The rate of mutation and the homozygous and heterozygous mutational effects for competitive viability: a long-term experiment with Drosophila melanogaster

Revisiting Dominance in Population Genetics

Dominance refers to the effect of a heterozygous genotype relative to that of the two homozygous genotypes. The degree of dominance of mutations for fitness can have a profound impact on how deleterious and beneficial mutations change in frequency over time as well as on the patterns of linked neutral genetic variation surrounding such selected alleles. Since dominance is such a fundamental concept, it has received immense attention throughout the history of population genetics. Early work from Fisher, Wright, and Haldane focused on understanding the conceptual basis for why dominance exists. More recent work has attempted to test these theories and conceptual models by estimating dominance effects of mutations. However, estimating dominance coefficients has been notoriously challenging and has only been done in a few species in a limited number of studies. In this review, we first describe some of the early theoretical and conceptual models for understanding the mechanisms for the existence of dominance. Second, we discuss several approaches used to estimate dominance coefficients and summarize estimates of dominance coefficients. We note trends that have been observed across species, types of mutations, and functional categories of genes. By comparing estimates of dominance coefficients for different types of genes, we test several hypotheses for the existence of dominance. Lastly, we discuss how dominance influences the dynamics of beneficial and deleterious mutations in populations and how the degree of dominance of deleterious mutations influences the impact of inbreeding on fitness.

Analysis of genetic dominance in the UK Biobank

Classical statistical genetics theory defines dominance as any deviation from a purely additive, or dosage, effect of a genotype on a trait, which is known as the dominance deviation. Dominance is well documented in plant and animal breeding. Outside of rare monogenic traits, however, evidence in humans is limited. We systematically examined common genetic variation across 1060 traits in a large population cohort (UK Biobank, N = 361,194 samples analyzed) for evidence of dominance effects. We then developed a computationally efficient method to rapidly assess the aggregate contribution of dominance deviations to heritability. Lastly, observing that dominance associations are inherently less correlated between sites at a genomic locus than their additive counterparts, we explored whether they may be leveraged to identify causal variants more confidently.

Obstruction of adaptation in diploids by recessive, strongly deleterious alleles

Recessive deleterious mutations are common, causing many genetic disorders in humans and producing inbreeding depression in the majority of sexually reproducing diploids. The abundance of recessive deleterious mutations in natural populations suggests they are likely to be present on a chromosome when a new adaptive mutation occurs, yet the dynamics of recessive deleterious hitchhikers and their impact on adaptation remains poorly understood. Here we model how a recessive deleterious mutation impacts the fate of a genetically linked dominant beneficial mutation. The frequency trajectory of the adaptive mutation in this case is dramatically altered and results in what we have termed a "staggered sweep." It is named for its three-phased trajectory: (i) Initially, the two linked mutations have a selective advantage while rare and will increase in frequency together, then (ii), at higher frequencies, the recessive hitchhiker is exposed to selection and can cause a balanced state via heterozygote advantage (the staggered phase), and (iii) finally, if recombination unlinks the two mutations, then the beneficial mutation can complete the sweep to fixation. Using both analytics and simulations, we show that strongly deleterious recessive mutations can substantially decrease the probability of fixation for nearby beneficial mutations, thus creating zones in the genome where adaptation is suppressed. These mutations can also significantly prolong the number of generations a beneficial mutation takes to sweep to fixation, and cause the genomic signature of selection to resemble that of soft or partial sweeps. We show that recessive deleterious variation could impact adaptation in humans and Drosophila.

The dominance effect of the adaptive transposable element insertion Bari-Jheh depends on the genetic background

Although adaptive mutations are often considered to be dominant, it has been recently shown that a substantial proportion of adaptive mutations should display heterozygote advantage. In this work, we take advantage of a recently characterized transposable element insertion mediating oxidative stress response in Drosophila melanogaster to test the dominance effect of an adaptive mutation. The comparison of the survival curves of heterozygous and the two corresponding homozygous flies indicated that the dominance effect of Bari-Jheh depends on the genetic background. Both in homozygous and in heterozygous flies, Bari-Jheh was associated with upregulation of Jheh1 (Juvenile Hormone Epoxyde Hydrolase 1) and/or Jheh2 genes. Our results add to the limited number of studies in which the dominance effect of adaptive mutations has been empirically estimated and highlights the complexity of their inheritance.

Fitness landscapes: an alternative theory for the dominance of mutation

Deleterious mutations tend to be recessive. Several theories, notably those of Fisher (based on selection) and Wright (based on metabolism), have been put forward to explain this pattern. Despite a long-lasting debate, the matter remains unresolved. This debate has focused on the average dominance of mutations. However, we also know very little about the distribution of dominance coefficients among mutations, and about its variation across environments. In this article we present a new approach to predicting this distribution. Our approach is based on a phenotypic fitness landscape model. First, we show that under a very broad range of conditions (and environments), the average dominance of mutation of small effects should be approximately one-quarter as long as adaptation of organisms to their environment can be well described by stabilizing selection on an arbitrary set of phenotypic traits. Second, the theory allows predicting the whole distribution of dominance coefficients among mutants. Because it provides quantitative rather than qualitative predictions, this theory can be directly compared to data. We found that its prediction on mean dominance (average dominance close to 0.25) agreed well with the data, based on a meta-analysis of dominance data for mildly deleterious mutations. However, a simple landscape model does not account for the dominance of mutations of large effects and we provide possible extension of the theory for this class of mutations. Because dominance is a central parameter for evolutionary theory, and because these predictions are quantitative, they set the stage for a wide range of applications and further empirical tests.

Frequent beneficial mutations during single-colony serial transfer of Streptococcus pneumoniae

The appearance of new mutations within a population provides the raw material for evolution. The consistent decline in fitness observed in classical mutation accumulation studies has provided support for the long-held view that deleterious mutations are more common than beneficial mutations. Here we present results of a study using a mutation accumulation design with the bacterium Streptococcus pneumoniae in which the fitness of the derived populations increased. This rise in fitness was associated specifically with adaptation to survival during brief stationary phase periods between single-colony population bottlenecks. To understand better the population dynamics behind this unanticipated adaptation, we developed a maximum likelihood model describing the processes of mutation and stationary-phase selection in the context of frequent population bottlenecks. Using this model, we estimate that the rate of beneficial mutations may be as high as 4.8×10⁻⁴ events per genome for each time interval corresponding to the pneumococcal generation time. This rate is several orders of magnitude higher than earlier estimates of beneficial mutation rates in bacteria but supports recent results obtained through the propagation of small populations of Escherichia coli. Our findings indicate that beneficial mutations may be relatively frequent in bacteria and suggest that in S. pneumoniae, which develops natural competence for transformation, a steady supply of such mutations may be available for sampling by recombination.

Beneficial mutations have long been considered extremely rare events and were thought to occur with a frequency of approximately one out of a billion times that a bacterium replicates its genome. Rare beneficial mutations would then be amplified by natural selection from the more frequent background of harmful mutations. Mutation accumulation experiments probe the nature of these spontaneous mutations by monitoring changes in fitness of model organisms propagated in the laboratory through numerous generations under conditions where the effects of selection are minimal. Previous mutation accumulation experiments have shown that organisms under study have declined in fitness as random mutations accrue in their genomes, consistent with a predominance of deleterious mutations. We conducted a mutation accumulation study with the bacterial pathogen S. pneumoniae in which a broad measure of fitness instead rose. We demonstrate that this unexpected adaptation was due to frequent beneficial mutations that were further amplified by selection in stationary-phase bacterial colonies. Together with recent work using E. coli, these results demonstrate that beneficial mutations can be common in bacteria and may contribute to our understanding of the evolution of traits such as antibiotic resistance and virulence.

Inferences about the distribution of dominance drawn from yeast gene knockout data

Data from several thousand knockout mutations in yeast (Saccharomyces cerevisiae) were used to estimate the distribution of dominance coefficients. We propose a new unbiased likelihood approach to measuring dominance coefficients. On average, deleterious mutations are partially recessive, with a mean dominance coefficient ~0.2. Alleles with large homozygous effects are more likely to be more recessive than are alleles of weaker effect. Our approach allows us to quantify, for the first time, the substantial variance and skew in the distribution of dominance coefficients. This heterogeneity is so great that many population genetic processes analyses based on the mean dominance coefficient alone will be in substantial error. These results are applied to the debate about various mechanisms for the evolution of dominance, and we conclude that they are most consistent with models that depend on indirect selection on homeostatic gene expression or on the ability to perform well under periods of high demand for a protein.

Regeneration of the variance of metric traits by spontaneous mutation in a Drosophila population

In the C1 population of Drosophila melanogaster of moderate effective size (≈500), which was genetically invariant in its origin, we studied the regeneration by spontaneous mutation of the genetic variance for two metric traits [abdominal (AB) and sternopleural (ST) bristle number] and that of the concealed mutation load for viability, together with their temporal stability, using alternative selection models based on mutational parameters estimated in the C1 genetic background. During generations 381–485 of mutation accumulation (MA), the additive variances of AB and ST approached the levels observed in standing laboratory populations, fluctuating around their expected equilibrium values under neutrality or under relatively weak causal stabilizing selection. This type of selection was required to simultaneously account for the observed additive variance in our population and for those previously reported in natural and laboratory populations, indicating that most mutations affecting bristle traits would only be subjected to weak selective constraints. Although gene action for bristles was essentially additive, transient situations occurred where inbreeding resulted in a depression of the mean and an increase of the additive variance. This was ascribed to the occasional segregation of mutations of large recessive effects. On the other hand, the observed non-lethal inbreeding depression for viability must be explained by the segregation of alleles of considerable and largely recessive deleterious effects, and the corresponding load concealed in the heterozygous condition was found to be temporally stable, as expected from tighter constraints imposed by natural selection.

The rate of unequal crossing over in the dumpy gene from Drosophila melanogaster

The PIGSFEAST (PF) exon of the Drosophila dumpy gene is undergoing concerted evolution by the process of unequal crossing over. We have developed a long-range PCR-based assay to amplify the approximately 12 kb long exon which contains variable numbers of 303 or 306 nt long repeats in a tandem array. We applied this procedure to mutation accumulation lines of Drosophila melanogaster established by M. Wayne and L. Higgins. Nine new repeat length variants were found in these lines allowing us to measure the rate of unequal crossing over in the PF exon. The rate, which for several reasons is an underestimate, is 7.05 x 10(-4) exchanges per generation.

The dynamics of the roo transposable element in mutation-accumulation lines and segregating populations of Drosophila melanogaster

We estimated the number of copies for the long terminal repeat (LTR) retrotransposable element roo in a set of long-standing Drosophila melanogaster mutation-accumulation full-sib lines and in two large laboratory populations maintained with effective population size approximately 500, all of them derived from the same isogenic origin. Estimates were based on real-time quantitative PCR and in situ hybridization. Considering previous estimates of roo copy numbers obtained at earlier stages of the experiment, the results imply a strong acceleration of the insertion rate in the accumulation lines. The detected acceleration is consistent with a model where only one (maybe a few) of the approximately 70 roo copies in the ancestral isogenic genome was active and each active copy caused new insertions with a relatively high rate ( approximately 10(-2)), with new inserts being active copies themselves. In the two laboratory populations, however, a stabilized copy number or no accelerated insertion was found. Our estimate of the average deleterious viability effects per accumulated insert [E(s) < 0.003] is too small to account for the latter finding, and we discuss the mechanisms that could contain copy number.

The build up of mutation-selection- drift balance in laboratory Drosophila populations

The build up of an equilibrium between mutation, selection, and drift in populations of moderate size is an important evolutionary issue, and can be critical in the conservation of endangered populations. We studied this process in two Drosophila melanogaster populations initially lacking genetic variability (C1 and C2) that were subsequently maintained during 431 or 165 generations with effective population size N(e) approximately 500 (estimated by lethal complementation analysis). Each population originated synchronously to a companion set of full-sib mutation accumulation (MA) lines, C1 and MA1 were derived from an isogenic origin and C2 and MA2 from a single MA1 line at generation 265. The results suggest that both C1 and C2 populations were close to the mutation-selection-drift balance for viability and bristle traits, and are consistent with a 2.5-fold increase of the mutation rate in C2 and MA2. Despite this increase, the average panmictic viability in C2 was only slightly below that of C1, indicating that the expressed loads due to segregating deleterious mutation were small, in agreement with the low deleterious mutation rate (0.015-0.045) previously reported for the MA1 lines. In C1, the nonlethal inbreeding depression rate for viability was 30% of that usually estimated in segregating populations. The genetic variance for bristles regenerated in C1 and C2 was moderately smaller than the average value reported for natural populations, implying that they have accumulated a substantial adaptive potential. In light of neutral and selective predictions, these results suggest that bristle additive variance was predominantly due to segregation of mutations with deleterious effects of the order of 10(-3), and is consistent with relatively weak causal stabilizing selection (V(s) approximately 30).

Hemiclonal reproduction slows down the speed of Muller's ratchet in the hybridogenetic frog Rana esculenta

Rare recombination in otherwise asexually reproducing organisms is known to beneficially influence the fitness in small populations. In most of the investigated organisms, asexual and rare sexual generations with recombination follow each other sequentially. Here we present a case where clonal reproduction and rare recombination occur simultaneously in the same population. The hybridogenetic water frog Rana esculenta (E), a hybrid between R. lessonae (L) and R. ridibunda (R) produces gametes that only contain the unaltered maternal R part of their genome. New generations of R. esculenta usually arise from E x L matings. Intraspecific E x E matings produce mostly inviable offspring, but in rare cases, female R. ridibunda arise from such matings which are capable of recombination. In the absence of conspecific males, these R females have to mate with E males, which results in further R females, or with L males, which produces new E lineages. This indirect mechanism reintroduces recombination into the otherwise clonally transmitted R genomes in R. esculenta populations. In this study, we show through Monte Carlo simulations that, in most cases, it is sufficient that only between 1 % and 10 % of mixed water frog populations consist of R females to prevent or significantly reduce the fixation and accumulation of deleterious mutations.

Increase of the spontaneous mutation rate in a long-term experiment with Drosophila melanogaster

In a previous experiment, the effect of 255 generations of mutation accumulation (MA) on the second chromosome viability of Drosophila melanogaster was studied using 200 full-sib MA1 lines and a large C1 control, both derived from a genetically homogeneous base population. At generation 265, one of those MA1 lines was expanded to start 150 new full-sib MA2 lines and a new C2 large control. After 46 generations, the rate of decline in mean viability in MA2 was approximately 2.5 times that estimated in MA1, while the average degree of dominance of mutations was small and nonsignificant by generation 40 and moderate by generation 80. In parallel, the inbreeding depression rate for viability and the amount of additive variance for two bristle traits in C2 were 2-3 times larger than those in C1. The results are consistent with a mutation rate in the line from which MA2 and C2 were derived about 2.5 times larger than that in MA1. The mean viability of C2 remained roughly similar to that of C1, but the rate of MA2 line extinction increased progressively, leading to mutational collapse, which can be ascribed to accelerated mutation and/or synergy after important deleterious accumulation.

Gene action of new mutations in Arabidopsis thaliana

For a newly arising mutation affecting a trait under selection, its degree of dominance relative to the preexisting allele(s) strongly influences its evolutionary impact. We have estimated dominance parameters for spontaneous mutations in a subset of lines derived from a highly inbred founder of Arabidopsis thaliana by at least 17 generations of mutation accumulation (MA). The labor-intensive nature of the crosses and the anticipated subtlety of effects limited the number of MA lines included in this study to 8. Each MA line was selfed and reciprocally crossed to plants representing the founder genotype, and progeny were assayed in the greenhouse. Significant mutational effects on reproductive fitness included a recessive fitness-enhancing effect in one line and fitness-reducing effects, one additive and the other slightly recessive. Mutations conferring earlier phenology or smaller leaves were significantly recessive. For effects increasing leaf number and reducing height at flowering, additive gene action accounted for the expression of the traits. The sole example of a significantly dominant mutational effect delayed phenology. Our findings of recessive action of a fitness-enhancing mutational effect and additive action of a deleterious effect counter a common expectation of (partial) dominance of alleles that increase fitness, but the frequency of occurrence of such mutations is unknown.

Relaxation of selection with equalization of parental contributions in conservation programs: an experimental test with Drosophila melanogaster

Equalization of parental contributions is one of the most simple and widely recognized methods to maintain genetic diversity in conservation programs, as it halves the rate of increase in inbreeding and genetic drift. It has, however, the negative side effect of implying a reduced intensity of natural selection so that deleterious genes are less efficiently removed from the population with possible negative consequences on the reproductive capacity of the individuals. Theoretical results suggest that the lower fitness resulting from equalization of family sizes relative to that for free contribution schemes is expected to be substantial only for relatively large population sizes and after many generations. We present a long-term experiment with Drosophila melanogaster, comparing the fitness performance of lines maintained with equalization of contributions (EC) and others maintained with no management (NM), allowing for free matings and contributions from parents. Two (five) replicates of size N = 100 (20) individuals of each type of line were maintained for 38 generations. As expected, EC lines retained higher gene diversity and allelic richness for four microsatellite markers and a higher heritability for sternopleural bristle number. Measures of life-history traits, such as egg-to-adult viability, mating success, and global fitness declined with generations, but no significant differences were observed between EC and NM lines. Our results, therefore, provide no evidence to suggest that equalization of family sizes entails a disadvantage on the reproductive capacity of conserved populations in comparison with no management procedures, even after long periods of captivity.

The effect of antagonistic pleiotropy on the estimation of the average coefficient of dominance of deleterious mutations

We investigate the impact of antagonistic pleiotropy on the most widely used methods of estimation of the average coefficient of dominance of deleterious mutations from segregating populations. A proportion of the deleterious mutations affecting a given studied fitness component are assumed to have an advantageous effect on another one, generating overdominance on global fitness. Using diffusion approximations and transition matrix methods, we obtain the distribution of gene frequencies for nonpleiotropic and pleiotropic mutations in populations at the mutation-selection-drift balance. From these distributions we build homozygous and heterozygous chromosomes and assess the behavior of the estimators of dominance. A very small number of deleterious mutations with antagonistic pleiotropy produces substantial increases on the estimate of the average degree of dominance of mutations affecting the fitness component under study. For example, estimates are increased three- to fivefold when 2% of segregating loci are over-dominant for fitness. In contrast, strengthening pleiotropy, where pleiotropic effects are assumed to be also deleterious, has little effect on the estimates of the average degree of dominance, supporting previous results. The antagonistic pleiotropy model considered, applied under mutational parameters described in the literature, produces patterns for the distribution of chromosomal viabilities, levels of genetic variance, and homozygous mutation load generally consistent with those observed empirically for viability in Drosophila melanogaster.

A measure of the within-chromosome synergistic epistasis for Drosophila viability

In order to detect possible synergistic epistasis for viability in Drosophila melanogaster we assayed the relative viability of chromosomes II in: (i) panmixia, (ii) forced total homozygosity, and (iii) homozygosity for, on the average, half of their loci. As these genotypes were constructed using exactly the same set of chromosomes in the three cases, the design allows us to estimate the inbreeding depression rate at two different inbreeding levels in the absence of purging natural selection. Overall, no consistent synergistic epistasis was found. However, there was a small fraction of chromosomes whose severely deleterious effect when homozygous was almost significantly larger than expected from their viability when homozygous for half of their loci. This suggests occasional but important synergistic epistasis, which might confer evolutionary advantage to recombination in tightly linked genomes. Nevertheless, such epistasis is unlikely to be an evolutionary advantage driving the evolution of sexual anisogamous reproduction, as its contribution to overall viability is small when compared with the two-fold cost of anisogamy.

Inferences on the role of insertion in a mutation accumulation experiment with Drosophila melanogaster using RAPDs

The genetic variability for RAPDs band pattern was studied in a set of 157 mutation accumulation (MA) lines of Drosophila melanogaster. These MA lines were derived from the same isogenic base population and subsequently maintained by full-sib mating during 132 generations. The ancestral pattern of the original isogenic base can be unambiguously established as the consensus pattern of the MA lines and, because these lines are expected to be homozygous, dominance for band pattern is not a concern. Only repeatable changes in band pattern were considered. The number of ancestral bands detected implies that nine-nucleotide targets are enough for repeatable PCR amplification. Compared with the ancestral pattern, one MA line lost one band and two MA lines gained a new one. These results can be accounted for by the insertion of transposable elements occurring at a rate 0.07 < i < 0.21 per whole haploid genome and generation. This range is typical for Drosophila and consistent with the previously observed mobility for the roo family, supporting the generality of previous estimates of spontaneous mutation rates for morphological and fitness traits based on these MA lines. The sequence of one of the new bands suggests that the Idefix family is also active in the lines.

Estimates of the genomic mutation rate for detrimental alleles in Drosophila melanogaster

The net rate of mutation to deleterious but nonlethal alleles and the sizes of effects of these mutations are of great significance for many evolutionary questions. Here we describe three replicate experiments in which mutations have been accumulated on chromosome 3 of Drosophila melanogaster by means of single-male backcrosses of heterozygotes for a wild-type third chromosome. Egg-to-adult viability was assayed for nonlethal homozygous chromosomes. The rates of decline in mean and increase in variance (DM and DV, respectively) were estimated. Scaled up to the diploid whole genome, the mean DM for homozygous detrimental mutations over the three experiments was between 0.8 and 1.8%. The corresponding DV estimate was approximately 0.11%. Overall, the results suggest a lower bound estimate of at least 12% for the diploid per genome mutation rate for detrimentals. The upper bound estimates for the mean selection coefficient were between 2 and 10%, depending on the method used. Mutations with selection coefficients of at least a few percent must be the major contributors to the effects detected here and are likely to be caused mostly by transposable element insertions or indels.

Analysis of the estimators of the average coefficient of dominance of deleterious mutations

We investigate the sources of bias that affect the most commonly used methods of estimation of the average degree of dominance (h) of deleterious mutations, focusing on estimates from segregating populations. The main emphasis is on the effect of the finite size of the populations, but other sources of bias are also considered. Using diffusion approximations to the distribution of gene frequencies in finite populations as well as stochastic simulations, we assess the behavior of the estimators obtained from populations at mutation-selection-drift balance under different mutational scenarios and compare averages of h for newly arisen and segregating mutations. Because of genetic drift, the inferences concerning newly arisen mutations based on the mutation-selection balance theory can have substantial upward bias depending upon the distribution of h. In addition, estimates usually refer to h weighted by the homozygous deleterious effect in different ways, so that inferences are complicated when these two variables are negatively correlated. Due to both sources of bias, the widely used regression of heterozygous on homozygous means underestimates the arithmetic mean of h for segregating mutations, in contrast to their repeatedly assumed equality in the literature. We conclude that none of the estimators from segregating populations provides, under general conditions, a useful tool to ascertain the properties of the degree of dominance, either for segregating or for newly arisen deleterious mutations. Direct estimates of the average h from mutation-accumulation experiments are shown to suffer some bias caused by purging selection but, because they do not require assumptions on the causes maintaining segregating variation, they appear to give a more reliable average dominance for newly arisen mutations.

Mutation accumulation in populations of varying size: the distribution of mutational effects for fitness correlates in Caenorhabditis elegans

The consequences of mutation for population-genetic and evolutionary processes depend on the rate and, especially, the frequency distribution of mutational effects on fitness. We sought to approximate the form of the distribution of mutational effects by conducting divergence experiments in which lines of a DNA repair-deficient strain of Caenorhabditis elegans, msh-2, were maintained at a range of population sizes. Assays of these lines conducted in parallel with the ancestral control suggest that the mutational variance is dominated by contributions from highly detrimental mutations. This was evidenced by the ability of all but the smallest population-size treatments to maintain relatively high levels of mean fitness even under the 100-fold increase in mutational pressure caused by knocking out the msh-2 gene. However, we show that the mean fitness decline experienced by larger populations is actually greater than expected on the basis of our estimates of mutational parameters, which could be consistent with the existence of a common class of mutations with small individual effects. Further, comparison of the total mutation rate estimated from direct sequencing of DNA to that detected from phenotypic analyses implies the existence of a large class of evolutionarily relevant mutations with no measurable effect on laboratory fitness.

On the rate and linearity of viability declines in Drosophila mutation-accumulation experiments: genomic mutation rates and synergistic epistasis revisited

High rates of deleterious mutations could severely reduce the fitness of populations, even endangering their persistence; these effects would be mitigated if mutations synergize each others' effects. An experiment by Mukai in the 1960s gave evidence that in Drosophila melanogaster, viability-depressing mutations occur at the surprisingly high rate of around one per zygote and that the mutations interact synergistically. A later experiment by Ohnishi seemed to support the high mutation rate, but gave no evidence for synergistic epistasis. Both of these studies, however, were flawed by the lack of suitable controls for assessing viability declines of the mutation-accumulation (MA) lines. By comparing homozygous viability of the MA lines to simultaneously estimated heterozygous viability and using estimates of the dominance of mutations in the experiments, I estimate the viability declines relative to an appropriate control. This approach yields two unexpected conclusions. First, in Ohnishi's experiment as well as in Mukai's, MA lines showed faster-than-linear declines in viability, indicative of synergistic epistasis. Second, while Mukai's estimate of the genomic mutation rate is supported, that from Ohnishi's experiment is an order of magnitude lower. The different results of the experiments most likely resulted from differences in the starting genotypes; even within Mukai's experiment, a subset of MA lines, which I argue probably resulted from a contamination event, showed much slower viability declines than did the majority of lines. Because different genotypes may show very different mutational behavior, only studies using many founding genotypes can determine the average rate and distribution of effects of mutations relevant to natural populations.

Influence of dominance, leptokurtosis and pleiotropy of deleterious mutations on quantitative genetic variation at mutation-selection balance

In models of maintenance of genetic variance (V (G)) it has often been assumed that mutant alleles act additively. However, experimental data show that the dominance coefficient varies among mutant alleles and those of large effect tend to be recessive. On the basis of empirical knowledge of mutations, a joint-effect model of pleiotropic and real stabilizing selection that includes dominance is constructed and analyzed. It is shown that dominance can dramatically alter the prediction of equilibrium V (G). Analysis indicates that for the situations where mutations are more recessive for fitness than for a quantitative trait, as supported by the available data, the joint-effect model predicts a significantly higher V (G) than does an additive model. Importantly, for what seem to be realistic distributions of mutational effects (i.e., many mutants may not affect the quantitative trait substantially but are likely to affect fitness), the observed high levels of genetic variation in the quantitative trait under strong apparent stabilizing selection can be generated. This investigation supports the hypothesis that most V (G) comes from the alleles nearly neutral for fitness in heterozygotes while apparent stabilizing selection is contributed mainly by the alleles of large effect on the quantitative trait. Thus considerations of dominance coefficients of mutations lend further support to our previous conclusion that mutation-selection balance is a plausible mechanism of the maintenance of the genetic variance in natural populations.

The interaction among evolutionary forces in the pathogenic fungus Mycosphaerella graminicola

The population genetic dynamic of a species is driven by interactions among mutation, migration, drift, mating system, and selection, but it is rare to have sufficient empirical data to estimate values for all of these forces and to allow comparison of the relative magnitudes of these evolutionary forces. We combined data from a mark-release-recapture experiment, extensive population surveys, and computer simulations to evaluate interactions among these evolutionary forces in the pathogenic fungus Mycosphaerella graminicola. The results from these studies showed that, on average, the immigration rate was 0.027, the fraction of outcrossing individuals was 0.035, and the selection coefficient associated with immigrants was 0.106 each generation. We also estimated that effective population sizes for this fungus were larger than 24,000 and the mutation rate for the RFLP markers used in surveys and field experiments was approximately 4 x 10(-5). Computer simulations based on these estimates indicate that, on average, the global population of M. graminicola has reached equilibrium. Population genetic parameters including number of alleles, gene diversity, and population subdivision estimated from the computer simulations were surprisingly close to empirical estimates. Simulations also revealed that random drift is the major evolutionary force decreasing genetic variation in this fungus, followed by natural selection. The major force adding to genetic variation was mutation, followed by gene flow and sexual recombination. Gene flow played the leading role in decreasing population subdivision while natural selection was the major factor increasing population subdivision.

Mutation-selection balance accounting for genetic variation for viability inDrosophila melanogasteras deduced from an inbreeding and artificial selection experiment

We carried out an experiment of inbreeding and upward artificial selection for egg-to-adult viability in a recently captured population of Drosophila melanogaster, as well as computer simulations of the experimental design, in order to obtain information on the nature of genetic variation for this important fitness component. The inbreeding depression was linear with a rate of 0.70 +/- 0.11% of the initial mean per 1% increase in inbreeding coefficient, and the realized heritability was 0.06 +/- 0.07. We compared the empirical observations of inbreeding depression and selection response with computer simulations assuming a balance between the occurrence of partially recessive deleterious mutations and their elimination by selection. Our results suggest that a model assuming mutation-selection balance with realistic mutational parameters can explain the genetic variation for viability in the natural population studied. Several mutational models are incompatible with some observations and can be discarded. Mutational models assuming a low rate of mutations of large average effect and highly recessive gene action, and others assuming a high rate of mutations of small average effect and close to additive gene action, are compatible with all the observations.

On the Rate and Linearity of Viability Declines in Drosophila Mutation-Accumulation Experiments: Genomic Mutation Rates and Synergistic Epistasis Revisited

High rates of deleterious mutations could severely reduce the fitness of populations, even endangering their persistence; these effects would be mitigated if mutations synergize each others’ effects. An experiment by Mukai in the 1960s gave evidence that in Drosophila melanogaster, viability-depressing mutations occur at the surprisingly high rate of around one per zygote and that the mutations interact synergistically. A later experiment by Ohnishi seemed to support the high mutation rate, but gave no evidence for synergistic epistasis. Both of these studies, however, were flawed by the lack of suitable controls for assessing viability declines of the mutation-accumulation (MA) lines. By comparing homozygous viability of the MA lines to simultaneously estimated heterozygous viability and using estimates of the dominance of mutations in the experiments, I estimate the viability declines relative to an appropriate control. This approach yields two unexpected conclusions. First, in Ohnishi’s experiment as well as in Mukai’s, MA lines showed faster-than-linear declines in viability, indicative of synergistic epistasis. Second, while Mukai’s estimate of the genomic mutation rate is supported, that from Ohnishi’s experiment is an order of magnitude lower. The different results of the experiments most likely resulted from differences in the starting genotypes; even within Mukai’s experiment, a subset of MA lines, which I argue probably resulted from a contamination event, showed much slower viability declines than did the majority of lines. Because different genotypes may show very different mutational behavior, only studies using many founding genotypes can determine the average rate and distribution of effects of mutations relevant to natural populations.

Multivariate stabilizing selection and pleiotropy in the maintenance of quantitative genetic variation

We investigate maintenance of quantitative genetic variation at mutation-selection balance for multiple traits. The intrinsic strength of real stabilizing selection on one of these traits denoted the "target trait" and the observed strength of apparent stabilizing selection on the target trait can be quite different: the latter, which is estimable, is much smaller (i.e., implying stronger selection) than the former. Distinguishing them may enable the mutation load to be relaxed when considering multivariate stabilizing selection. It is shown that both correlations among mutational effects and among strengths of real stabilizing selection on the traits are not important unless they are high. The analysis for independent situations thus provides a good approximation to the case where mutant and stabilizing selection effects are correlated. Multivariate stabilizing selection can be regarded as a combination of stabilizing selection on the target trait and the pleiotropic direct selection on fitness that is solely due to the effects of real stabilizing selection on the hidden traits. As the overall fitness approaches a constant value as the number of traits increases, multivariate stabilizing selection can maintain abundant genetic variance only under quite weak selection. The common observations of high polygenic variance and strong stabilizing selection thus imply that if the mutation-selection balance is the true mechanism of maintenance of genetic variation, the apparent stabilizing selection cannot arise solely by real stabilizing selection simultaneously on many metric traits.

The effect of neutral nonadditive gene action on the quantitative index of population divergence

For neutral additive genes, the quantitative index of population divergence (Q(ST)) is equivalent to Wright's fixation index (F(ST)). Thus, divergent or convergent selection is usually invoked, respectively, as a cause of the observed increase (Q(ST) > F(ST)) or decrease (Q(ST) < F(ST)) of Q(ST) from its neutral expectation (Q(ST) = F(ST)). However, neutral nonadditive gene action can mimic the additive expectations under selection. We have studied theoretically the effect of consecutive population bottlenecks on the difference F(ST) - Q(ST) for two neutral biallelic epistatic loci, covering all types of marginal gene action. With simple dominance, Q(ST) < F(ST) for only low to moderate frequencies of the recessive alleles; otherwise, Q(ST) > F(ST). Additional epistasis extends the condition Q(ST) < F(ST) to a broader range of frequencies. Irrespective of the type of nonadditive action, Q(ST) < F(ST) generally implies an increase of both the within-line additive variance after bottlenecks over its ancestral value (V(A)) and the between-line variance over its additive expectation (2F(ST)V(A)). Thus, both the redistribution of the genetic variance after bottlenecks and the F(ST) - Q(ST) value are governed largely by the marginal properties of single loci. The results indicate that the use of the F(ST) - Q(ST) criterion to investigate the relative importance of drift and selection in population differentiation should be restricted to pure additive traits.

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.

Rapid fitness recovery in mutationally degraded lines of Caenorhabditis elegans

Deleterious mutation accumulation has been implicated in many biological phenomena and as a potentially significant threat to human health and the persistence of small populations. The vast majority of mutations with effects on fitness are known to be deleterious in a given environment, and their accumulation results in mean population fitness decline. However, whether populations are capable of recovering from negative effects of prolonged genetic bottlenecks via beneficial or compensatory mutation accumulation has not previously been tested. To address this question, long-term mutation-accumulation lines of the nematode Caenorhabditis elegans, previously propagated as single individuals each generation, were maintained in large population sizes under competitive conditions. Fitness assays of these lines and comparison to parallel mutation-accumulation lines and the ancestral control show that, while the process of fitness restoration was incomplete for some lines, full recovery of mean fitness was achieved in fewer than 80 generations. Several lines of evidence indicate that this fitness restoration was at least partially driven by compensatory mutation accumulation rather than a result of a generic form of laboratory adaptation. This surprising result has broad implications for the influence of the mutational process on many issues in evolutionary and conservation biology.

Dominance of mutations affecting viability in Drosophila melanogaster

There have been several attempts to estimate the average dominance (ratio of heterozygous to homozygous effects) of spontaneous deleterious mutations in Drosophila melanogaster, but these have given inconsistent results. We investigated whether transposable element (TE) insertions have higher average dominance for egg-to-adult viability than do point mutations, a possibility suggested by the types of fitness-depressing effects that TEs are believed to have. If so, then variation in dominance estimates among strains and crosses would be expected as a consequence of variation in TE activity. As a first test, we estimated the average dominance of all mutations and of copia insertions in a set of lines that had accumulated spontaneous mutations for 33 generations. A traditional regression method gave a dominance estimate for all mutations of 0.17, whereas average dominance of copia insertions was 0.51; the difference between these two estimates approached significance (P = 0.08). As a second test, we reanalyzed Ohnishi 1974 data on dominance of spontaneous and EMS-induced mutations. Because a considerable fraction of spontaneous mutations are caused by TE insertions, whereas EMS induces mainly point mutations, we predicted that average dominance would decline with increasing EMS concentration. This pattern was observed, but again fell short of formal significance (P = 0.07). Taken together, however, the two results give modest support for the hypothesis that TE insertions have greater average dominance in their viability effects than do point mutations, possibly as a result of deleterious effects of expression of TE-encoded genes.

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.

Joint Effects of Pleiotropic Selection and Stabilizing Selection on the Maintenance of Quantitative Genetic Variation at Mutation-Selection Balance

In quantitative genetics, there are two basic “conflicting” observations: abundant polygenic variation and strong stabilizing selection that should rapidly deplete that variation. This conflict, although having attracted much theoretical attention, still stands open. Two classes of model have been proposed: real stabilizing selection directly on the metric trait under study and apparent stabilizing selection caused solely by the deleterious pleiotropic side effects of mutations on fitness. Here these models are combined and the total stabilizing selection observed is assumed to derive simultaneously through these two different mechanisms. Mutations have effects on a metric trait and on fitness, and both effects vary continuously. The genetic variance (VG) and the observed strength of total stabilizing selection (Vs,t) are analyzed with a rare-alleles model. Both kinds of selection reduce VG but their roles in depleting it are not independent: The magnitude of pleiotropic selection depends on real stabilizing selection and such dependence is subject to the shape of the distributions of mutational effects. The genetic variation maintained thus depends on the kurtosis as well as the variance of mutational effects: All else being equal, VG increases with increasing leptokurtosis of mutational effects on fitness, while for a given distribution of mutational effects on fitness, VG decreases with increasing leptokurtosis of mutational effects on the trait. The VG and Vs,t are determined primarily by real stabilizing selection while pleiotropic effects, which can be large, have only a limited impact. This finding provides some promise that a high heritability can be explained under strong total stabilizing selection for what are regarded as typical values of mutation and selection parameters.

Environment dependence of mutational parameters for viability in Drosophila melanogaster

The genomic rate of mildly deleterious mutations (U) figures prominently in much evolutionary and ecological theory. In Drosophila melanogaster, estimates of U have varied widely, from <0.1 to nearly 1 per zygote. The source of this variation is unknown, but could include differences in the conditions used for assaying fitness traits. We examined how assay conditions affect estimates of the rates and effects of viability-depressing mutations in two sets of lines with accumulated spontaneous mutations on the second chromosome. In each set, the among-line variance in egg-to-adult viability was significantly greater when viability was assayed using a high parental density than when it was assayed using a low density. In contrast, the proportional decline in viability due to new mutations did not differ between densities. Two other manipulations, lowering the temperature and adding ethanol to the medium, had no significant effects on either the mean decline or among-line variance. Cross-environment genetic correlations in viability were generally close to one, implying that most mutations reduced viability in all environments. Using data from the low-density, lower-bound estimates of U approached the classic, high values of Mukai and Ohnishi; at the high density, U estimates were similar to recently reported low values. The difference in estimated mutation rates, taken at face value, would imply that many mutations affected fitness at low density but not at high density, but this is shown to be incompatible with the observed high cross-environment correlations. Possible reasons for this discrepancy are discussed. Regardless of the interpretation, the results show that assay conditions can have a large effect on estimates of mutational parameters for fitness traits.

Accumulation of deleterious mutations: additional Drosophila melanogaster estimates and a simulation of the effects of selection

We report an assay of egg-to-adult viability in full-sibling mutation accumulation (MA) lines derived from a completely homozygous population of Drosophila melanogaster and maintained for 210 generations. A simultaneous evaluation was also made of a large population derived from the same origin and maintained as a control for the same period. We also present computer simulations to explore the possible decline in viability of the control population due to mutation accumulation and the possible effect of selection within and between MA lines. For this purpose, we used two mutational models independent from the data analyzed and based on radically different assumptions. The first model implies a large number of mutations of small effect, whereas the second implies a much smaller number of mutations with much larger effects. The observed rate of decline in mean viability was very small but significant (0.077%). The rate of increase in among line variance (0.189 x 10(-3)) was similar to those obtained previously in the same lines. The simulation results indicated that a model of many mutations of small effect is incompatible with the evolution of the mean viability of the control and MA lines over generations, the distribution of line means after 210 generations of mutation accumulation, and the pattern of line extinction over generations. Basically, this model predicted a large drop in viability, both in the control and particularly the MA lines, that is not observed empirically. It also predicted a rate of line extinction too low in the early generations and too high in the later ones. In contrast, the model based on few mutations of large effect was generally consistent with all the observations.

Pleiotropic model of maintenance of quantitative genetic variation at mutation-selection balance

A pleiotropic model of maintenance of quantitative genetic variation at mutation-selection balance is investigated. Mutations have effects on a metric trait and deleterious effects on fitness, for which a bivariate gamma distribution is assumed. Equations for calculating the strength of apparent stabilizing selection (V(s)) and the genetic variance maintained in segregating populations (V(G)) were derived. A large population can hold a high genetic variance but the apparent stabilizing selection may or may not be relatively strong, depending on other properties such as the distribution of mutation effects. If the distribution of mutation effects on fitness is continuous such that there are few nearly neutral mutants, or a minimum fitness effect is assumed if most mutations are nearly neutral, V(G) increases to an asymptote as the population size increases. Both V(G) and V(s) are strongly affected by the shape of the distribution of mutation effects. Compared with mutants of equal effect, allowing their effects on fitness to vary across loci can produce a much higher V(G) but also a high V(s) (V(s) in phenotypic standard deviation units, which is always larger than the ratio V(P)/V(m)), implying weak apparent stabilizing selection. If the mutational variance V(m) is approximately 10(-3)V(e) (V(e), environmental variance), the model can explain typical values of heritability and also apparent stabilizing selection, provided the latter is quite weak as suggested by a recent review.

A comprehensive model of mutations affecting fitness and inferences for Arabidopsis thaliana

As the ultimate source of genetic variation, spontaneous mutation is essential to evolutionary change. Theoretical studies over several decades have revealed the dependence of evolutionary consequences of mutation on specific mutational properties, including genomic mutation rates, U, and the effects of newly arising mutations on individual fitness, s. The recent resurgence of empirical effort to infer these properties for diverse organisms has not achieved consensus. Estimates, which have been obtained by methods that assume mutations are unidirectional in their effects on fitness, are imprecise. Both because a general approach must allow for occurrence of fitness-enhancing mutations, even if these are rare, and because recent evidence demands it, we present a new method for inferring mutational parameters. For the distribution of mutational effects, we retain Keightley's assumption of the gamma distribution, to take advantage of the flexibility of its shape. Because the conventional gamma is one sided, restricting it to unidirectional effects, we include an additional parameter, rho, as an amount it is displaced from zero. Estimation is accomplished by Markov chain Monte Carlo maximum likelihood. Through a limited set of simulations, we verify the accuracy of this approach. We apply it to analyze data on two reproductive fitness components from a 17-generation mutation-accumulation study of a Columbia accession of Arabidopsis thaliana in which 40 lines sampled in three generations were assayed simultaneously. For these traits, U approximately/= 0.1-0.2, with distributions of mutational effects broadly spanning zero, such that roughly half the mutations reduce reproductive fitness. One evolutionary consequence of these results is lower extinction risks of small populations of A. thaliana than expected from the process of mutational meltdown. A comprehensive view of the evolutionary consequences of mutation will depend on quantitatively accounting for fitness-enhancing, as well as fitness-reducing, mutations.