutation rates are higher in mildly stressful environments. If mutation rate is a function of condition, then individuals carrying more mutations will tend to be in worse condition and therefore produce more mutations. Here I examine the mean fitnesses of sexual and asexual populations evolving under such condition‐dependent mutation rates. The equilibrium mean fitness of a sexual population depends on the shape of the curve relating fitness to mutation rate. If mutation rate declines synergistically with increasing condition the mean fitness will be much lower than if mutation rate declines at a diminishing rate. In contrast, asexual populations are less affected by condition‐dependent mutation rates. The equilibrium mean fitness of an asexual population only depends on the mutation rate of the individuals in the least loaded class. Because such individuals have high fitness and therefore a low mutation rate, asexual populations experience less genetic load than sexual populations, thus increasing the twofold cost of sex.     

Beneficial mutations, hitchhiking and the evolution of mutation rates in sexual populations

Natural selection acts in three ways on heritable variation for mutation rates. A modifier allele that increases the mutation rate is (i) disfavored due to association with deleterious mutations, but is also favored due to (ii) association with beneficial mutations and (iii) the reduced costs of lower fidelity replication. When a unique beneficial mutation arises and sweeps to fixation, genetic hitchhiking may cause a substantial change in the frequency of a modifier of mutation rate. In previous studies of the evolution of mutation rates in sexual populations, this effect has been underestimated. This article models the long-term effect of a series of such hitchhiking events and determines the resulting strength of indirect selection on the modifier. This is compared to the indirect selection due to deleterious mutations, when both types of mutations are randomly scattered over a given genetic map. Relative to an asexual population, increased levels of recombination reduce the effects of beneficial mutations more rapidly than those of deleterious mutations. However, the role of beneficial mutations in determining the evolutionarily stable mutation rate may still be significant if the function describing the cost of high-fidelity replication has a shallow gradient.     

Recessive mutations and the maintenance of sex in structured populations

The evolutionary maintenance of sexual reproduction remains a controversial problem. It was recently shown that recessive deleterious mutations create differences in the mutation load of sexual vs. asexual populations. Here we show that low levels of population structure or inbreeding can greatly enhance the importance of recessive deleterious mutations in the context of sexual vs. asexual populations. With population structure, the cost of sex can be substantially reduced or even eliminated for realistic levels of dominance.     

Muller's ratchet and the accumulation of favourable mutations

Under the influence of recurrent deleterious mutation and selection, asexual and sexual populations reach a deterministic equilibrium with individuals carrying 0,1,2,. . . harmful mutations. When a favourable mutation (aA) occurs in an asexual population it will usually occur in an individual who has one or more (k) deleterious mutations. Muller's ratchet then applies as A will thereafter never occur in an individual with less than k mutations. If the selective advantage of A is less than the selective disadvantage of k harmful mutations then A will not spread. If it is greater it may spread carrying k deleterious mutations to fixation. Sexual populations are not affected in this way. A will spread through the population experiencing genomes with 0,1,2,. . . deleterious mutations in accordance with the deterministic equilibrium.     

The balance between mutators and nonmutators in asexual populations

Mutator alleles, which elevate an individual's mutation rate from 10 to 10,000-fold, have been found at high frequencies in many natural and experimental populations. Mutators are continually produced from nonmutators, often due to mutations in mismatch-repair genes. These mutators gradually accumulate deleterious mutations, limiting their spread. However, they can occasionally hitchhike to high frequencies with beneficial mutations. We study the interplay between these effects. We first analyze the dynamics of the balance between the production of mutator alleles and their elimination due to deleterious mutations. We find that when deleterious mutation rates are high in mutators, there will often be many "young," recently produced mutators in the population, and the fact that deleterious mutations only gradually eliminate individuals from a population is important. We then consider how this mutator-nonmutator balance can be disrupted by beneficial mutations and analyze the circumstances in which fixation of mutator alleles is likely. We find that dynamics is crucial: even in situations where selection on average acts against mutators, so they cannot stably invade, the mutators can still occasionally generate beneficial mutations and hence be important to the evolution of the population.     

Rapid evolutionary escape by large populations from local fitness peaks is likely in nature

Fitness interactions between loci in the genome, or epistasis, can result in mutations that are individually deleterious but jointly beneficial. Such epistasis gives rise to multiple peaks on the genotypic fitness landscape. The problem of evolutionary escape from such local peaks has been a central problem of evolutionary genetics for at least 75 years. Much attention has focused on models of small populations, in which the sequential fixation of valley genotypes carrying individually deleterious mutations operates most quickly owing to genetic drift. However, valley genotypes can also be subject to mutation while transiently segregating, giving rise to copies of the high fitness escape genotype carrying the jointly beneficial mutations. In the absence of genetic recombination, these mutations may then fix simultaneously. The time for this process declines sharply with increasing population size, and it eventually comes to dominate evolutionary behavior. Here we develop an analytic expression for N(crit), the critical population size that defines the boundary between these regimes, which shows that both are likely to operate in nature. Frequent recombination may disrupt high-fitness escape genotypes produced in populations larger than N(crit) before they reach fixation, defining a third regime whose rate again slows with increasing population size. We develop a novel expression for this critical recombination rate, which shows that in large populations the simultaneous fixation of mutations that are beneficial only jointly is unlikely to be disrupted by genetic recombination if their map distance is on the order of the size of single genes. Thus, counterintuitively, mass selection alone offers a biologically realistic resolution to the problem of evolutionary escape from local fitness peaks in natural populations.     

The Effect of Deleterious Mutations on Neutral Molecular Variation

Selection against deleterious alleles maintained by mutation may cause a reduction in the amount of genetic variability at linked neutral sites. This is because a new neutral variant can only remain in a large population for a long period of time if it is maintained in gametes that are free of deleterious alleles, and hence are not destined for rapid elimination from the population by selection. Approximate formulas are derived for the reduction below classical neutral values resulting from such background selection against deleterious mutations, for the mean times to fixation and loss of new mutations, nucleotide site diversity, and number of segregating sites. These formulas apply to random-mating populations with no genetic recombination, and to populations reproducing exclusively asexually or by self-fertilization. For a given selection regime and mating system, the reduction is an exponential function of the total mutation rate to deleterious mutations for the section of the genome involved. Simulations show that the effect decreases rapidly with increasing recombination frequency or rate of outcrossing. The mean time to loss of new neutral mutations and the total number of segregating neutral sites are less sensitive to background selection than the other statistics, unless the population size is of the order of a hundred thousand or more. The stationary distribution of allele frequencies at the neutral sites is correspondingly skewed in favor of rare alleles, compared with the classical neutral result. Observed reductions in molecular variation in low recombination genomic regions of sufficiently large size, for instance in the centromere-proximal regions of Drosophila autosomes or in highly selfing plant populations, may be partly due to background selection against deleterious mutations.     

Evolutionary Invasion and Escape in the Presence of Deleterious Mutations

Replicators such as parasites invading a new host species, species invading a new ecological niche, or cancer cells invading a new tissue often must mutate to adapt to a new environment. It is often argued that a higher mutation rate will favor evolutionary invasion and escape from extinction. However, most mutations are deleterious, and even lethal. We study the probability that the lineage will survive and invade successfully as a function of the mutation rate when both the initial strain and an adaptive mutant strain are threatened by lethal mutations. We show that mutations are beneficial, i.e. a non-zero mutation rate increases survival compared to the limit of no mutations, if in the no-mutation limit the survival probability of the initial strain is smaller than the average survival probability of the strains which are one mutation away. The mutation rate that maximizes survival depends on the characteristics of both the initial strain and the adaptive mutant, but if one strain is closer to the threshold governing survival then its properties will have greater influence. These conclusions are robust for more realistic or mechanistic depictions of the fitness landscapes such as a more detailed viral life history, or non-lethal deleterious mutations.     

Evolutionary traction: the cost of adaptation and the evolution of sex

The advantage of sexual reproduction remains a puzzle for evolutionary biologists. Everything else being equal, asexual populations are expected to have twice the number of offspring produced by similar sexual populations. Yet, asexual species are uncommon among higher eukaryotes. In models assuming small populations, high mutation rates, or frequent environmental changes, sexual reproduction seems to have at least a two-fold advantage over asexuality. But the advantage of sex for large populations, low mutation rates, and rare or mild environmental changes remains a conundrum. Here we show that without recombination, rare advantageous mutations can result in increased accumulation of deleterious mutations ('evolutionary traction'), which explains the long-term advantage of sex under a wide parameter range.     

Deleterious Mutations as an Evolutionary Factor. II. Facultative Apomixis and Selfing

A population with u deleterious mutations per genome per generation is considered in which only those individuals that carry less than a critical number k of mutations are viable. Besides a large number of loci subject to mutation and selection, the genome contains one or two special loci responsible for the mode of reproduction. Amphimixis vs. apomixis and amphimixis vs. selfing are considered separately. In the first case, the genome degradation rate v (= u/square root k) is found to play the decisive role, as in the case of recombination. When v greater than 1.25, obligate amphimixis is established. If v decreases below this value, the alleles with first low and then larger penetrance are fixed, until alleles conferring obligate asexual reproduction become advantageous. The proportion of resources allocated to produce seeds also increases with decrease of v. These results are unlikely to depend on the genetic basis of the mode of reproduction. The result of competition between outcrossing and selfing depends on both u and k, as well as on whether the mutations are recessive. The alleles for selfing with low penetrance are selected against if the mutations are at all recessive. The fitness of alleles with high penetrance depends primarily on u, decreasing when u increases. There may exist conditions when only the alleles providing intermediate selfing rates can be fixed in a population. In other cases a population may exist with either obligate outcrossing or selfing at a high rate. Thus, truncation selection against deleterious mutations may be a factor supporting obligate or facultative sex despite the twofold advantage of apomixis or selfing.     

Mutation accumulation in space and the maintenance of sexual reproduction

The maintenance of sexual reproduction remains one of the major puzzles of evolutionary biology, since, all else being equal, an asexual mutant should have a twofold fitness advantage over the sexual wildtype. Most theories suggest that sex helps either to purge deleterious mutations, or to adapt to changing environments. Both mechanisms have their limitations if they act in isolation because they require either high genomic mutation rates or very virulent pathogens, and it is therefore often thought that they must act together to maintain sex. Typically, however, these theories have in common that they are not based on spatial processes. Here, we show that local dispersal and local competition can explain the maintenance of sexual reproduction as a means of purging deleterious mutations. Using a spatially explicit individual-based model, we find that even with reasonably low genomic mutation rates and large total population sizes, asexual clones cannot invade a sexual population. Our results demonstrate how spatial processes affect mutation accumulation such that it can fully erode the twofold benefit of asexuality faster than an asexual clone can take over a sexual population. Thus, the cost of sex is generally overestimated in models that ignore the effects of space on mutation accumulation.     

Fixation of new alleles and the extinction of small populations: drift load, beneficial alleles, and sexual selection

With a small effective population size, random genetic drift is more important than selection in determining the fate of new alleles. Small populations therefore accumulate deleterious mutations. Left unchecked, the effect of these fixed alleles is to reduce the reproductive capacity of a species, eventually to the point of extinction. New beneficial mutations, if fixed by selection, can restore some of this lost fitness. This paper derives the overall change in fitness due to fixation of new deleterious and beneficial alleles, as a function of the distribution of effects of new mutations and the effective population size. There is a critical effective size below which a population will on average decline in fitness, but above which beneficial mutations allow the population to persist. With reasonable estimates of the relevant parameters, this critical effective size is likely to be a few hundred. Furthermore, sexual selection can act to reduce the fixation probability of deleterious new mutations and increase the probability of fixing new beneficial mutations. Sexual selection can therefore reduce the risk of extinction of small populations.     

Natural populations of the Closterium ehrenbergii (Desmidiales, Chlorophyta) species complex in Nepal

Several natural populations of the Closterium ehrenbergii Meneghini ex Ralfs species complex were collected in Nepal, in October–December 1982. Water temperature and pH were also recorded. Clonal isolates from these populations were identified to one of four mating groups (H, I, J and M) by test crossing with standard mating-type strains of known mating groups. Groups H and M have smooth walled zygospores, while Groups I and J have scrobiculated zygospore walls. Several undetermined isolates were found in some population samples. In contrast to the previously reported population samples from Nepal, especially from dried soil samples, some of these populations appeared to be rather heavily loaded with mutations that are deleterious to the sexual cycle (i.e. sexual compatibility, zygospore formation and germination). By genetic analysis, a zygote maturation-defective mutation (zym) was detected. One reason for such a heavy genetic load was suggested to be that most population samples had been maintained exclusively by asexual reproduction for a long period in large lakes and nearby ponds, or left-over vegetative populations in paddy fields after other members entered into dormancy through sexual reproduction. The significance of studying such mutations at sexual gene loci is discussed in the light of speciation problems in microalgae.     

Limited Dispersal, Deleterious Mutations and the Evolution of Sex

This study presents a mathematical model that allows for some offspring to be dispersed at random, while others stay close to their mothers. A single genetic locus is assumed to control fertility, and this locus is subject to the occurrence of deleterious mutations. It is shown that, at equilibrium, the frequency of deleterious mutations in the population is inversely related to the rate of dispersal. This is because dispersal of offspring leads to enhanced competition among adults. The results also show that sexual reproduction can lead to a decrease in the equilibrium frequency of deleterious mutations. The reason for this relationship is that sex involves the dispersal of genetic material, and thus, like the dispersal of offspring, sex enhances competition among adults. The model is described using the example of a hermaphroditic plant population. However, the results should apply to animal populations as well.     

Sexual selection and its effect on the fixation of an asexual clone

Sexual selection is a powerful and ubiquitous force in sexual populations. It has recently been argued that sexual selection can eliminate the twofold cost of sex even with low genomic mutation rates. By means of differential male mating success, deleterious mutations in males become more deleterious than in females, and it has been shown that sexual selection can drastically reduce the mutational load in a sexual population, with or without any form of epistasis. However, any mechanism that claims to maintain sexual reproduction must be able to prevent the fixation of an asexual mutant clone with a twofold fitness advantage. Here, I show that despite very strong sexual selection, the fixation of an asexual mutant cannot be prevented under reasonable genomic mutation rates. Sexual selection can have a strong effect on the average mutational load in a sexual population, but as it cannot prevent the fixation of an asexual mutant, it is unlikely to play a key role on the maintenance of sexual reproduction.     

The Ratchet and the Red Queen: the maintenance of sex in parasites

The adaptive significance of sexual reproduction remains as an unsolved problem in evolutionary biology. One promising hypothesis is that frequency‐dependent selection by parasites selects for sexual reproduction in hosts, but it is unclear whether such selection on hosts would feed back to select for sexual reproduction in parasites. Here we used individual‐based computer simulations to explore this possibility. Specifically, we tracked the dynamics of asexual parasites following their introduction into sexual parasite populations for different combinations of parasite virulence and transmission. Our results suggest that coevolutionary interactions with hosts would generally lead to a stable coexistence between sexual parasites and a single parasite clone. However, if multiple mutations to asexual reproduction were allowed, we found that the interaction led to the accumulation of clonal diversity in the asexual parasite population, which led to the eventual extinction of the sexual parasites. Thus, coevolution with sexual hosts may not be generally sufficient to select for sex in parasites. We then allowed for the stochastic accumulation of mutations in the finite parasite populations (Muller's Ratchet). We found that, for higher levels of parasite virulence and transmission, the population bottlenecks resulting from host–parasite coevolution led to the rapid accumulation of mutations in the clonal parasites and their elimination from the population. This result may explain the observation that sexual reproduction is more common in parasitic animals than in their free‐living relatives.     

Lack of Evidence for Sign Epistasis Between Beneficial Mutations in an RNA Bacteriophage

In previous work (Betancourt, Genetics 181:1535, 2009), I propagated three large laboratory populations of an RNA phage (MS2) as they adapted to a controlled laboratory environment. These populations were large enough so that evolution might be expected to be mostly repeatable, but they nevertheless fixed different suites of mutations over the course of the experiment. Here, I investigate one possible explanation for these results: epistasis, in which the effect of a mutation depends on its genetic background, may have prevented populations with different initial substitutions from fixing the same set of subsequent mutations. I show that two mutations that previously occurred in different genetic backgrounds are beneficial on either background. This result suggests that sign epistasis-in which a mutation is beneficial on one background, but deleterious on another-is not the cause of different evolutionary trajectories observed in the Betancourt (2009) experiment. However, they can be explained by either magnitude epistasis-in which mutations have stronger or weaker beneficial effects depending on the background-or by the simultaneous fixation of multiple beneficial mutations. Surprisingly, the large populations of the previous experiment showed less parallel evolution than the small populations of this experiment, which lends support to the fixation of multiple beneficial mutations contributing to the patterns seen in both experiments.     

The evolution of concerted evolution

Concerted evolution is a consequence of processes that convert copies of a gene in a multigene family into the same copy. Here we ask whether this homogenization may be adaptive. Analysis of a modifier of homogenization reveals (1) that the trait is most likely to spread if interactions between deleterious mutations are not strongly synergistic; (2) that selection on the modifier is of the order of the mutation rate, hence the modifier is most likely to be favoured by selection when the species has a large effective population size and/or if the modifier affects many genes simultaneously; and (3) that linkage between the genes in the family, and between these genes and the modifier, makes invasion of the modifier easier, suggesting that selection may favour multigene families being in clustered arrays. It follows from the first conclusion that genes for which mutations may often be dominant or semi-dominant should undergo concerted evolution more commonly than others. By analysis of the mouse knockout database, we show that mutations affecting growth-related genes are more commonly associated with dominant lethality than expected by chance. We predict then that selection will favour homogenization of such genes, and possibly others that are significantly dosage dependent, more often than it favours homogenization in other genes. The first condition is almost the opposite of that required for the maintenance of sexual reproduction according to the mutation-deterministic theory. The analysis here therefore suggests that sexual organisms can simultaneously minimize both the effects of deleterious, strongly synergistically, interacting mutations and those that interact either weakly synergistically, multiplicatively, or antagonistically, assuming the latter class belong to a multicopy gene family. Recombination and an absence of homogenization are efficient in purging deleterious mutations in the former class, homogenization and an absence of recombination are efficient at minimizing the costs imposed by the latter classes.     

PURGING THE GENOME WITH SEXUAL SELECTION: REDUCING MUTATION LOAD THROUGH SELECTION ON MALES

Healthy males are likely to have higher mating success than unhealthy males because of differential expression of condition‐dependent traits such as mate searching intensity, fighting ability, display vigor, and some types of exaggerated morphological characters. We therefore expect that most new mutations that are deleterious for overall fitness may also be deleterious for male mating success. From this perspective, sexual selection is not limited to influencing those genes directly involved in exaggerated morphological traits but rather affects most, if not all, genes in the genome. If true, sexual selection can be an important force acting to reduce the frequency of deleterious mutations and, as a result, mutation load. We review the literature and find various forms of indirect evidence that sexual selection helps to eliminate deleterious mutations. However, direct evidence is scant, and there are almost no data available to address a key issue: is selection in males stronger than selection in females? In addition, the total effect of sexual selection on mutation load is complicated by possible increases in mutation rate that may be attributable to sexual selection. Finally, sexual selection affects population fitness not only through mutation load but also through sexual conflict, making it difficult to empirically measure how sexual selection affects load. Several lines of enquiry are suggested to better fill large gaps in our understanding of sexual selection and its effect on genetic load.     

Diminishing returns of population size in the rate of RNA virus adaptation

Whenever an asexual viral population evolves by adapting to new environmental conditions, beneficial mutations, the ultimate cause of adaptation, are randomly produced and then fixed in the population. The larger the population size and the higher the mutation rate, the more beneficial mutations can be produced per unit time. With the usually high mutation rate of RNA viruses and in a large enough population, several beneficial mutations could arise at the same time but in different genetic backgrounds, and if the virus is asexual, they will never be brought together through recombination. Thus, the best of these genotypes must outcompete each other on their way to fixation. This competition among beneficial mutations has the effect of slowing the overall rate of adaptation. This phenomenon is known as clonal interference. Clonal interference predicts a speed limit for adaptation as the population size increases. In the present report, by varying the size of evolving vesicular stomatitis virus populations, we found evidence clearly demonstrating this speed limit and thus indicating that clonal interference might be an important factor modulating the rate of adaptation to an in vitro cell system. Several evolutionary and epidemiological implications of the clonal interference model applied to RNA viruses are discussed.