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.     

The effects of deleterious mutations in cyclically parthenogenetic organisms

Cyclically parthenogenetic organisms experience benefits of both sexual and asexual reproductive modes in a constant environment. Sexual reproduction generates new genotypes and may facilitate the purging of deleterious mutations whereas asexuality has a two-fold advantage and enables maintenance of well-fitted genotypes. Asexual reproduction can have a drawback as increased linkage may lead to the accumulation of deleterious mutations. This study presents the results of Monte Carlo simulations of small and infinite diploid populations, with deleterious mutations occurring at multiple loci. The recombination rate and the length of the asexual period, interrupted by sexual reproduction, are allowed to vary. Here I show that the fitness of cyclical parthenogenetic population is dependent on the length of the asexual period. Increased length of the asexual period can lead both to increased segregational load following sexual reproduction and to a stronger effect of deleterious mutations on variation at a linked neutral marker, either by reducing or increasing the variation.     

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.     

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.     

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.     

Radical amino acid mutations persist longer in the absence of sex

Harmful mutations are ubiquitous and inevitable, and the rate at which these mutations are removed from populations is a critical determinant of evolutionary fate. Closely related sexual and asexual taxa provide a particularly powerful setting to study deleterious mutation elimination because sexual reproduction should facilitate mutational clearance by reducing selective interference between sites and by allowing the production of offspring with different mutational complements than their parents. Here, we compared the rate of removal of conservative (i.e., similar biochemical properties) and radical (i.e., distinct biochemical properties) nonsynonymous mutations from mitochondrial genomes of sexual versus asexual Potamopyrgus antipodarum, a New Zealand freshwater snail characterized by coexisting and ecologically similar sexual and asexual lineages. Our analyses revealed that radical nonsynonymous mutations are cleared at higher rates than conservative changes and that sexual lineages eliminate radical changes more rapidly than asexual counterparts. These results are consistent with reduced efficacy of purifying selection in asexual lineages allowing harmful mutations to remain polymorphic longer than in sexual lineages. Together, these data illuminate some of the population‐level processes contributing to mitochondrial mutation accumulation and suggest that mutation accumulation could influence the outcome of competition between sexual and asexual lineages.     

Muller's ratchet and the degeneration of Y chromosomes: a simulation study

A typical pattern in sex chromosome evolution is that Y chromosomes are small and have lost many of their genes. One mechanism that might explain the degeneration of Y chromosomes is Muller's ratchet, the perpetual stochastic loss of linkage groups carrying the fewest number of deleterious mutations. This process has been investigated theoretically mainly for asexual, haploid populations. Here, I construct a model of a sexual population where deleterious mutations arise on both X and Y chromosomes. Simulation results of this model demonstrate that mutations on the X chromosome can considerably slow down the ratchet. On the other hand, a lower mutation rate in females than in males, background selection, and the emergence of dosage compensation are expected to accelerate the process.     

Deleterious mutation accumulation in asexual Timema stick insects

Sexual reproduction is extremely widespread in spite of its presumed costs relative to asexual reproduction, indicating that it must provide significant advantages. One postulated benefit of sex and recombination is that they facilitate the purging of mildly deleterious mutations, which would accumulate in asexual lineages and contribute to their short evolutionary life span. To test this prediction, we estimated the accumulation rate of coding (nonsynonymous) mutations, which are expected to be deleterious, in parts of one mitochondrial (COI) and two nuclear (Actin and Hsp70) genes in six independently derived asexual lineages and related sexual species of Timema stick insects. We found signatures of increased coding mutation accumulation in all six asexual Timema and for each of the three analyzed genes, with 3.6- to 13.4-fold higher rates in the asexuals as compared with the sexuals. In addition, because coding mutations in the asexuals often resulted in considerable hydrophobicity changes at the concerned amino acid positions, coding mutations in the asexuals are likely associated with more strongly deleterious effects than in the sexuals. Our results demonstrate that deleterious mutation accumulation can differentially affect sexual and asexual lineages and support the idea that deleterious mutation accumulation plays an important role in limiting the long-term persistence of all-female lineages.     

The rate of adaptation in asexuals

I study the population genetics of adaptation in asexuals. I show that the rate of adaptive substitution in an asexual species or nonrecombining chromosome region is a bell-shaped function of the mutation rate: at some point, increasing the mutation rate decreases the rate of substitution. Curiously, the mutation rate that maximizes the rate of adaptation depends solely on the strength of selection against deleterious mutations. In particular, adaptation is fastest when the genomic rate of mutation, U, equals the harmonic mean of selection coefficients against deleterious mutations, where we assume that selection for favorable alleles is milder than that against deleterious ones. This simple result is independent of the shape of the distribution of effects among favorable and deleterious mutations, population size, and the action of clonal interference. In the course of this work, I derive an approximation to the probability of fixation of a favorable mutation in an asexual genome or nonrecombining chromosome region in which both favorable and deleterious mutations occur.     

Advantages of sexual reproduction

Despite the obvious efficiencies of many forms of asexual reproduction, sexual reproduction abounds. Asexual species, for the most part, are relatively short-lived offshoots of sexual ancestors. From the nineteenth century, it has been recognized that, since there is no obvious advantage to the individuals involved, the advantages of sexual reproduction must be evolutionary. Furthermore, the advantage must be substantial; for example, producing males entails a two-fold cost, compared to dispensing with them and reproducing by parthenogenetic females. There are a large number of plausible hypotheses. To me the most convincing of these are two. The first hypothesis, and the oldest, is that sexual reproduction offers the opportunity to produce recombinant types that can make the population better able to keep up with changes in the environment. Although the subject of a great deal of work, and despite its great plausibility, the hypothesis has been very difficult to test by critical observations or experiments. Second, species with recombination can bunch harmful mutations together and eliminate several in a single “genetic death.” Asexual species, can eliminate them only in the same genotype in which they occurred. If the rate of occurrence of deleterious mutations is one or more per zygote, some mechanism for eliminating them efficiently must exist. A test of this mutation load hypothesis for sexual reproduction, then, is to find whether deleterious mutation rates in general are this high-as Drosophila data argue. Unfortunately, although molecular and evolutionary studies can give information on the total mutation rate, they cannot determine what fraction are deleterious. In addition, there are short discussions of the advantages of diploidy, anisogamy, and separate sexes. © 1994 Wiley-Liss, Inc.     

Does Diploidy Increase the Rate of Adaptation?

Explanations of the evolution of diploidy have focused on the advantages gained from masking deleterious alleles. Recent theory has shown, however, that masking does not always provide an advantage to diploidy and would never favor diploidy in predominantly asexual organisms. We explore a neglected alternative theory which posits that, by doubling the genome size, diploids double the rate at which favorable mutations arise. Consequently, the rate of adaptation in diploids is presumed to be faster than in haploids. The rate of adaptation, however, depends not only on the rate of appearance of new favorable mutations but also on the rate at which these mutations are incorporated (which depends on the population size and on the dominance of favorable mutations). We show that, in both asexuals and sexuals, doubling the mutation rate via diploidy often does not accelerate the rate of adaptation. Indeed, under many conditions, diploidy slows adaptation.     

A Ruby in the Rubbish: Beneficial Mutations, Deleterious Mutations and the Evolution of Sex

This study presents a mathematical model in which a single beneficial mutation arises in a very large population that is subject to frequent deleterious mutations. The results suggest that, if the population is sexual, then the deleterious mutations will have little effect on the ultimate fate of the beneficial mutation. However, if most offspring are produced asexually, then the probability that the beneficial mutation will be lost from the population may be greatly enhanced by the deleterious mutations. Thus, sexual populations may adapt much more quickly than populations where most reproduction is asexual. Some of the results were produced using computer simulation methods, and a technique was developed that allows treatment of arbitrarily large numbers of individuals in a reasonable amount of computer time. This technique may be of prove useful for the analysis of a wide variety of models, though there are some constraints on its applicability. For example, the technique requires that reproduction can be described by Poisson processes.     

Sex and the fixation of single favourable mutations

Sexual populations will accumulate favourable mutations more rapidly than asexual populations. This is true if it is often the case that two different favourable mutations can be found to be spreading simultaneously through populations. It is argued here that sexual species will incorporate single favourable mutations more quickly than asexual “species”, if the latter are multi-clonal. Thus one mutation can spread to fixation within a sexual species but in an asexual “species” with N_c clones at least N_c mutations must occur if the mutation is to be subsequently found in every member of the “species”. Asexual “species” may minimise this disadvantage by evolving polyploidy or occasional episodes of hybridisation. Both are in fact common in asexual “species”.     

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.     

MUTATIONAL MELTDOWNS IN SEXUAL POPULATIONS

Although it is widely acknowledged that the gradual accumulation of mildly deleterious mutations is an important source of extinction for asexual populations, it is generally assumed that this process is of little relevance to sexual species. Here we present results, based on computer simulations and supported by analytical approximations, that indicate that mutation accumulation in small, random-mating monoecious populations can lead to mean extinction times less than a few hundred to a few thousand generations. Unlike the situation in obligate asexuals in which the mean time to extinction (t?_e) increases more slowly than linearly with the population carrying capacity (K), t?_e increases approximately exponentially with K in outcrossing sexual populations. The mean time to extinction for obligately selfing populations is shown to be equivalent to that for asexual populations of the same size, but with half the mutation rate and twice the mutational effect; this suggests that obligate selfing, like obligate asexuality, is inviable as a long-term reproductive strategy. Under all mating systems, the mean time to extinction increases relatively slowly with the logarithm of fecundity, and mutations with intermediate effects (similar to those observed empirically) cause the greatest risk of extinction. Because our analyses ignore sources of demographic and environmental stochasticity, which have synergistic effects that exacerbate the accumulation of deleterious mutations, our results should yield liberal upper bounds to the mean time to extinction caused by mutational degradation. Thus, deleterious mutation accumulation cannot be ruled out generally as a significant source of extinction vulnerability in small sexual populations or as a selective force influencing mating-system evolution.     

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.     

The ecology and genetics of fitness in Chlamydomonas. XIII. Fitness of long-term sexual and asexual populations in benign environments

We measured the mean fitness of populations of Chlamydomonas reinhardtii maintained in the laboratory as obligately sexual or asexual populations for about 100 sexual cycles and about 1000 asexual generations. Sexuality (random gamete fusion followed by meiosis) is expected to reduce mutational load and increase mean fitness by combining deleterious mutations from different lines of descent. We found no evidence for this process of mutation clearance: the mean fitness of sexual populations did not exceed that of asexual populations, whether measured through competition or in pure culture. We found instead that sexual progeny suffer an immediate loss in fitness, and that sexual lines maintain genetic variance for fitness. We suggest that sexual populations at equilibrium with selection in a benign environment may be mixtures of several or many epistatic genotypes with nearly equal fitness. Recombination between these genotypes reduces mean fitness and creates genetic variance for fitness. This may provide fuel for continued selection should the environment change.     

Dynamic mutation-selection balance as an evolutionary attractor

The vast majority of mutations are deleterious and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller's ratchet: once lost by stochastic drift, the most-fit class of genotypes is lost forever. If deleterious mutations are weakly selected, Muller's ratchet can lead to a rapid degradation of population fitness. Evidently, the long-term stability of an asexual population requires an influx of beneficial mutations that continuously compensate for the accumulation of the weakly deleterious ones. Hence any stable evolutionary state of a population in a static environment must involve a dynamic mutation-selection balance, where accumulation of deleterious mutations is on average offset by the influx of beneficial mutations. We argue that such a state can exist for any population size N and mutation rate U and calculate the fraction of beneficial mutations, ε, that maintains the balanced state. We find that a surprisingly low ε suffices to achieve stability, even in small populations in the face of high mutation rates and weak selection, maintaining a well-adapted population in spite of Muller's ratchet. This may explain the maintenance of mitochondria and other asexual genomes.     

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.     

Aging asexual lineages and the evolutionary maintenance of sex

Finite populations of asexual and highly selfing species suffer from a reduced efficacy of selection. Such populations are thought to decline in fitness over time due to accumulating slightly deleterious mutations or failing to adapt to changing conditions. These within‐population processes that lead nonrecombining species to extinction may help maintain sex and outcrossing through species level selection. Although inefficient selection is proposed to elevate extinction rates over time, previous models of species selection for sex assumed constant diversification rates. For sex to persist, classic models require that asexual species diversify at rates lower than sexual species; the validity of this requirement is questionable, both conceptually and empirically. We extend past models by allowing asexual lineages to decline in diversification rates as they age, that is nonrecombining lineages “senesce” in diversification rates. At equilibrium, senescing diversification rates maintain sex even when asexual lineages, at young ages, diversify faster than their sexual progenitors. In such cases, the age distribution of asexual lineages contains a peak at intermediate values rather than showing the exponential decline predicted by the classic model. Coexistence requires only that the average rate of diversification in asexuals be lower than that of sexuals.