The Rate of Compensatory Evolution

A two-locus model is presented to analyze the evolution of compensatory mutations occurring in stems of RNA secondary structures. Single mutations are assumed to be deleterious but harmless (neutral) in appropriate combinations. In proceeding under mutation pressure, natural selection and genetic drift from one fitness peak to another one, a population must therefore pass through a valley of intermediate deleterious states of individual fitness. The expected time for this transition is calculated using diffusion theory. The rate of compensatory evolution, k(c), is then defined as the inverse of the expected transition time. When selection against deleterious single mutations is strong, k(c) depends on the recombination fraction r between the two loci. Recombination generally reduces the rate of compensatory evolution because it breaks up favorable combinations of double mutants. For complete linkage, k(c) is given by the rate at which favorable combinations of double mutants are produced by compensatory mutation. For r>0, k(c) decreases exponentially with r. In contrast, k(c) becomes independent of r for weak selection. We discuss the dynamics of evolutionary substitutions of compensatory mutants in relation to WRIGHT's shifting balance theory of evolution and use our results to analyze the substitution process in helices of mRNA secondary structures.     

RNA Folding in Drosophila Shows a Distance Effect for Compensatory Fitness Interactions

Phylogenetic-comparative analysis was used to construct a secondary structure of Adh precursor messenger RNA (pre-mRNA) in Drosophila. The analysis revealed that the rate of coevolution of base-pairing residues decreases with their physical distance. This result is in qualitative agreement with a model of compensatory fitness interactions which assumes that mutations are individually deleterious but become harmless (neutral) in appropriate combinations. This model predicts that coupled mutations can become fixed in a population under mutation pressure and random genetic drift, when the mutations are closely linked. However, the rate of joint fixation drops as distance between sites increases and recombination breaks up favorable combinations. RNA secondary structure was also used to interpret patterns of linkage disequilibrium at Adh.     

The Evolutionary Advantage of Recombination

The controversy over the evolutionary advantage of recombination initially discovered by Fisher and by Muller is reviewed. Those authors whose models had finite-population effects found an advantage of recombination, and those whose models had infinite populations found none. The advantage of recombination is that it breaks down random linkage disequilibrium generated by genetic drift. Hill and Robertson found that the average effect of this randomly-generated linkage disequilibrium was to cause linked loci to interfere with each other's response to selection, even where there was no gene interaction between the loci. This effect is shown to be identical to the original argument of Fisher and Muller. It also predicts the "ratchet mechanism" discovered by Muller, who pointed out that deleterious mutants would more readily increase in a population without recombination. Computer simulations of substitution of favorable mutants and of the long-term increase of deleterious mutants verified the essential correctness of the original Fisher-Muller argument and the reality of the Muller ratchet mechanism. It is argued that these constitute an intrinsic advantage of recombination capable of accounting for its persistence in the face of selection for tighter linkage between interacting polymorphisms, and possibly capable of accounting for its origin.     

Increased recombination in a multi-locus system during environmental fluctuations

The role of variability of environment as a factor of recombination evolution is studied. It was shown that selection in multilocus system under cyclic or random fluctuations of external conditions results in rapid increase in recombination frequency, even under free recombination between the rec-modificator and the selected system (SS). If so, pair-vise linkage disequilibrium coefficients have unchanged signs and are negative, and the advantage of rec+ alleles is provided by changes in signs of disequilibriums of higher order. The low frequency environmental fluctuations maintain recombination as it is, while high frequency ones induce the substitution of the low level by high. It was established that the recombination promoting mechanism of crossing-over maintenance, due to elimination of non-optimal allelic combinations of SS loci under temporal optimum variations, may be accomplished by smaller genetic load, than under elimination of deleterious mutations.     

Purging deleterious mutations under self fertilization: paradoxical recovery in fitness with increasing mutation rate in Caenorhabditis elegans

Background

The accumulation of deleterious mutations can drastically reduce population mean fitness. Self-fertilization is thought to be an effective means of purging deleterious mutations. However, widespread linkage disequilibrium generated and maintained by self-fertilization is predicted to reduce the efficacy of purging when mutations are present at multiple loci.

Methodology/Principal Findings

We tested the ability of self-fertilizing populations to purge deleterious mutations at multiple loci by exposing obligately self-fertilizing populations of Caenorhabditis elegans to a range of elevated mutation rates and found that mutations accumulated, as evidenced by a reduction in mean fitness, in each population. Therefore, purging in obligate selfing populations is overwhelmed by an increase in mutation rate. Surprisingly, we also found that obligate and predominantly self-fertilizing populations exposed to very high mutation rates exhibited consistently greater fitness than those subject to lesser increases in mutation rate, which contradicts the assumption that increases in mutation rate are negatively correlated with fitness. The high levels of genetic linkage inherent in self-fertilization could drive this fitness increase.

Conclusions

Compensatory mutations can be more frequent under high mutation rates and may alleviate a portion of the fitness lost due to the accumulation of deleterious mutations through epistatic interactions with deleterious mutations. The prolonged maintenance of tightly linked compensatory and deleterious mutations facilitated by self-fertilization may be responsible for the fitness increase as linkage disequilibrium between the compensatory and deleterious mutations preserves their epistatic interaction.     

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.     

Expected Linkage Disequilibrium for a Neutral Locus Linked to a Chromosomal Arrangement

The expected value of the squared linkage disequilibrium is derived for a neutral locus associated with a chromosomal arrangement that is maintained in the population by strong balancing selection. For a given value of recombination, the expected squared linkage disequilibrium is shown to decrease as the intensity of selection maintaining the arrangement increases. The transient behavior of the expected square linkage disequilibrium is also derived. This theory applies to loci that are closely linked to inversions in Drosophila species and to loci closely linked to the differential segments of the translocation complexes in ring-forming species of Oenothera. In both cases the strong linkage disequilibria that have been observed in natural populations can be explained by random drift.     

Effect of epistasis and linkage on fixation probability in three-locus models: an ancestral recombination-selection graph approach

We study the probability of ultimate fixation of a single new mutant arising in an individual chosen at random at a locus linked to two other loci carrying previously arisen mutations. This is done using the Ancestral Recombination-Selection Graph (ARSG) in a finite population in the limit of a large population size, which is also known as the Ancestral Influence Graph (AIG). An analytical expansion of the fixation probability with respect to population-scaled recombination rates and selection intensities is obtained. The coefficients of the expansion are expressed in terms of the initial state of the population and the epistatic interactions among the selected loci. Under the assumption of weak selection at tightly linked loci, the sign of the leading term, which depends on the signs of epistasis and initial linkage disequilibrium, determines whether an increase in recombination rates increases the chance of ultimate fixation of the new mutant. If mutants are advantageous, this is the case when epistasis is positive or null and the initial linkage disequilibrium is negative, which is an expected state in a finite population under directional selection. Moreover, this is also the case for a neutral mutant modifier coding for higher recombination rates if the same conditions hold at the selected loci. Under the same conditions, deleterious mutants are disfavored for ultimate fixation and neutral modifiers for higher recombination rates still favored. The recombination rates between the modifier locus and the selected loci do not come into play in the leading terms of the approximation for the fixation probability, but they do in higher-order terms.     

On the effects of background selection in small populations on comparisons of molecular variation

Deleterious mutations affect genetic variation at linked neutral loci. Neutral variation can be reduced due to background selection, but in small population and with tight linkage such variation may increase due to associative overdominance. Here I report the results of computer simulations of diploid genotypes in small populations, where I look at the effect of deleterious mutations and linkage on comparisons of intra- and interspecific variation. Each chromosome consisted of 2000 loci where deleterious and neutral mutations occurred. The ratio of nonsynonymous to synonymous substitution rates (Ka/Ks) either increases with tight linkage or is unaffected, depending on the strength of selection. The ratio of the numbers of segregating mutations to the number of fixed mutations decreases under the conditions leading to background selection but can increase at tight linkage. Numbers of segregating sites (Sn) are less affected than nucleotide site diversity (pi), pi reduces more than Sn at intermediate linkage, but pi increases more than Sn when linkage is tight. Similar effects as found for Sn and pi are observed for heterozygosity and variance in allele size of tandem repeat loci.     

Compensatory evolution in diploid populations

Compensatory mutations are individually deleterious but harmless in appropriate combinations either at more than two sites within a gene or on separate genes. Considering that dominance effects of selection and heterodimer formation of gene products may affect the rate of compensatory evolution, we investigate compensatory neutral mutation models for diploid populations. Our theoretical analysis on the average time until fixation of compensatory mutations shows that these factors play an important role in reducing the fixation time of compensatory mutations if mutation rates are not low. Compensatory evolution of heterodimers is shown to occur more easily if the deleterious effects of single mutants are recessive.     

Background selection and population differentiation

A general analytical formula is derived, which predicts the effects of background selection on population differentiation at a neutral locus as a result of its linkage with selected loci of deleterious mutations. The theory is based on the assumptions of random mating, multiplicative fitness, and weak selection in hermaphrodite plants in the island model of population structure. The analytical results show that Fst at the neutral locus increases as a result of the effects of background selection, regardless of the dependence or independence among linked background selective loci. The increment in Fst is closely related to the magnitude of linkage disequilibria between the neutral locus and selected loci, and can be estimated by the ratio of Fst with background selection to Fst without background selection minus one. The steady-state linkage disequilibrium between a neutral locus and a selected locus in subpopulations, primarily attained by gene flow, decreases with the recombination rate, and can be enhanced when there are dependence among linked selected loci. Monte Carlo computer simulations with two- and three-locus models show that the analytical formulae perform well under general conditions. Application of the present theory may aid in analyzing the genome-wide mapping of the effect of background selection in terms of Fst.     

The effect of deleterious mutations and age on recombination in Drosophila melanogaster

At the population level, recombination mediates the efficiency with which selection can eliminate deleterious mutations. At the individual level, deleterious alleles may influence recombination, which would change the rate at which linkage disequilibrium is eroded and thereby alter the efficiency with which deleterious alleles are purged. Here, we test whether the presence of a deleterious allele on one autosome affects recombination on another autosome. We find that deleterious alleles not only alter the rate but also the pattern of recombination. However, there is little support that different deleterious alleles affect recombination in a consistent manner. Because we have detailed information on individual females across their lifetimes, we are able to examine how recombination patterns change with age and find that these patterns are also affected by the presence of deleterious alleles. The differences among genotypes or among age classes are large enough to add substantial noise to genetic mapping experiments that do not consider these sources of variation.     

Linkage disequilibrium under skewed offspring distribution among individuals in a population

Correlations in coalescence times between two loci are derived under selectively neutral population models in which the offspring of an individual can number on the order of the population size. The correlations depend on the rates of recombination and random drift and are shown to be functions of the parameters controlling the size and frequency of these large reproduction events. Since a prediction of linkage disequilibrium can be written in terms of correlations in coalescence times, it follows that the prediction of linkage disequilibrium is a function not only of the rate of recombination but also of the reproduction parameters. Low linkage disequilibrium is predicted if the offspring of a single individual frequently replace almost the entire population. However, high linkage disequilibrium can be predicted if the offspring of a single individual replace an intermediate fraction of the population. In some cases the model reproduces the standard Wright-Fisher predictions. Contrary to common intuition, high linkage disequilibrium can be predicted despite frequent recombination, and low linkage disequilibrium under infrequent recombination. Simulations support the analytical results but show that the variance of linkage disequilibrium is very large.     

Evolution of recombination due to random drift

In finite populations subject to selection, genetic drift generates negative linkage disequilibrium, on average, even if selection acts independently (i.e., multiplicatively) upon all loci. Negative disequilibrium reduces the variance in fitness and hence, by Fisher's (1930) fundamental theorem, slows the rate of increase in mean fitness. Modifiers that increase recombination eliminate the negative disequilibria that impede selection and consequently increase in frequency by "hitchhiking." Thus, stochastic fluctuations in linkage disequilibrium in finite populations favor the evolution of increased rates of recombination, even in the absence of epistatic interactions among loci and even when disequilibrium is initially absent. The method developed within this article allows us to quantify the strength of selection acting on a modifier allele that increases recombination in a finite population. The analysis indicates that stochastically generated linkage disequilibria do select for increased recombination, a result that is confirmed by Monte Carlo simulations. Selection for a modifier that increases recombination is highest when linkage among loci is tight, when beneficial alleles rise from low to high frequency, and when the population size is small.     

Time for Spreading of Compensatory Mutations under Gene Duplication

Evolution by compensatory mutations is accelerated by gene duplication because selective constraint is relaxed by gene redundancy. A mutation is called compensatory if it corrects the effect of an earlier deleterious mutation. Without duplication, Kimura has shown that the time for spreading of compensatory mutations is much reduced by tight linkage between the two chromosomal sites of mutations. In this report, the time for spreading with gene duplication was studied by using the diffusion equation method of Kimura, together with computer simulations. It was shown that, when 2Nv- is much less than unity, the time for spreading is greatly shortened by gene duplication as compared with the case of complete linkage between the two sites of mutations, where 2N is the effective population size (haploid) and v- is the rate of compensatory mutations. However, if 2Nv- greater than 1, gene duplication is not effective for accelerating the evolution by such mutations.     

The Sampling Distribution of Linkage Disequilibrium under an Infinite Allele Model without Selection

The sampling distributions of several statistics that measure the association of alleles on gametes (linkage disequilibrium) are estimated under a two-locus neutral infinite allele model using an efficient Monte Carlo method. An often used approximation for the mean squared linkage disequilibrium is shown to be inaccurate unless the proper statistical conditioning is used. The joint distribution of linkage disequilibrium and the allele frequencies in the sample is studied. This estimated joint distribution is sufficient for obtaining an approximate maximum likelihood estimate of C = 4Nc, where N is the population size and c is the recombination rate. It has been suggested that observations of high linkage disequilibrium might be a good basis for rejecting a neutral model in favor of a model in which natural selection maintains genetic variation. It is found that a single sample of chromosomes, examined at two loci cannot provide sufficient information for such a test if C less than 10, because with C this small, very high levels of linkage disequilibrium are not unexpected under the neutral model. In samples of size 50, it is found that, even when C is as large as 50, the distribution of linkage disequilibrium conditional on the allele frequencies is substantially different from the distribution when there is no linkage between the loci. When conditioned on the number of alleles at each locus in the sample, all of the sample statistics examined are nearly independent of theta = 4N mu, where mu is the neutral mutation rate.     

The joint effects of background selection and genetic recombination on local gene genealogies

Background selection, the effects of the continual removal of deleterious mutations by natural selection on variability at linked sites, is potentially a major determinant of DNA sequence variability. However, the joint effects of background selection and genetic recombination on the shape of the neutral gene genealogy have proved hard to study analytically. The only existing formula concerns the mean coalescent time for a pair of alleles, making it difficult to assess the importance of background selection from genome-wide data on sequence polymorphism. Here we develop a structured coalescent model of background selection with recombination and implement it in a computer program that efficiently generates neutral gene genealogies for an arbitrary sample size. We check the validity of the structured coalescent model against forward-in-time simulations and show that it accurately captures the effects of background selection. The model produces more accurate predictions of the mean coalescent time than the existing formula and supports the conclusion that the effect of background selection is greater in the interior of a deleterious region than at its boundaries. The level of linkage disequilibrium between sites is elevated by background selection, to an extent that is well summarized by a change in effective population size. The structured coalescent model is readily extendable to more realistic situations and should prove useful for analyzing genome-wide polymorphism data.     

Maintenance of Genetic Variability under the Joint Effect of Mutation, Selection and Random Drift

Formulae are developed for the distribution of allele frequencies (the frequency spectrum), the mean number of alleles in a sample, and the mean and variance of heterozygosity under mutation pressure and under either genic or recessive selection. Numerical computations are carried out by using these formulae and Watterson's (1977) formula for the distribution of allele frequencies under overdominant selection. The following properties are observed: (1) The effect of selection on the distribution of allele frequencies is slight when 4Ns 相似文献   

Sexual recombination under the joint effects of mutation,selection, and random sampling drift

The advantage or disadvantage of sexual reproduction or recombination for the accumulation of mutant genes in a population is studied under the joint effects of recurrent mutations, selection, and random sampling drift. To obtain the rate at which mutant genes are incorporated three different methods are used; numerical integration of Kolmogorov backward equations, simulation of stochastic difference equations, and Monte Carlo experiments. The first two methods are used in a two-locus system to obtain the fixation probability of double mutants and other related quantities under five different selection models. The third one is conducted for a multiple-locus system and the rate of accumulation of mutant genes per locus is studied. Comparison of the results between sexual and asexual populations shows that the effect of recombination depends on initial linkage disequilibrium, mutation rate v, selection intensity s, and population size N_e. The mode of selection is also an important factor and the large effect of recombination is observed when mutant genes are individually deleterious but collectively favorable. Under a given model of selection, the great advantage or disadvantage of recombination is achieved when a large extent of genetic polymorphism is produced not by mutation but by recombination. Extreme values of N_es and N_ev make the effect insignificant. The results of Monte Carlo experiments also reveal the presence of interaction between selection and sampling drift even when the loci segregate independently and selection is multiplicative. Although this interaction is usually small, there are cases in which one locus theory cannot be used freely. In those cases, the effect of recombination is prominent and one locus theory gives an overestimate of the rate.     

Inferring Selective History from Multilocus Frequency Data: Wright Meets the Hamiltonian

We describe a method to study characteristics of the dynamics of multilocus population genetic models without specifying the form of selection a priori. Our approach consists of specifying initial and final genotypic frequencies (either completely or partially) and then determining the minimum time to go from the initial condition to the final condition according to a continuous time genetic model, with arbitrary constraints on the strength and possibly the form of selection. In analyzing a two-locus, two-allele model with this approach, we show that--so long as r is not much larger than s--substantial linkage disequilibrium can be generated from an initial state of linkage equilibrium in a few hundred generations. We also show that unless recombination is much larger than selection, there is only weak dependence on r of the minimum time to reach a specified state. Thus, similar strengths of selection can lead to similar levels of disequilibrium over a fixed time and a range of small recombination rates. This implies that, within the level of a single gene, selection cannot in general be assumed to lead to any particular relationship between recombination rate and levels of disequilibrium. We indicate a number of other ways in which our method can be useful in asking theoretical questions and in interpreting data.