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.     

Fluctuations of Fitness Distributions and the Rate of Muller's Ratchet

The accumulation of deleterious mutations is driven by rare fluctuations that lead to the loss of all mutation free individuals, a process known as Muller's ratchet. Even though Muller's ratchet is a paradigmatic process in population genetics, a quantitative understanding of its rate is still lacking. The difficulty lies in the nontrivial nature of fluctuations in the fitness distribution, which control the rate of extinction of the fittest genotype. We address this problem using the simple but classic model of mutation selection balance with deleterious mutations all having the same effect on fitness. We show analytically how fluctuations among the fittest individuals propagate to individuals of lower fitness and have dramatically amplified effects on the bulk of the population at a later time. If a reduction in the size of the fittest class reduces the mean fitness only after a delay, selection opposing this reduction is also delayed. This delayed restoring force speeds up Muller's ratchet. We show how the delayed response can be accounted for using a path-integral formulation of the stochastic dynamics and provide an expression for the rate of the ratchet that is accurate across a broad range of parameters.     

Kick-starting the ratchet: the fate of mutators in an asexual population

Muller's ratchet operates in asexual populations without intergenomic recombination. In this case, deleterious mutations will accumulate and population fitness will decline over time, possibly endangering the survival of the species. Mutator mutations, i.e., mutations that lead to an increased mutation rate, will play a special role for the behavior of the ratchet. First, they are part of the ratchet and can come to dominance through accumulation in the ratchet. Second, the fitness-loss rate of the ratchet is very sensitive to changes in the mutation rate and even a modest increase can easily set the ratchet in motion. In this article we simulate the interplay between fitness loss from Muller's ratchet and the evolution of the mutation rate from the fixation of mutator mutations. As long as the mutation rate is increased in sufficiently small steps, an accelerating ratchet and eventual extinction are inevitable. If this can be countered by antimutators, i.e., mutations that reduce the mutation rate, an equilibrium can be established for the mutation rate at some level that may allow survival. However, the presence of the ratchet amplifies fluctuations in the mutation rate and, even at equilibrium, these fluctuations can lead to dangerous bursts in the ratchet. We investigate the timescales of these processes and discuss the results with reference to the genome degradation of the aphid endosymbiont Buchnera aphidicola.     

The temporal dynamics of processes underlying Y chromosome degeneration

Y chromosomes originate from ordinary autosomes and degenerate by accumulating deleterious mutations. This accumulation results from a lack of recombination on the Y and is driven by interference among deleterious mutations (Muller's ratchet and background selection) and the fixation of beneficial alleles (genetic hitchhiking). Here I show that the relative importance of these processes is expected to vary over the course of Y chromosome evolution due to changes in the number of active genes. The dominant mode of degeneration on a newly formed gene-rich Y chromosome is expected to be Muller's ratchet and/or background selection due to the large numbers of deleterious mutations arising in active genes. However, the relative importance of these modes of degeneration declines rapidly as active genes are lost. In contrast, the rate of degeneration due to hitchhiking is predicted to be highest on Y chromosomes containing an intermediate number of active genes. The temporal dynamics of these processes imply that a gradual restriction of recombination, as inferred in mammals, will increase the importance of genetic hitchhiking relative to Muller's ratchet and background selection.     

Muller''s Ratchet under Epistatic Selection

In a finite asexual population mean fitness may decrease by a process known as Muller's ratchet, which proceeds if all individuals with the minimum number of deleterious alleles are randomly lost. If these alleles have independent effects on fitness, previous analysis suggested that the rate of this decrease either remains constant or, if accumulation of mutations leads to the decline of the population size, grows. Here I show that this conclusion is quite sensitive to the assumption of independence. If deleterious alleles have synergistic fitness effects, then, as the ratchet advances, the frequency of the best available genotype will necessarily increase, making its loss less and less probable. As a result, sufficiently strong synergistic epistasis can effectively halt the action of Muller's ratchet. Instead of being driven extinct, a finite asexual population could then survive practically indefinitely, although with lower mean fitness than without random drift.     

Muller's ratchet and the pattern of variation at a neutral locus

The levels and patterns of variation at a neutral locus are analyzed in a haploid asexual population undergoing accumulation of deleterious mutations due to Muller's ratchet. We find that the movement of Muller's ratchet can be associated with a considerable reduction in genetic diversity below classical neutral expectation. The extent to which variability is reduced is a function of the deleterious mutation rate, the fitness effects of the mutations, and the population size. Approximate analytical expressions for the expected genetic diversity are compared with simulation results under two different models of deleterious mutations: a model where all deleterious mutations have equal effects and a model where there are two classes of deleterious mutations. We also find that Muller's ratchet can produce a considerable distortion in the neutral frequency spectrum toward an excess of rare variants.     

The speed of Muller's ratchet with background selection, and the degeneration of Y chromosomes.

The rate of accumulation of deleterious mutations by Muller's ratchet is investigated in large asexual haploid populations, for a range of parameters with potential biological relevance. The rate of this process is studied by considering a very simple model in which mutations can have two types of effect: either strongly deleterious or mildly deleterious. It is shown that the rate of accumulation of mildly deleterious mutations can be greatly increased by the presence of strongly deleterious mutations, and that this can be predicted from the associated reduction in effective population size (the background selection effect). We also examine the rate of the ratchet when there are two classes of mutation of similar but unequal effects on fitness. The accuracy of analytical approximations for the rate of this process is analysed. Its possible role in causing the degeneration of Y and neo-Y chromosomes is discussed in the light of our present knowledge of deleterious mutation rates and selection coefficients.     

Mutation accumulation in selfing populations under fluctuating selection

Selfing species are prone to extinction, possibly because highly selfing populations can suffer from a continuous accumulation of deleterious mutations, a process analogous to Muller's ratchet in asexual populations. However, current theory provides little insight into which types of genes are most likely to accumulate deleterious alleles and what environmental circumstances may accelerate genomic degradation. Here, we investigate temporal changes in the environment that cause fluctuations in the strength of purifying selection. We simulate selfing populations with genomes containing a mixture of loci experiencing constant selection and loci experiencing selection that fluctuates in strength (but not direction). Even when both types of loci experience the same average strength of selection, loci under fluctuating selection contribute disproportionately more to deleterious mutation accumulation. Moreover, the presence of loci experiencing fluctuating selection in the genome increases the deleterious fixation rate at loci under constant selection; under most realistic scenarios, this effect of linked selection can be attributed to a reduction in N_e. Fluctuating selection is particularly injurious when selective environments are strongly autocorrelated over time and when selection is concentrated into rare bouts of strong selection. These results imply that loci under fluctuating selection are likely important drivers of extinction in selfing species.     

Molecular basis of fitness loss and fitness recovery in vesicular stomatitis virus

Viral populations subjected to repeated genetic bottleneck accumulate deleterious mutations in a process known as Muller's ratchet. Asexual viruses, such as vesicular stomatitis virus (VSV) can recover from Muller's ratchet by replication with large effective population sizes. However, mutants with a history of bottleneck transmissions often show decreased adaptability when compared to non-bottlenecked populations. We have generated a collection of bottlenecked mutants and allowed them to recover by large population passages. We have characterized fitness changes and the complete genomes of these strains. Mutations accumulated during the operation of Muller's ratchet led to the identification of two potential mutational hot spots in the VSV genome. As in other viral systems, transitions were more common than transversions. Both back mutation and compensatory mutations contributed to recovery, although a significant level of fitness increase was observed in nine of the 13 bottlenecked strains with no obvious changes in the consensus sequence. Additional replication of three strains resulted in the fixation of single point mutations. Only two mutations previously found in non-bottlenecked, high-fitness populations that had been adapting to the same environment were identified in the recovered strains.     

The degeneration of asexual haploid populations and the speed of Muller's ratchet

The accumulation of deleterious mutations due to the process known as Muller's ratchet can lead to the degeneration of nonrecombining populations. We present an analytical approximation for the rate at which this process is expected to occur in a haploid population. The approximation is based on a diffusion equation and is valid when N exp(-u/s) > 1, where N is the population size, u is the rate at which deleterious mutations occur, and s is the effect of each mutation on fitness. Simulation results are presented to show that the approximation estimates the rate of the process better than previous approximations for values of mutation rates and selection coefficients that are compatible with the biological data. Under certain conditions, the ratchet can turn at a biologically significant rate when the deterministic equilibrium number of individuals free of mutations is substantially >100. The relevance of this process for the degeneration of Y or neo-Y chromosomes is discussed.     

Muller''s Ratchet, Epistasis and Mutation Effects

In this study, computer simulation is used to show that despite synergistic epistasis for fitness, Muller's ratchet can lead to lethal fitness loss in a population of asexuals through the accumulation of deleterious mutations. This result contradicts previous work that indicated that epistasis will halt the ratchet. The present results show that epistasis will not halt the ratchet provided that rather than a single deleterious mutation effect, there is a distribution of deleterious mutation effects with sufficient density near zero. In addition to epistasis and mutation distribution, the ability of Muller's ratchet to lead to the extinction of an asexual population under epistasis for fitness depends strongly on the expected number of offspring that survive to reproductive age. This strong dependence is not present in the nonepistatic model and suggests that interpreting the population growth parameter as fecundity is inadequate. Because a continuous distribution of mutation effects is used in this model, an emphasis is placed on the dynamics of the mutation effect distribution rather than on the dynamics of the number of least mutation loaded individuals. This perspective suggests that current models of gene interaction are too simple to apply directly to long-term prediction for populations undergoing the ratchet.     

Evolution of mutation rates in bacteria

Evolutionary success of bacteria relies on the constant fine-tuning of their mutation rates, which optimizes their adaptability to constantly changing environmental conditions. When adaptation is limited by the mutation supply rate, under some conditions, natural selection favours increased mutation rates by acting on allelic variation of the genetic systems that control fidelity of DNA replication and repair. Mutator alleles are carried to high frequency through hitchhiking with the adaptive mutations they generate. However, when fitness gain no longer counterbalances the fitness loss due to continuous generation of deleterious mutations, natural selection favours reduction of mutation rates. Selection and counter-selection of high mutation rates depends on many factors: the number of mutations required for adaptation, the strength of mutator alleles, bacterial population size, competition with other strains, migration, and spatial and temporal environmental heterogeneity. Such modulations of mutation rates may also play a role in the evolution of antibiotic resistance.     

Fitness declines in Tobacco etch virus upon serial bottleneck transfers

It has been well established that populations of RNA viruses transmitted throughout serial bottlenecks suffer from significant fitness declines as a consequence of the accumulation of deleterious mutations by the onset of Muller's ratchet. Bottlenecks are unavoidably linked to different steps of the infectious cycle of most plant RNA viruses, such as vector-mediated transmissions and systemic colonization of new leaves. Here we report evidence for fitness declines by the accumulation of deleterious mutations in the potyvirus Tobacco etch virus (TEV). TEV was inoculated into the nonsystemic host Chenopodium quinoa, and local lesions were isolated and used to initiate 20 independent mutation accumulation lineages. Weekly, a random lesion from each lineage was isolated and used to inoculate the next set of plants. At each transfer, the Malthusian growth rate was estimated. After 11 consecutive transfers, all lineages suffered significant fitness losses, and one even became extinct. The average rate of fitness decline was 5% per day. The average pattern of fitness decline was consistent with antagonistic epistasis between deleterious mutations, as postulated for antiredundant genomes. Temporal fitness fluctuations were not explained by random noise but reflected more complex underlying processes related to emergence and self-organization phenomena.     

Adaptive evolution of asexual populations under Muller's ratchet

We study the population genetics of adaptation in nonequilibrium haploid asexual populations. We find that the accumulation of deleterious mutations, due to the operation of Muller's ratchet, can considerably reduce the rate of fixation of advantageous alleles. Such reduction can be approximated reasonably well by a reduction in the effective population size. In the absence of Muller's ratchet, a beneficial mutation can only become fixed if it creates the best possible genotype; if Muller's ratchet operates, however, mutations initially arising in a nonoptimal genotype can also become fixed in the population, since the loss of the least-loaded class implies that an initially nonoptimal background can become optimal. We show that, while the rate at which adaptive mutations become fixed is reduced, the rate of fixation of deleterious mutations due to the ratchet is not changed by the presence of beneficial mutations as long as the rate of their occurrence is low and the deleterious effects of mutations (s(d)) are higher than the beneficial effects (s(a)). When s(a) > s(d), the advantage of a beneficial mutation can outweigh the deleterious effects of associated mutations. Under these conditions, a beneficial allele can drag to fixation deleterious mutations initially associated with it at a higher rate than in the absence of advantageous alleles. We propose analytical approximations for the rates of accumulation of deleterious and beneficial mutations. Furthermore, when allowing for the possible occurrence of interference between beneficial alleles, we find that the presence of deleterious mutations of either very weak or very strong effect can marginally increase the rate of accumulation of beneficial mutations over that observed in the absence of such deleterious mutations.     

Sex and deleterious mutations

The evolutionary advantage of sexual reproduction has been considered as one of the most pressing questions in evolutionary biology. While a pluralistic view of the evolution of sex and recombination has been suggested by some, here we take a simpler view and try to quantify the conditions under which sex can evolve given a set of minimal assumptions. Since real populations are finite and also subject to recurrent deleterious mutations, this minimal model should apply generally to all populations. We show that the maximum advantage of recombination occurs for an intermediate value of the deleterious effect of mutations. Furthermore we show that the conditions under which the biggest advantage of sex is achieved are those that produce the fastest fitness decline in the corresponding asexual population and are therefore the conditions for which Muller's ratchet has the strongest effect. We also show that the selective advantage of a modifier of the recombination rate depends on its strength. The quantification of the range of selective effects that favors recombination then leads us to suggest that, if in stressful environments the effect of deleterious mutations is enhanced, a connection between sex and stress could be expected, as it is found in several species.     

Drastic fitness loss in human immunodeficiency virus type 1 upon serial bottleneck events

Muller's ratchet predicts fitness losses in small populations of asexual organisms because of the irreversible accumulation of deleterious mutations and genetic drift. This effect should be enhanced if population bottlenecks intervene and fixation of mutations is not compensated by recombination. To study whether Muller's ratchet could operate in a retrovirus, 10 biological clones were derived from a human immunodeficiency virus type 1 (HIV-1) field isolate by MT-4 plaque assay. Each clone was subjected to 15 plaque-to-plaque passages. Surprisingly, genetic deterioration of viral clones was very drastic, and only 4 of the 10 initial clones were able to produce viable progeny after the serial plaque transfers. Two of the initial clones stopped forming plaques at passage 7, two others stopped at passage 13, and only four of the remaining six clones yielded infectious virus. Of these four, three displayed important fitness losses. Thus, despite virions carrying two copies of genomic RNA and the system displaying frequent recombination, HIV-1 manifested a drastic fitness loss as a result of an accentuation of Muller's ratchet effect.     

Evolution of sex: role of deleterious mutation and mobile elements

Prevalence of sexual reproduction is still enigma. The main character of sex is alleles mixing that could be advantageous either in unstable environment (in this case sex provides high temp of evolution) or in unstable genotype (in this case sex provides purge of genome from deleterious mutations). As long as not all species inhabit highly changeable environments, variation of genotypes is more important factor. As the majority of new mutations is deleterious, effective mechanism of genome purging is needed. Maintenance of "purging mechanism" may be a single role of sex. Two promising mutational hypotheses--clade selection (Muller's ratchet and Nunney's hypothesis) and mutational deterministic hypothesis of Kondrashov claim that more effective elimination of slightly-deleterious mutations provides main advantage to sexual population in comparison with asexual. Despite prima facie similarity, these hypotheses differ in mechanisms, work at different temporal scales and have different consequences. Kondrashov's hypothesis reveals short-term advantage of sexual reproduction, and thus, based on the individual selection. Clade selection displays long-term advantage of sexual reproduction that could be realized only by group selection. The role of mobile elements in evolution of sexual reproduction is also discussed. Firstly, mobile elements ("sexual molecular parasites") can complicate the problem: having been domesticated in asexual genomes and remaining active in sexual genomes they lead to higher mutational rate in sexual organisms and so violate assumption critical for both mutational hypotheses of "other things being equal". Secondly, mobile elements could be leader factor of origin of sex (hypothesis proposed by Hickey). Because theory of group selection could explain maintenance of sex, but not its origin, mobile elements could induce the origin of sex but were not able to maintain it, so the next scenario of evolution of sex is proposed: mobile elements induced origin of sex, which was established later by group selection because provided long term benefit (Muller's ratchet and Nunney's hypothesis). So, on all stages of evolution, sex was not advantageous for the organism per se.     

QUANTITATIVE VARIATION IN FINITE PARTHENOGENETIC POPULATIONS: WHAT STOPS MULLER'S RATCHET IN THE ABSENCE OF RECOMBINATION?

Finite parthenogenetic populations with high genomic mutation rates accumulate deleterious mutations if back mutations are rare. This mechanism, known as Muller's ratchet, can explain the rarity of parthenogenetic species among so called higher organisms. However, estimates of genomic mutation rates for deleterious alleles and their average effect in the diploid condition in Drosophila suggest that Muller's ratchet should eliminate parthenogenetic insect populations within several hundred generations, provided all mutations are unconditionally deleterious. This fact is inconsistent with the existence of obligatory parthenogenetic insect species. In this paper an analysis of the extent to which compensatory mutations can counter Muller's ratchet is presented. Compensatory mutations are defined as all mutations that compensate for the phenotypic effects of a deleterious mutation. In the case of quantitative traits under stabilizing selection, the rate of compensatory mutations is easily predicted. It is shown that there is a strong analogy between the Muller's ratchet model of Felsenstein (1974) and the quantitative genetic model considered here, except for the frequency of compensatory mutations. If the intensity of stabilizing selection is too small or the mutation rate too high, the optimal genotype becomes extinct and the population mean drifts from the optimum but still reaches a stationary distribution. This distance is essentially the same as predicted for sexually reproducing populations under the same circumstances. Hence, at least in the short run, compensatory mutations for quantitative characters are as effective as recombination in halting the decline of mean fitness otherwise caused by Muller's ratchet. However, it is questionable whether compensatory mutations can prevent Muller's ratchet in the long run because there might be a limit to the capacity of the genome to provide compensatory mutations without eliminating deleterious mutations at least during occasional episodes of sex.