Stabilizing selection,mutational bias,and the evolution of sex*

Stabilizing selection around a fixed phenotypic optimum is expected to disfavor sexual reproduction, since asexually reproducing organisms can maintain a higher fitness at equilibrium, while sex disrupts combinations of compensatory mutations. This conclusion rests on the assumption that mutational effects on phenotypic traits are unbiased, that is, mutation does not tend to push phenotypes in any particular direction. In this article, we consider a model of stabilizing selection acting on an arbitrary number of polygenic traits coded by bialellic loci, and show that mutational bias may greatly reduce the mean fitness of asexual populations compared with sexual ones in regimes where mutations have weak to moderate fitness effects. Indeed, mutation and drift tend to push the population mean phenotype away from the optimum, this effect being enhanced by the low effective population size of asexual populations. In a second part, we present results from individual‐based simulations showing that positive rates of sex are favored when mutational bias is present, while the population evolves toward complete asexuality in the absence of bias. We also present analytical (QLE) approximations for the selective forces acting on sex in terms of the effect of sex on the mean and variance in fitness among offspring.     

Mutational bias for body size in rhabditid nematodes

Mutational bias is a potentially important agent of evolution, but it is difficult to disentangle the effects of mutation from those of natural selection. Mutation-accumulation experiments, in which mutations are allowed to accumulate at very small population size, thus minimizing the efficiency of natural selection, are the best way to separate the effects of mutation from those of selection. Body size varies greatly among species of nematode in the family rhabditidae; mutational biases are both a potential cause and a consequence of that variation. We report data on the cumulative effects of mutations that affect body size in three species of rhabditid nematode that vary fivefold in adult size. Results are very consistent with previous studies of mutations underlying fitness in the same strains: two strains of Caenorhabditis briggsae decline in body size about twice as fast as two strains of C. elegans, with a concomitant higher point estimate of the genomic mutation rate; the confamilial Oscheius myriophila is intermediate. There is an overall mutational bias, such that mutations reduce size on average, but the bias appears consistent between species. The genetic correlation between mutations that affect size and those underlying fitness is large and positive, on average.     

EPISTASIS,PLEIOTROPY, AND THE MUTATION LOAD IN SEXUAL AND ASEXUAL POPULATIONS

Mutation may impose a substantial load on populations, which varies according to the reproductive mode of organisms. Over the past years, various authors used adaptive landscape models to predict the long‐term effect of mutation on mean fitness; however, many of these studies assumed very weak mutation rates, so that at most one mutation segregates in the population. In this article, we derive several simple approximations (confirmed by simulations) for the mutation load at high mutation rate (U), using a general model that allows us to play with the number of selected traits (n), the degree of pleiotropy of mutations, and the shape of the fitness function (which affects the average sign and magnitude of epistasis among mutations). When mutations have strong fitness effects, the equilibrium fitness of sexuals and asexuals is close to ; under weaker mutational effects, sexuals reach a different regime where is a simple function of U and of a parameter describing the shape of the fitness function. Contrarily to weak mutation results showing that is an increasing function of population size and a decreasing function of n, these parameters may have opposite effects in sexual populations at high mutation rate.     

Mutation accumulation in populations of varying size: large effect mutations cause most mutational decline in the rotifer Brachionus calyciflorus under UV‐C radiation

Theory predicts that fitness decline via mutation accumulation will depend on population size, but there are only a few direct tests of this key idea. To gain a qualitative understanding of the fitness effect of new mutations, we performed a mutation accumulation experiment with the facultative sexual rotifer Brachionus calyciflorus at six different population sizes under UV‐C radiation. Lifetime reproduction assays conducted after ten and sixteen UV‐C radiations showed that while small populations lost fitness, fitness losses diminished rapidly with increasing population size. Populations kept as low as 10 individuals were able to maintain fitness close to the nonmutagenized populations throughout the experiment indicating that selection was able to remove the majority of large effect mutations in small populations. Although our results also seem to imply that small populations are effectively immune to mutational decay, we caution against this interpretation. Given sufficient time, populations of moderate to large size can experience declines in fitness from accumulating weakly deleterious mutations as demonstrated by fitness estimates from simulations and, tentatively, from a long‐term experiment with populations of moderate size. There is mounting evidence to suggest that mutational distributions contain a heavier tail of large effects. Our results suggest that this is also true when the mutational spectrum is altered by UV radiation.     

The mutational structure of metabolism in Caenorhabditis elegans

A properly functioning organism must maintain metabolic homeostasis. Deleterious mutations degrade organismal function, presumably at least in part via effects on metabolic function. Here we present an initial investigation into the mutational structure of the Caenorhabditis elegans metabolome by means of a mutation accumulation experiment. We find that pool sizes of 29 metabolites vary greatly in their vulnerability to mutation, both in terms of the rate of accumulation of genetic variance (the mutational variance, VM) and the rate of change of the trait mean (the mutational bias, ΔM). Strikingly, some metabolites are much more vulnerable to mutation than any other trait previously studied in the same way. Although we cannot statistically assess the strength of mutational correlations between individual metabolites, principal component analysis provides strong evidence that some metabolite pools are genetically correlated, but also that there is substantial scope for independent evolution of different groups of metabolites. Averaged over mutation accumulation lines, PC3 is positively correlated with relative fitness, but a model in which metabolites are uncorrelated with fitness is nearly as good by Akaike's Information Criterion.     

Sexual selection on spontaneous mutations strengthens the between‐sex genetic correlation for fitness

A proposed benefit to sexual selection is that it promotes purging of deleterious mutations from populations. For this benefit to be realized, sexual selection, which is usually stronger on males, must purge mutations deleterious to both sexes. Here, we experimentally test the hypothesis that sexual selection on males purges deleterious mutations that affect both male and female fitness. We measured male and female fitness in two panels of spontaneous mutation‐accumulation lines of the fly, Drosophila serrata, each established from a common ancestor. One panel of mutation accumulation lines limited both natural and sexual selection (LS lines), whereas the other panel limited natural selection, but allowed sexual selection to operate (SS lines). Although mutation accumulation caused a significant reduction in male and female fitness in both the LS and SS lines, sexual selection had no detectable effect on the extent of the fitness reduction. Similarly, despite evidence of mutational variance for fitness in males and females of both treatments, sexual selection had no significant impact on the amount of mutational genetic variance for fitness. However, sexual selection did reshape the between‐sex correlation for fitness: significantly strengthening it in the SS lines. After 25 generations, the between‐sex correlation for fitness was positive but considerably less than one in the LS lines, suggesting that, although most mutations had sexually concordant fitness effects, sex‐limited, and/or sex‐biased mutations contributed substantially to the mutational variance. In the SS lines this correlation was strong and could not be distinguished from unity. Individual‐based simulations that mimick the experimental setup reveal two conditions that may drive our results: (1) a modest‐to‐large fraction of mutations have sex‐limited (or highly sex‐biased) fitness effects, and (2) the average fitness effect of sex‐limited mutations is larger than the average fitness effect of mutations that affect both sexes similarly.     

MUTATIONAL MELTDOWN IN LABORATORY YEAST POPULATIONS

Abstract.— In small or repeatedly bottlenecked populations, mutations are expected to accumulate by genetic drift, causing fitness declines. In mutational meltdown models, such fitness declines further reduce population size, thus accelerating additional mutation accumulation and leading to extinction. Because the rate of mutation accumulation is determined partly by the mutation rate, the risk and rate of meltdown are predicted to increase with increasing mutation rate. We established 12 replicate populations of Saccharomyces cerevisiae from each of two isogenic strains whose genomewide mutation rates differ by approximately two orders of magnitude. Each population was transferred daily by a fixed dilution that resulted in an effective population size near 250. Fitness declines that reduce growth rates were expected to reduce the numbers of cells transferred after dilution, thus reducing population size and leading to mutational meltdown. Through 175 daily transfers and approximately 2900 generations, two extinctions occurred, both in populations with elevated mutation rates. For one of these populations there is direct evidence that extinction resulted from mutational meltdown: Extinction immediately followed a major fitness decline, and it recurred consistently in replicate populations reestablished from a sample frozen after this fitness decline, but not in populations founded from a predecline sample. Wild‐type populations showed no trend to decrease in size and, on average, they increased in fitness.     

Fitness change in relation to mutation number in spontaneous mutation accumulation lines of Chlamydomonas reinhardtii

Although all genetic variation ultimately stems from mutations, their properties are difficult to study directly. Here, we used multiple mutation accumulation (MA) lines derived from five genetic backgrounds of the green algae Chlamydomonas reinhardtii that have been previously subjected to whole genome sequencing to investigate the relationship between the number of spontaneous mutations and change in fitness from a nonevolved ancestor. MA lines were on average less fit than their ancestors and we detected a significantly negative correlation between the change in fitness and the total number of accumulated mutations in the genome. Likewise, the number of mutations located within coding regions significantly and negatively impacted MA line fitness. We used the fitness data to parameterize a maximum likelihood model to estimate discrete categories of mutational effects, and found that models containing one to two mutational effect categories (one neutral and one deleterious category) fitted the data best. However, the best‐fitting mutational effects models were highly dependent on the genetic background of the ancestral strain.     

Analysis and implications of mutational variation

Variation from new mutations is important for several questions in quantitative genetics. Key parameters are the genomic mutation rate and the distribution of effects of mutations (DEM), which determine the amount of new quantitative variation that arises per generation from mutation (V _M ). Here, we review methods and empirical results concerning mutation accumulation (MA) experiments that have shed light on properties of mutations affecting quantitative traits. Surprisingly, most data on fitness traits from laboratory assays of MA lines indicate that the DEM is platykurtic in form (i.e., substantially less leptokurtic than an exponential distribution), and imply that most variation is produced by mutations of moderate to large effect. This finding contrasts with results from MA or mutagenesis experiments in which mutational changes to the DNA can be assayed directly, which imply that the vast majority of mutations have very small phenotypic effects, and that the distribution has a leptokurtic form. We compare these findings with recent approaches that attempt to infer the DEM for fitness based on comparing the frequency spectra of segregating nucleotide polymorphisms at putatively neutral and selected sites in population samples. When applied to data for humans and Drosophila, these analyses also indicate that the DEM is strongly leptokurtic. However, by combining the resultant estimates of parameters of the DEM with estimates of the mutation rate per nucleotide, the predicted V _M for fitness is only a tiny fraction of V _M observed in MA experiments. This discrepancy can be explained if we postulate that a few deleterious mutations of large effect contribute most of the mutational variation observed in MA experiments and that such mutations segregate at very low frequencies in natural populations, and effectively are never seen in population samples.     

The accumulation of mutations in asexual populations and the structure of genealogical trees in the presence of selection

We study the accumulation of unfavourable mutations in asexual populations by the process of Muller's ratchet, and the consequent inevitable decrease in fitness of the population. Simulations show that it is mutations with only moderate unfavourable effect that lead to the most rapid decrease in fitness. We measure the number of fixations as a function of time and show that the fixation rate must be equal to the ratchet rate once a steady state is reached. Large bursts of fixations are observed to occur simultaneously. We relate this to the structure of the genealogical tree. We derive equations relating the rate of the ratchet to the moments of the distribution of the number of mutations k per individual. These equations interpolate between the deterministic limit (an infinite population with selection present) and the neutral limit (a finite size population with no selection). Both these limits are exactly soluble. In the neutral case, the distribution of k is shown to be non-self-averaging, i.e. the fluctuations remain very large even for very large populations. We also consider the strong-selection limit in which only individuals in the fittest surviving class have offspring. This limit is again exactly soluble. We investigate the structure of the genealogical tree relating individuals in the same population, and consider the probability (T) that two individuals had their latest common ancestor T generations in the past. The function (T) is exactly calculable in the neutral limit and the strong-selection limit, and we obtain an empirical solution for intermediate selection strengths.     

Biased sex ratios in the dioecious annual Croton texensis (Euphorbiaceae) are not due to environmental sex determination

At Arapaho Prairie, in the sandhills of western Nebraska, the dioecious annual Croton texensis (Euphorbiaceae) exhibits biased sex ratios. Moreover, the direction of bias changes from year to year: in 1994 the study population was significantly female biased, in 1995 and 1996 it was significantly male biased, and in 1997 and 1998 the sex ratio did not differ from 1 : 1. Such variation in the observed sex ratio in plants is frequently attributed to environmental sex determination (ESD), which is favored by natural selection if the rate of fitness gain across an environmental gradient is greater for one sex than the other. We performed experiments to determine: (1) whether variation in the sex ratio is correlated with environmental conditions, as would be expected if ESD is operating, and (2) whether ESD, if present, would be favored by natural selection. In a common garden experiment in which water and fertilizer were manipulated the sex ratio was marginally male biased in treatments in which water was added, but not different from 1 : 1 in other treatments. In field plots into which seeds were planted none of several soil characteristics, nor overall plot quality for C. texensis (measured as average plant biomass) were correlated with plot sex ratio. However, plots in which a large number of planted seeds emerged tended to be female biased. These results provide very weak evidence for sex ratio bias across an environmental gradient, and thus provide little evidence for ESD. Moreover, sex-by-environment interactions for fitness, which are required for the evolution of ESD, were absent for all measured variables. Thus, ESD does not appear to be favored by natural selection in this population. Instead, these biases may have been caused by differences between the sexes in germination and/or early mortality.     

Compensatory mutations cause excess of antagonistic epistasis in RNA secondary structure folding

Background

The rate at which fitness declines as an organism's genome accumulates random mutations is an important variable in several evolutionary theories. At an intuitive level, it might seem natural that random mutations should tend to interact synergistically, such that the rate of mean fitness decline accelerates as the number of random mutations is increased. However, in a number of recent studies, a prevalence of antagonistic epistasis (the tendency of multiple mutations to have a mitigating rather than reinforcing effect) has been observed.

Results

We studied in silico the net amount and form of epistatic interactions in RNA secondary structure folding by measuring the fraction of neutral mutants as a function of mutational distance d. We found a clear prevalence of antagonistic epistasis in RNA secondary structure folding. By relating the fraction of neutral mutants at distance d to the average neutrality at distance d, we showed that this prevalence derives from the existence of many compensatory mutations at larger mutational distances.

Conclusions

Our findings imply that the average direction of epistasis in simple fitness landscapes is directly related to the density with which fitness peaks are distributed in these landscapes.

     

Fitness decline under osmotic stress in Caenorhabditis elegans populations subjected to spontaneous mutation accumulation at varying population sizes

The consequences of mutations for population fitness depends on their individual selection coefficients and the effective population size. An earlier study of Caenorhabditis elegans spontaneous mutation accumulation lines evolved for 409 generations at three population sizes found that N_e  = 1 populations declined significantly in fitness whereas the fitness of larger populations (N_e  = 5, 50) was indistinguishable from the ancestral control under benign conditions. To test if larger MA populations harbor a load of cryptic deleterious mutations that are obscured under benign laboratory conditions, we measured fitness under osmotic stress via exposure to hypersaline conditions. The fitness of N_e  = 1 lines exhibited a further decline under osmotic stress compared to benign conditions. However, the fitness of larger populations remained indistinguishable from that of the ancestral control. The average effects of deleterious mutations in N_e  = 1 lines were estimated to be 22% for productivity and 14% for survivorship, exceeding values previously detected under benign conditions. Our results suggest that fitness decline is due to large effect mutations that are rapidly removed via selection even in small populations, with implications for conservation practices. Genetic stochasticity may not be as potent and immediate a threat to the persistence of small populations as other demographic and environmental stochastic factors.     

SEXUAL SELECTION CAN REMOVE AN EXPERIMENTALLY INDUCED MUTATION LOAD

Sexual selection is argued to be important for the removal of deleterious mutations, promoting population fitness, accelerating adaptation, and compensating for the two‐fold cost of sex. Here we induced mutations in the dung beetle Onthophagus taurus using ionizing radiation, and tested the efficacy of sexual selection in their removal. Mutations reduced male precopulatory (strength) and postcopulatory (testes mass) sexual traits. Two generations of sexual selection were sufficient to remove mutations that affected male strength, but not testes mass. Induced mutations did not affect female productivity, which was elevated by sexual selection. Our results provide empirical support for the hypothesis that condition‐dependent traits offer a large target for mutational variation, and that sexual selection can purge the genome of deleterious mutations and promote population fitness.     

THE CONTRIBUTION OF NEW MUTATIONS TO GENOTYPE-ENVIRONMENT INTERACTION FOR FITNESS IN DROSOPHILA MELANOGASTER

Many studies have documented the existence of genotype-environment interaction (GEI) for traits closely related to fitness in natural populations. A type of GEI that is commonly observed is changes in the fitness ranking of genetic groups (families, clones, or inbred lines) in different environments. We refer to such changes in ranking as crossing of reaction norms for fitness. A common interpretation of crossing of reaction norms for fitness is that selection favors different alleles in the different environments (i.e., that “trade-offs” exist). If this is the case, selection could maintain genetic variation, and even lead to reproductive isolation between subpopulations using different environments. Even if the same alleles are favored in every environment, however, deleterious mutations that vary in the magnitude of their effect depending on environment could cause reaction norms for fitness to cross. If deleterious mutations with environment-dependent effects are responsible for maintaining much of the variation leading to crossing of reaction norms for fitness in natural populations, it should be possible to observe crossing of reaction norms for fitness among otherwise genetically identical lines bearing newly arisen spontaneous mutations. We examined the contribution of new mutations to GEI for fitness in Drosophila melanogaster. Eighteen lines were derived from a common, highly inbred base stock, and maintained at a population size of 10 pairs for over 200 generations, to allow them to accumulate spontaneous mutations. Because of the small population size of the lines, selection against mildly deleterious mutations should have been relatively ineffective. The lines were tested for productivity (number of surviving adult progeny from a standard number of parents) in five different environmental treatments, comprising different food media, temperatures, and levels of competition. The lines showed highly significant GEI for productivity, owing largely to considerable changes in ranking in the different environments. We conclude that mutations that are deleterious on average, but whose quantitative effects depend on environment, could be responsible for maintaining much of the variation leading to crossing of reaction norms for fitness that has been observed in samples of D. melanogaster from the wild.     

A POPULATION GENETIC THEORY OF CANALIZATION

Canalization is the suppression of phenotypic variation. Depending on the causes of phenotypic variation, one speaks either of genetic or environmental canalization. Genetic canalization describes insensitivity of a character to mutations, and the insensitivity to environmental factors is called environmental canalization. Genetic canalization is of interest because it influences the availability of heritable phenotypic variation to natural selection, and is thus potentially important in determining the pattern of phenotypic evolution. In this paper a number of population genetic models are considered of a quantitative character under stabilizing selection. The main purpose of this study is to define the population genetic conditions and constraints for the evolution of canalization. Environmental canalization is modeled as genotype specific environmental variance. It is shown that stabilizing selection favors genes that decrease environmental variance of quantitative characters. However, the theoretical limit of zero environmental variance has never been observed. Of the many ways to explain this fact, two are addressed by our model. It is shown that a “canalization limit” is reached if canalizing effects of mutations are correlated with direct effects on the same character. This canalization limit is predicted to be independent of the strength of stabilizing selection, which is inconsistent with recent experimental data (Sterns et al. 1995). The second model assumes that the canalizing genes have deleterious pleiotropic effects. If these deleterious effects are of the same magnitude as all the other mutations affecting fitness very strong stabilizing selection is required to allow the evolution of environmental canalization. Genetic canalization is modeled as an influence on the average effect of mutations at a locus of other genes. It is found that the selection for genetic canalization critically depends on the amount of genetic variation present in the population. The more genetic variation, the stronger the selection for canalizing effects. All factors that increase genetic variation favor the evolution of genetic canalization (large population size, high mutation rate, large number of genes). If genetic variation is maintained by mutation-selection balance, strong stabilizing selection can inhibit the evolution of genetic canalization. Strong stabilizing selection eliminates genetic variation to a level where selection for canalization does not work anymore. It is predicted that the most important characters (in terms of fitness) are not necessarily the most canalized ones, if they are under very strong stabilizing selection (k > 0.2V_e). The rate of decrease of mutational variance V_m is found to be less than 10% of the initial V_m. From this result it is concluded that characters with typical mutational variances of about 10^–3 V_e are in a metastable state where further evolution of genetic canalization is too slow to be of importance at a microevolutionary time scale. The implications for the explanation of macroevolutionary patterns are discussed.     

Interaction between directional epistasis and average mutational effects.

We investigate the relationship between the average fitness decay due to single mutations and the strength of epistatic interactions in genetic sequences. We observe that epistatic interactions between mutations are correlated to the average fitness decay, both in RNA secondary structure prediction as well as in digital organisms replicating in silico. This correlation implies that, during adaptation, epistasis and average mutational effect cannot be optimized independently. In experiments with RNA sequences evolving on a neutral network, the selective pressure to decrease the mutational load then leads to a reduction in the amount of sequences with strong antagonistic interactions between deleterious mutations in the population.     

Fitness effects of new mutations in Chlamydomonas reinhardtii across two stress gradients

Most spontaneous mutations affecting fitness are likely to be deleterious, but the strength of selection acting on them might be impacted by environmental stress. Such stress‐dependent selection could expose hidden genetic variation, which in turn might increase the adaptive potential of stressed populations. On the other hand, this variation might represent a genetic load and thus lead to population extinction under stress. Previous studies to determine the link between stress and mutational effects on fitness, however, have produced inconsistent results. Here, we determined the net change in fitness in 29 genotypes of the green algae Chlamydomonas reinhardtii that accumulated mutations in the near absence of selection for approximately 1000 generations across two stress gradients, increasing NaCl and decreasing phosphate. We found mutational effects to be magnified under extremely stressful conditions, but such effects were specific both to the type of stress and to the genetic background. The detection of stress‐dependent fitness effects of mutations depended on accurately scaling relative fitness measures by generation times, thus offering an explanation for the inconsistencies among previous studies.     

Accumulation of Spontaneous Mutations in the Ciliate Tetrahymena thermophila

Knowledge of the rate and fitness effects of mutations is essential for understanding the process of evolution. Mutations are inherently difficult to study because they are rare and are frequently eliminated by natural selection. In the ciliate Tetrahymena thermophila, mutations can accumulate in the germline genome without being exposed to selection. We have conducted a mutation accumulation (MA) experiment in this species. Assuming that all mutations are deleterious and have the same effect, we estimate that the deleterious mutation rate per haploid germline genome per generation is U = 0.0047 (95% credible interval: 0.0015, 0.0125), and that germline mutations decrease fitness by s = 11% when expressed in a homozygous state (95% CI: 4.4%, 27%). We also estimate that deleterious mutations are partially recessive on average (h = 0.26; 95% CI: –0.022, 0.62) and that the rate of lethal mutations is <10% of the deleterious mutation rate. Comparisons between the observed evolutionary responses in the germline and somatic genomes and the results from individual-based simulations of MA suggest that the two genomes have similar mutational parameters. These are the first estimates of the deleterious mutation rate and fitness effects from the eukaryotic supergroup Chromalveolata and are within the range of those of other eukaryotes.     

Measures of Variation at DNA Repeat Loci under a General Stepwise Mutation Model

Polymorphisms at tandem repeat loci are caused by mutations with allele sizes occasionally altered by more than one repeat unit in both forward and backward directions. Such mutational changes may occur with asymmetric probabilities. Therefore, a one-step symmetric stepwise mutation model may not be appropriate for studying the population dynamics at all repeat loci. In this work, we evaluated the expectation and variance of the within-population variance of the allele size distribution in a finite population, and the expected homozygosity at a locus by the coalescence approach under a general stepwise mutation model, where mutational transitions of allele sizes can be arbitrary, including being asymmetric. Under the special cases of symmetric one-step, two-step, and multi-step geometric distributions of mutations, our general results reduce to the corresponding results obtained by earlier investigators. The general results indicate that in a finite population, which has reached a steady state under the (general stepwise) mutation and drift balance, the within-population variance of allele sizes has a simple expectation (i.e., proportional toNν, the product of the mutation rate,ν, and effective population size,N). However, its stochastic variance is a quadratic function of this composite parameter,Nν. Furthermore, this second-order variance does not decay with the number of alleles sampled from a population. Application of this theory to data on allele size distributions in unrelated Caucasians from the CEPH pedigree (obtained from the Genome Data Base) shows that the relationship of the variance and mean of within-population variance of allele sizes at tandem repeat loci, grouped by their chromosomal assignment, has a trend compatible with the theory. However, there is an indication that the second-order variance is generally underestimated. One reason for this departure might be that the CEPH sample may not represent a single homogeneous population that reached equilibrium at all tandem repeat loci.