EMS-induced polygenic mutation rates for nine quantitative characters in Drosophila melanogaster

Mapping multiple Quantitative Trait Loci by Bayesian classification

We developed a classification approach to multiple quantitative trait loci (QTL) mapping built upon a Bayesian framework that incorporates the important prior information that most genotypic markers are not cotransmitted with a QTL or their QTL effects are negligible. The genetic effect of each marker is modeled using a three-component mixture prior with a class for markers having negligible effects and separate classes for markers having positive or negative effects on the trait. The posterior probability of a marker's classification provides a natural statistic for evaluating credibility of identified QTL. This approach performs well, especially with a large number of markers but a relatively small sample size. A heat map to visualize the results is proposed so as to allow investigators to be more or less conservative when identifying QTL. We validated the method using a well-characterized data set for barley heading values from the North American Barley Genome Mapping Project. Application of the method to a new data set revealed sex-specific QTL underlying differences in glucose-6-phosphate dehydrogenase enzyme activity between two Drosophila species. A simulation study demonstrated the power of this approach across levels of trait heritability and when marker data were sparse.

Modularity and the cost of complexity

In this work we consider the geometrical model of R. A. Fisher, in which individuals are characterized by a number of phenotypic characters under optimizing selection. Recent work on this model by H. A. Orr has demonstrated that as the number of characters increases, there is a significant reduction in the rate of adaptation. Orr has dubbed this a "cost of complexity." Although there is little evidence as to whether such a cost applies in the natural world, we suggest that the prediction is surprising, at least naively. With this in mind, we examine the robustness of Orr's prediction by modifiying the model in various ways that might reduce or remove the cost. In particular, we explore the suggestion that modular pleiotropy, in which mutations affect only a subset of the traits, could play an important role. We conclude that although modifications of the model can mitigate the cost to a limited extent, Orr's finding is robust.

The anomalous effects of biased mutation

A model is presented in which alleles at a number of loci combine to influence the value of a quantitative trait that is subject to stabilizing selection. Mutations can occur to alleles at the loci under consideration. Some of these mutations will tend to increase the value of the trait, while others will tend to decrease it. In contrast to most previous models, we allow the mean effect of mutations to be nonzero. This means that, on average, mutations can have a bias, such that they tend to either increase or decrease the value of the trait. We find, unsurprisingly, that biased mutation moves the equilibrium mean value of the quantitative trait in the direction of the bias. What is more surprising is the behavior of the deviation of the equilibrium mean value of the trait from its optimal value. This has a nonmonotonic dependence on the degree of bias, so that increasing the degree of bias can actually bring the mean phenotype closer to the optimal phenotype. Furthermore, there is a definite maximum to the extent to which biased mutation can cause a difference between the mean phenotype and the optimum. For plausible parameter values, this maximum-possible difference is small. Typically, quantitative-genetics models assume an unconstrained model of mutation, where the expected difference in effect between a parental allele and a mutant allele is independent of the current state of the parental allele. Our results show that models of this sort can easily lead to biologically implausible consequences when mutations are biased. In particular, unconstrained mutation typically leads to a continual increase or decrease in the mean allelic effects at all trait-controlling loci. Thus at each of these loci, the mean allelic effect eventually becomes extreme. This suggests that some of the models of mutation most commonly used in quantitative genetics should be modified so as to introduce genetic constraints.

Testing for epistasis between deleterious mutations in a parasitoid wasp

Determining the way in which deleterious mutations interact to effect fitness is crucial to numerous areas in evolutionary biology. For example, if each additional mutation leads to a greater decrease in log fitness than the last, termed synergistic epistasis, then sex and recombination provide an advantage because they enable deleterious mutations to be eliminated more efficiently. However, there is a severe shortage of relevant empirical data, especially of the form that can help test mutational explanations for the widespread occurrence of sex. Here, we test for epistasis in the parasitic wasp Nasonia vitripennis, examining the fitness consequences of chemically induced deleterious mutations. We examine two components of fitness, both of which are thought to be important in natural populations of parasitic wasps: longevity and egg production. Our results show synergistic epistasis for longevity, but not for egg production.

Comparing analysis methods for mutation-accumulation data: a simulation study

We simulated single-generation data for a fitness trait in mutation-accumulation (MA) experiments, and we compared three methods of analysis. Bateman-Mukai (BM) and maximum likelihood (ML) need information on both the MA lines and control lines, while minimum distance (MD) can be applied with or without the control. Both MD and ML assume gamma-distributed mutational effects. ML estimates of the rate of deleterious mutation had larger mean square error (MSE) than MD or BM had due to large outliers. MD estimates obtained by ignoring the mean decline observed from comparison to a control are often better than those obtained using that information. When effects are simulated using the gamma distribution, reducing the precision with which the trait is assayed increases the probability of obtaining no ML or MD estimates but causes no appreciable increase of the MSE. When the residual errors for the means of the simulated lines are sampled from the empirical distribution in a MA experiment, instead of from a normal one, the MSEs of BM, ML, and MD are practically unaffected. When the simulated gamma distribution accounts for a high rate of mild deleterious mutation, BM detects only approximately 30% of the true deleterious mutation rate, while MD or ML detects substantially larger fractions. To test the robustness of the methods, we also added a high rate of common contaminant mutations with constant mild deleterious effect to a low rate of mutations with gamma-distributed deleterious effects and moderate average. In that case, BM detects roughly the same fraction as before, regardless of the precision of the assay, while ML fails to provide estimates. However, MD estimates are obtained by ignoring the control information, detecting approximately 70% of the total mutation rate when the mean of the lines is assayed with good precision, but only 15% for low-precision assays. Contaminant mutations with only tiny deleterious effects could not be detected with acceptable accuracy by any of the above methods.

Toward a realistic model of mutations affecting fitness

Analysis of a recent mutation accumulation (MA) experiment has led to the suggestion that as many as one-half of spontaneous mutations in Arabidopsis are advantageous for fitness. We evaluate this in the light of data from other MA experiments, along with molecular evidence, that suggest the vast majority of new mutations are deleterious.

Spontaneous mutational variation for body size in Caenorhabditis elegans

We measured the impact of new mutations on genetic variation for body size in two independent sets of C. elegans spontaneous mutation-accumulation (MA) lines, derived from the N2 strain, that had been maintained by selfing for 60 or 152 generations. The two sets of lines gave broadly consistent results. The change of among-line genetic variation between cryopreserved controls and the MA lines implied that broad sense heritability increased by 0.4% per generation. Overall, MA reduced mean body size by approximately 0.1% per generation. The genome-wide rate for mutations with detectable effects on size was estimated to be approximately 0.0025 per haploid genome per generation, and their mean effects were approximately 20%. The proportion of mutations that increase body size was estimated by maximum likelihood to be no more than 20%, suggesting that the amount of mutational variation available for selection for increased size could be quite small. This hypothesis was supported by an artificial selection experiment on adult body size, started from a single highly inbred N2 individual. We observed a strongly asymmetrical response to selection of a magnitude consistent with the input of mutational variance observed in the MA experiment.

Nonequivalent Loci and the distribution of mutant effects

It has been observed repeatedly that the distribution of new mutations of a quantitative trait has a kurtosis (a statistical measure of the distribution's shape) that is systematically larger than that of a normal distribution. Here we suggest that rather than being a property of individual loci that control the trait, the enhanced kurtosis is highly likely to be an emergent property that arises directly from the loci being mutationally nonequivalent. We present a method of incorporating nonequivalent loci into quantitative genetic modeling and give an approximate relation between the kurtosis of the mutant distribution and the degree of mutational nonequivalence of loci. We go on to ask whether incorporating the experimentally observed kurtosis through nonequivalent loci, rather than at locus level, affects any biologically important conclusions of quantitative genetic modeling. Concentrating on the maintenance of quantitative genetic variation by mutation-selection balance, we conclude that typically nonequivalent loci yield a genetic variance that is of order 10% smaller than that obtained from the previous approaches. For large populations, when the kurtosis is large, the genetic variance may be <50% of the result of equivalent loci, with Gaussian distributions of mutant effects.

Whole-genome effects of ethyl methanesulfonate-induced mutation on nine quantitative traits in outbred Drosophila melanogaster

We induced mutations in Drosophila melanogaster males by treating them with 21.2 mm ethyl methanesulfonate (EMS). Nine quantitative traits (developmental time, viability, fecundity, longevity, metabolic rate, motility, body weight, and abdominal and sternopleural bristle numbers) were measured in outbred heterozygous F3 (viability) or F2 (all other traits) offspring from the treated males. The mean values of the first four traits, which are all directly related to the life history, were substantially affected by EMS mutagenesis: the developmental time increased while viability, fecundity, and longevity declined. In contrast, the mean values of the other five traits were not significantly affected. Rates of recessive X-linked lethals and of recessive mutations at several loci affecting eye color imply that our EMS treatment was equivalent to approximately 100 generations of spontaneous mutation. If so, our data imply that one generation of spontaneous mutation increases the developmental time by 0.09% at 20 degrees and by 0.04% at 25 degrees, and reduces viability under harsh conditions, fecundity, and longevity by 1.35, 0.21, and 0.08%, respectively. Comparison of flies with none, one, and two grandfathers (or greatgrandfathers, in the case of viability) treated with EMS did not reveal any significant epistasis among the induced mutations.

A test for epistasis among induced mutations in Caenorhabditis elegans

Synergistic epistasis, in which deleterious mutations tend to magnify each other's effects, is a necessary component of the mutational deterministic hypothesis for the maintenance of sexual production. We tested for epistasis for life-history traits in the soil nematode Caenorhabditis elegans by inducing mutations in two genetic backgrounds: a wild-type strain and a set of genetically loaded lines that contain large numbers of independent mildly detrimental mutations. There was no significant difference between the effect of new mutations on the wild-type background and the genetically loaded background for four out of five fitness correlates. In these four cases, the maximum level of epistasis compatible with the data was very low. The fifth trait, late productivity, is not likely to be an important component of fitness. This suggests either that specific environmental conditions are required to cause epistasis or that synergistic epistasis is not a general phenomenon. We also suggest a new mechanism by which deleterious mutations may provide an advantage to sexual reproduction under low selection coefficients.

Properties of ethylmethane sulfonate-induced mutations affecting life-history traits in Caenorhabditis elegans and inferences about bivariate distributions of mutation effects

The homozygous effects of ethylmethane sulfonate (EMS)-induced mutations in Caenorhabditis elegans are compared across life-history traits. Mutagenesis has a greater effect on early than late reproductive output, since EMS-induced mutations tend to cause delayed reproduction. Mutagenesis changes the mean and variance of longevity much less than reproductive output traits. Mutations that increase total or early productivity are not detected, but the net effect of mutations is to increase and decrease late productivity to approximately equal extents. Although most mutations decrease longevity, a mutant line with increased longevity was found. A flattening of mortality curves with age is noted, particularly in EMS lines. We infer that less than one-tenth of mutations that have fitness effects in natural conditions are detected in the laboratory, and such mutations have moderately large effects ( approximately 20% of the mean). Mutational correlations for life-history traits are strong and positive. Correlations between early or late productivity and longevity are of similar magnitude. We develop a maximum-likelihood procedure to infer bivariate distributions of mutation effects. We show that strong mutation-induced genetic correlations do not necessarily imply strong directional correlations between mutational effects, since correlation is also generated by lines carrying different numbers of mutations.

The fitness effects of spontaneous mutations in Caenorhabditis elegans

Spontaneous mutation to mildly deleterious alleles has emerged as a potentially unifying component of a variety of observations in evolutionary genetics and molecular evolution. However, the biological significance of hypotheses based on mildly deleterious mutation depends critically on the rate at which new mutations arise and on their average effects. A long-term mutation-accumulation experiment with replicate lines of the nematode Caenorhabditis elegans maintained by single-progeny descent indicates that recurrent spontaneous mutation causes approximately 0.1% decline in fitness per generation, which is about an order of magnitude less than that suggested by previous studies with Drosophila. Two rather different approaches, Bateman-Mukai and maximum likelihood, suggest that this observation, along with the observed rate of increase in the variance of fitness among lines, is consistent with a genomic deleterious mutation rate for fitness of approximately 0.03 per generation and with an average homozygous effect of approximately 12%. The distribution of mutational effects for fitness appears to have a relatively low coefficient of variation, being no more extreme than expected for a negative exponential, and for one composite fitness measure (total progeny production) approaches constancy of effects. These results are derived from assays in a benign environment. At stressful temperatures, estimates of the genomic deleterious mutation rate (for genes expressed at such temperatures) is sixfold lower, whereas those for the average homozygous effect is approximately eightfold higher. Our results are reasonably compatible with existing estimates for flies, when one considers the differences between these species in the number of germ-line cell divisions per generation and the magnitude of transposable element activity.

High frequency of cryptic deleterious mutations in Caenorhabditis elegans

Deleterious mutations with very small phenotypic effects could be important for several evolutionary phenomena, but the extent of their contribution has been unknown. Fitness effects of induced mutations in lines of Caenorhabditis elegans were measured using a system for which the number of deleterious point mutations in the DNA can be estimated. In fitness assays, only about 4 percent of the deleterious mutations fixed in each line were detectable. The remaining 96 percent, though cryptic, are significant for mutation load and, potentially, for the evolution of sex.

New estimates of the rates and effects of mildly deleterious mutation in Drosophila melanogaster

The genomic rate and distribution of effects of deleterious mutations are important parameters in evolutionary theory. The most detailed information comes from the work of Mukai and Ohnishi, who allowed mutations to accumulate on Drosophila melanogaster second chromosomes, shielded from selection and recombination by being maintained heterozygous in males. Averaged over studies, the estimated rate of nonlethal viability mutations per second chromosome per generation under an equal-effects model, UBM, was 0. 12, suggesting a high genomic mutation rate. We have performed a mutation-accumulation experiment similar to those of Mukai and Ohnishi, except that three large homozygous control populations were maintained. Egg-to-adult viability of 72 nonlethal mutation-accumulation (MA) lines and the controls was assayed after 27-33 generations of mutation accumulation. The rate of decline in mean viability was significantly lower than observed by Mukai, and the rate of increase in among-line variance was significantly higher. Our UBM estimate of 0.02 is much lower than the previous estimates. Our results suggest that the rate of mutations that detectably reduce viability may not be much greater than the lethal mutation rate (0.01 in these lines), but the results also are consistent with models that include many mutations with very small effects.

Inference of genome-wide mutation rates and distributions of mutation effects for fitness traits: a simulation study

The properties and limitations of maximum likelihood (ML) inference of genome-wide mutation rates (U) and parameters of distributions of mutation effects are investigated. Mutation parameters are estimated from simulated experiments in which mutations randomly accumulate in inbred lines. ML produces more accurate estimates than the procedure of Bateman and Mukai and is more robust if the data do not conform to the model assumed. Unbiased ML estimates of the mutation effects distribution parameters can be obtained if a value for U can be assumed, but if U is estimated simultaneously with the distribution parameters, likelihood may increase monotonically as a function of U. If the distribution of mutation effects is leptokurtic, the number of mutation events per line is large, or if genotypic values are poorly estimated, only a lower limit for U, an upper limit for the mean mutation effect, and a lower limit for the kurtosis of the distribution can be given. It is argued that such lower (upper) limits are appropriate minima (maxima). Estimates of the mean mutational effect are unbiased but may convey little about the properties of the distribution if it is leptokurtic.

Bottleneck effect on genetic variance. A theoretical investigation of the role of dominance

The phenomenon that the genetic variance of fitness components increase following a bottleneck or inbreeding is supported by a growing number of experiments and is explained theoretically by either dominance or epistasis. In this article, diffusion approximations under the infinite sites model are used to quantify the effect of dominance, using data on viability in Drosophila melanogaster. The model is based on mutation parameters from mutation accumulation experiments involving balancer chromosomes (set I) or inbred lines (set II). In essence, set I assumes many mutations of small effect, whereas set II assumes fewer mutations of large effect. Compared to empirical estimates from large outbred populations, set I predicts reasonable genetic variances but too low mean viability. In contrast, set II predicts a reasonable mean viability but a low genetic variance. Both sets of parameters predict the changes in mean viability (depression), additive variance, between-line variance and heritability following bottlenecks generally compatible with empirical results, and these changes are mainly caused by lethals and deleterious mutants of large effect. This article suggests that dominance is the main cause for increased genetic variances for fitness components and fitness-related traits after bottlenecks observed in various experiments.

Testing for epistasis between deleterious mutations

Determining the way in which deleterious mutations interact in their effects on fitness is crucial to numerous areas in population genetics and evolutionary biology. For example, if each additional mutation leads to a greater decrease in log fitness than the last (synergistic epistasis), then the evolution of sex and recombination may be favored to facilitate the elimination of deleterious mutations. However, there is a severe shortage of relevant data. Three relatively simple experimental methods to test for epistasis between deleterious mutations in haploid species have recently been proposed. These methods involve crossing individuals and examining the mean and/or skew in log fitness of the offspring and parents. The main aim of this paper is to formalize these methods, and determine the most effective way in which tests for epistasis could be carried out. We show that only one of these methods is likely to give useful results: crossing individuals that have very different numbers of deleterious mutations, and comparing the mean log fitness of the parents with that of their offspring. We also reconsider experimental data collected on Chlamydomonas moewussi using two of the three methods. Finally, we suggest how the test could be applied to diploid species.