Mutation Load under Vegetative Reproduction and Cytoplasmic Inheritance

For reasons that remain unclear, even multicellular organisms usually originate from a single cell. Here I consider the balance between deleterious mutations and selection against them in a population with obligate vegetative reproduction, when every offspring is initiated by more than one cell of a parent. The mutation load depends on the genomic deleterious mutation rate U, strictness of selection, number of cells which initiate an offspring n, and the relatedness among the initial cells. The load grows with increasing U, n and strictness of selection, and declines when an offspring is initiated by more closely related cells. If Un >> 1, the load under obligate vegetative reproduction may be substantially higher than under sexual or asexual reproduction, which may account for its rarity. In nature obligate vegetative reproduction seems to be more common and long term in taxa whose cytological features ensure a relatively low load under it. The same model also describes the mutation load under two other modes of inheritance: (1) uniparental transmission of organelles and (2) reproduction by division of multinuclear cells, where each daughter cell receives many nuclei. The load declines substantially when the deleterious mutation rate per organelle genome gets lower or when the number of nuclei in a cell sometimes drops. This may explain the small sizes of organelle genomes in sexual lineages and the presence of karyonic cycles in asexual unicellular multinuclear eukaryotes.     

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.     

Fixation probability of rare nonmutator and evolution of mutation rates

Although mutations drive the evolutionary process, the rates at which the mutations occur are themselves subject to evolutionary forces. Our purpose here is to understand the role of selection and random genetic drift in the evolution of mutation rates, and we address this question in asexual populations at mutation‐selection equilibrium neglecting selective sweeps. Using a multitype branching process, we calculate the fixation probability of a rare nonmutator in a large asexual population of mutators and find that a nonmutator is more likely to fix when the deleterious mutation rate of the mutator population is high. Compensatory mutations in the mutator population are found to decrease the fixation probability of a nonmutator when the selection coefficient is large. But, surprisingly, the fixation probability changes nonmonotonically with increasing compensatory mutation rate when the selection is mild. Using these results for the fixation probability and a drift‐barrier argument, we find a novel relationship between the mutation rates and the population size. We also discuss the time to fix the nonmutator in an adapted population of asexual mutators, and compare our results with experiments.     

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.     

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.     

On the potential for evolutionary change in meristematic cell lineages through intraorganismal selection

In the absence of sexual recombination somatic mutations represent the only source of genetic variation in clonally propagating plants. We analyse the probability of such somatic mutations in the shoot apical meristem being fixed in descendant generations of meristems. A model of meristem cell dynamics is presented for the unstratified shoot apical meristem. The fate of one mutant initial is studied for a two- and three-celled shoot apical meristem. The main parameters of the model are the number of apical initials, the time between selection cycles, number of selection cycles and cell viability of the mutant genotype. As the number of mitotic divisions per selection cycle and number of selection cycles increases the chimeric state dissipates and the probability of mutation fixation approaches an asymptote. The value of this fixation asymptote depends primarily on cell viability, while the time to reach it is mainly influenced by the total number of mitotic divisions as well as the number of initials. In contrast to the presumed operation of Muller’s Ratchet in plants the chimeric state may represent an opportunity for deleterious mutations to be eliminated through intraorganismal selection or random drift. We conclude that intraorganismal selection not only can be a substantial force for the elimination of deleterious mutations, but also can have the potential to confer an evolutionary change through a meristematic cell lineage alone.     

The conservation of redundancy in genetic systems: effects of sexual and asexual reproduction

The relationship between probability of survival and the number of deleterious mutations in the genome is investigated using three different models of highly redundant systems that interact with a threatening environment. Model one is a system that counters a potentially lethal infection; it has multiple identical components that act in sequence and in parallel. Model two has many different overlapping components that provide three-fold coverage of a large number of vital functions. The third model is based on statistical decision theory: an ideal detector, following an optimum decision strategy, makes crucial decisions in an uncertain world. The probability of a fatal error is reduced by a redundant sampling system, but the chance of error rises as the system is impaired by deleterious mutations. In all three cases the survival profile shows a synergistic pattern in that the probability of survival falls slowly and then more rapidly. This is different than the multiplicative or independent survival profile that is often used in mathematical models. It is suggested that a synergistic profile is a property of redundant systems. Model one is then used to study the conservation of redundancy during sexual and asexual reproduction. A unicellular haploid organism reproducing asexually retains redundancy when the mutation rate is very low (0001 per cell division), but tends to lose high levels of redundancy if the mutation rate is increased (001 to 01 per cell division). If a similar unicellular haploid organism has a sexual phase then redundancy is retained for mutation rates between 0001 and 01 per cell division. The sexual organism outgrows the asexual organism when the above mutation rates apply. If they compete for finite resources the asexual organism will be extinguished. Variants of the sexual organism with increased redundancy will outgrow those with lower levels of redundancy and the sexual process facilitates the evolution of more complex forms. There is a limit to the extent that complexity can be increased by increasing the size of the genome and in asexual organisms this leads to progressive accumulation of mutations with loss of redundancy and eventual extinction. If complexity is increased by using genes in new combinations, the asexual form can reach a stable equilibrium, although it is associated with some loss of redundancy. The sexual form, by comparison, can survive, with retention of redundancy, even if the mutation rate is above one per generation. The conservation and evolution of redundancy, which is essential for complexity, depends on the sexual process of reproduction.     

Anisogamy,sexual selection,and the evolution and maintenance of sex

Summary In the present paper we distinguish between two aspects of sexual reproduction. Genetic recombination is a universal features of the sexual process. It is a primitive condition found in simple, single-celled organisms, as well as in higher plants and animals. Its function is primarily to repair genetic damage and eliminate deleterious mutations. Recombination also produces new variation, however, and this can provide the basis for adaptive evolutionary change in spatially and temporally variable environments.The other feature usually associated with sexual reproduction, differentiated male and female roles, is a derived condition, largely restricted to complex, diploid, multicellular organisms. The evolution of anisogamous gametes (small, mobile male gametes containing only genetic material, and large, relatively immobile female gametes containing both genetic material and resources for the developing offspring) not only established the fundamental basis for maleness and femaleness, it also led to an asymmetry between the sexes in the allocation of resources to mating and offspring. Whereas females allocate their resources primarily to offspring, the existence of many male gametes for each female one results in sexual selection on males to allocate their resources to traits that enhance success in competition for fertilizations. A consequence of this reproductive competition, higher variance in male than female reproductive success, results in more intense selection on males.The greater response of males to both stabilizing and directional selection constitutes an evolutionary advantage of males that partially compensates for the cost of producing them. The increased fitness contributed by sexual selection on males will complement the advantages of genetic recombination for DNA repair and elimination of deleterious mutations in any outcrossing breeding system in which males contribute only genetic material to their offspring. Higher plants and animals tend to maintain sexual reproduction in part because of the enhanced fitness of offspring resulting from sexual selection at the level of individual organisms, and in part because of the superiority of sexual populations in competition with asexual clones.     

Rates of deleterious mutation and the evolution of sex in Caenorhabditis

A variety of models propose that the accumulation of deleterious mutations plays an important role in the evolution of breeding systems. These models make predictions regarding the relative rates of protein evolution and deleterious mutation in taxa with contrasting modes of reproduction. Here we compare available coding sequences from one obligately outcrossing and two primarily selfing species of Caenorhabditis to explore the potential for mutational models to explain the evolution of breeding system in this clade. If deleterious mutations interact synergistically, the mutational deterministic hypothesis predicts that a high genomic deleterious mutation rate (U) will offset the reproductive disadvantage of outcrossing relative to asexual or selfing reproduction. Therefore, C. elegans and C. briggsae (both largely selfing) should both exhibit lower rates of deleterious mutation than the obligately outcrossing relative C. remanei. Using a comparative approach, we estimate U to be equivalent (and < 1) among all three related species. Stochastic mutational models, Muller's ratchet and Hill-Robertson interference, are expected to cause reductions in the effective population size in species that rarely outcross, thereby allowing deleterious mutations to accumulate at an elevated rate. We find only limited support for more rapid molecular evolution in selfing lineages. Overall, our analyses indicate that the evolution of breeding system in this group is unlikely to be explained solely by available mutational models.     

The role of pleiotropy in the maintenance of sex in yeast

In facultatively sexual species, lineages that reproduce asexually for a period of time can accumulate mutations that reduce their ability to undergo sexual reproduction when sex is favorable. We propagated Saccharomyces cerevisiae asexually for approximately 800 generations, after which we measured the change in sexual fitness, measured as the proportion of asci observed in sporulation medium. The sporulation rate in cultures propagated asexually at small population size declined by 8%, on average, over this time period, indicating that the majority of mutations that affect sporulation rate are deleterious. Interestingly, the sporulation rate in cultures propagated asexually at large population size improved by 11%, on average, indicating that selection on asexual function effectively eliminated most of the mutations deleterious to sporulation ability. These results suggest that pleiotropy between mutations' effects on asexual fitness and sexual fitness was predominantly positive, at least for the mutations accumulated in this experimental evolution study. A positive correlation between growth rate and sporulation rate among lines also provided evidence for positive pleiotropy. These results demonstrate that, at least under certain circumstances, selection acting on asexual fitness can help to maintain sexual function.     

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.     

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.     

Elimination of altered karyotypes by sexual reproduction preserves species identity.

Resolving the persistence of sexual reproduction despite its overwhelming costs (known as the paradox of sex) is one of the most persistent challenges of evolutionary biology. In thinking about this paradox, the focus has traditionally been on the evolutionary benefits of genetic recombination in generating offspring diversity and purging deleterious mutations. The similarity of pattern between evolution of organisms and evolution among cancer cells suggests that the asexual process generates more diverse genomes owing to less controlled reproduction systems, while sexual reproduction generates more stable genomes because the sexual process can serve as a mechanism to "filter out" aberrations at the chromosome level. Our reinterpretation of data from the literature strongly supports this hypothesis. Thus, the principal consequence of sexual reproduction is the reduction of drastic genetic diversity at the genome or chromosome level, resulting in the preservation of species identity rather than the provision of evolutionary diversity for future environmental challenges. Genetic recombination does contribute to genetic diversity, but it does so secondarily and within the framework of the chromosomally defined genome.     

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.     

Muller’s ratchet in symbiont populations

Muller’s ratchet, the inevitable accumulation of deleterious mutations in asexual populations, has been proposed as a major factor in genome degradation of obligate symbiont organisms. Essentially, if left unchecked the ratchet will with certainty cause extinction due to the ever increasing mutational load. This paper examines the evolutionary fate of insect symbionts, using mathematical modelling to simulate the accumulation of deleterious mutations. We investigate the effects of a hierarchical two level population structure. Since each host contains its own subpopulation of symbionts, there will be a large number of small symbiont populations linked indirectly via selection on the host level. We show that although the separate subpopulations will accumulate deleterious mutations quickly, the symbiont population as a whole will be protected from extinction by selection acting on the hosts. As a consequence, the extent of genome degradation observed in present day symbionts is more likely to represent loss of functions that were (near-) neutral to the host, rather than a snap shot of a decline towards complete genetic collapse.     

The impact of population size on the evolution of asexual microbes on smooth versus rugged fitness landscapes

Background  

It is commonly thought that large asexual populations evolve more rapidly than smaller ones, due to their increased rate of beneficial mutations. Less clear is how population size influences the level of fitness an asexual population can attain. Here, we simulate the evolution of bacteria in repeated serial passage experiments to explore how features such as fitness landscape ruggedness, the size of the mutational target under selection, and the mutation supply rate, interact to affect the evolution of microbial populations of different sizes.     

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.     

An Experimental Test for Synergistic Epistasis and Its Application in Chlamydomonas

Theoretically, one of the most general benefits of sex is given by its function in facilitating selection against deleterious mutations. This advantage of sex may be deterministic if deleterious mutations affect the fitness of an individual in a synergistic way, i.e., if mutations increase each others' negative fitness effect. We present a new test for synergistic epistasis that considers the skewness of the log fitness distribution of offspring from a cross. We applied this test to data of the unicellular alga Chlamydomonas moewussii. For this purpose, two crosses were made: one between two strains that are presumed to have accumulated slightly deleterious mutations, the other between two strains without a history of mutation accumulation. Fitness was measured by estimating the two parameters of logistic growth in batch culture, the maximum growth rate (r) and the carrying capacity (K). The finding of a negatively skewed distribution for K in the accumulation cross suggests synergism between mutations affecting the carrying capacity, while the absence of skewness for r in both crosses is consistent with independent effects of mutations affecting this parameter. The results suggest a possible alternative explanation for the general observation that sex is related to constant environments, where selection on K predominates, while asexual reproduction is found in more variable environments, where selection on r is more important.     

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 effect of deleterious alleles on adaptation in asexual populations

We calculate the fixation probability of a beneficial allele that arises as the result of a unique mutation in an asexual population that is subject to recurrent deleterious mutation at rate U. Our analysis is an extension of previous works, which make a biologically restrictive assumption that selection against deleterious alleles is stronger than that on the beneficial allele of interest. We show that when selection against deleterious alleles is weak, beneficial alleles that confer a selective advantage that is small relative to U have greatly reduced probabilities of fixation. We discuss the consequences of this effect for the distribution of effects of alleles fixed during adaptation. We show that a selective sweep will increase the fixation probabilities of other beneficial mutations arising during some short interval afterward. We use the calculated fixation probabilities to estimate the expected rate of fitness improvement in an asexual population when beneficial alleles arise continually at some low rate proportional to U. We estimate the rate of mutation that is optimal in the sense that it maximizes this rate of fitness improvement. Again, this analysis relaxes the assumption made previously that selection against deleterious alleles is stronger than on beneficial alleles.