Apparent directional selection by biased pleiotropic mutation

Pleiotropic effects of deleterious mutations are considered to be among the factors responsible for genetic constraints on evolution by long-term directional selection acting on a quantitative trait. If pleiotropic phenotypic effects are biased in a particular direction, mutations generate apparent directional selection, which refers to the covariance between fitness and the trait owing to a linear association between the number of mutations possessed by individuals and the genotypic values of the trait. The present analysis has shown how the equilibrium mean value of the trait is determined by a balance between directional selection and biased pleiotropic mutations. Assuming that genes act additively both on the trait and on fitness, the total variance-standardized directional selection gradient was decomposed into apparent and true components. Experimental data on mutation bias from the bristle traits of Drosophila and life history traits of Daphnia suggest that apparent selection explains a small but significant fraction of directional selection pressure that is observed in nature; the data suggest that changes induced in a trait by biased pleiotropic mutation (i.e., by apparent directional selection) are easily compensated for by (true) directional selection.     

A finite locus effect diffusion model for the evolution of a quantitative trait

A diffusion model is constructed for the joint distribution of absolute locus effect sizes and allele frequencies for loci contributing to an additive quantitative trait under selection in a haploid, panmictic population. The model is designed to approximate a discrete model exactly in the limit as both population size and the number of loci affecting the trait tend to infinity. For the case when all loci have the same absolute effect size, formal multiple-timescale asymptotics are used to predict the long-time response of the population trait mean to selection. For the case where loci can take on either of two distinct effect sizes, not necessarily with equal probability, numerical solutions of the system indicate that response to selection of a quantitative trait is insensitive to the variability of the distribution of effect sizes when mutation is negligible.     

Clines in polygenic traits

This article outlines theoretical models of clines in additive polygenic traits, which are maintained by stabilizing selection towards a spatially varying optimum. Clines in the trait mean can be accurately predicted, given knowledge of the genetic variance. However, predicting the variance is difficult, because it depends on genetic details. Changes in genetic variance arise from changes in allele frequency, and in linkage disequilibria. Allele frequency changes dominate when selection is weak relative to recombination, and when there are a moderate number of loci. With a continuum of alleles, gene flow inflates the genetic variance in the same way as a source of mutations of small effect. The variance can be approximated by assuming a Gaussian distribution of allelic effects; with a sufficiently steep cline, this is accurate even when mutation and selection alone are better described by the 'House of Cards' approximation. With just two alleles at each locus, the phenotype changes in a similar way: the mean remains close to the optimum, while the variance changes more slowly, and over a wider region. However, there may be substantial cryptic divergence at the underlying loci. With strong selection and many loci, linkage disequilibria are the main cause of changes in genetic variance. Even for strong selection, the infinitesimal model can be closely approximated by assuming a Gaussian distribution of breeding values. Linkage disequilibria can generate a substantial increase in genetic variance, which is concentrated at sharp gradients in trait means.     

Mutation Patterns at Dinucleotide Microsatellite Loci in Humans

Microsatellites are a major type of molecular markers in genetics studies. Their mutational dynamics are not clear. We investigated the patterns and characteristics of 97 mutation events unambiguously identified, from 53 multigenerational pedigrees with 630 subjects, at 362 autosomal dinucleotide microsatellite loci. A size-dependent mutation bias (in which long alleles are biased toward contraction, whereas short alleles are biased toward expansion) is observed. There is a statistically significant negative relationship between the magnitude (repeat numbers changed during mutation) and direction (contraction or expansion) of mutations and standardized allele size. Contrasting with earlier findings in humans, most mutation events (63%) in our study are multistep events that involve changes of more than one repeat unit. There was no correlation between mutation rate and recombination rate. Our data indicate that mutational dynamics at microsatellite loci are more complicated than the generalized stepwise mutation models.     

Allelic mapping bias in RNA-sequencing is not a major confounder in eQTL studies

Background

RNA sequencing (RNA-seq) is the current gold-standard method to quantify gene expression for expression quantitative trait locus (eQTL) studies. However, a potential caveat in these studies is that RNA-seq reads carrying the non-reference allele of variant loci can have lower probability to map correctly to the reference genome, which could bias gene quantifications and cause false positive eQTL associations. In this study, we analyze the effect of this allelic mapping bias in eQTL discovery.

Results

We simulate RNA-seq read mapping over 9.5 M common SNPs and indels, with 15.6% of variants showing biased mapping rate for reference versus non-reference reads. However, removing potentially biased RNA-seq reads from an eQTL dataset of 185 individuals has a very small effect on gene and exon quantifications and eQTL discovery. We detect only a handful of likely false positive eQTLs, and overall eQTL SNPs show no significant enrichment for high mapping bias.

Conclusion

Our results suggest that RNA-seq quantifications are generally robust against allelic mapping bias, and that this does not have a severe effect on eQTL discovery. Nevertheless, we provide our catalog of putatively biased loci to allow better controlling for mapping bias to obtain more accurate results in future RNA-seq studies.

Electronic supplementary material

The online version of this article (doi:10.1186/s13059-014-0467-2) contains supplementary material, which is available to authorized users.     

Estimation of the upper limit of the mutation rate and mean heterozygous effect of deleterious mutations

Deng et al. have recently proposed that estimates of an upper limit to the rate of spontaneous mutations and their average heterozygous effect can be obtained from the mean and variance of a given fitness trait in naturally segregating populations, provided that allele frequencies are maintained at the balance between mutation and selection. Using simulations they show that this estimation method generally has little bias and is very robust to violations of the mutation-selection balance assumption. Here I show that the particular parameters and models used in these simulations generally reduce the amount of bias that can occur with this estimation method. In particular, the assumption of a large mutation rate in the simulations always implies a low bias of estimates. In addition, the specific model of overdominance used to check the violation of the mutation-selection balance assumption is such that there is not a dramatic decline in mean fitness from overdominant mutations, again implying a low bias of estimates. The assumption of lower mutation rates and/or other models of balancing selection may imply considerably larger biases of the estimates, making the reliability of the proposed method highly questionable.     

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.     

A population genetics model for multiple quantitative traits exhibiting pleiotropy and epistasis

We study a population genetics model of an organism with a genome of L(tot)loci that determine the values of T quantitative traits. Each trait is controlled by a subset of L loci assigned randomly from the genome. There is an optimum value for each trait, and stabilizing selection acts on the phenotype as a whole to maintain actual trait values close to their optima. The model contains pleiotropic effects (loci can affect more than one trait) and epistasis in fitness. We use adaptive walk simulations to find high-fitness genotypes and to study the way these genotypes are distributed in sequence space. We then simulate the evolution of haploid and diploid populations on these fitness landscapes and show that the genotypes of populations are able to drift through sequence space despite stabilizing selection on the phenotype. We study the way the rate of drift and the extent of the accessible region of sequence space is affected by mutation rate, selection strength, population size, recombination rate, and the parameters L and T that control the landscape shape. There are three regimes of the model. If LTL(tot), there are many small peaks that can be spread over a wide region of sequence space. Compensatory neutral mutations are important in the population dynamics in this case.     

Simultaneous estimation of all the parameters of a stepwise mutation model.

Minisatellite and microsatellite are short tandemly repetitive sequences dispersed in eukaryotic genomes, many of which are highly polymorphic due to copy number variation of the repeats. Because mutation changes copy numbers of the repeat sequences in a generalized stepwise fashion, stepwise mutation models are widely used for studying the dynamics of these loci. We propose a minimum chi-square (MCS) method for simultaneous estimation of all the parameters in a stepwise mutation model and the ancestral allelic type of a sample. The MCS estimator requires knowing the mean number of alleles of a certain size in a sample, which can be estimated using Monte Carlo samples generated by a coalescent algorithm. The method is applied to samples of seven (CA)n repeat loci from eight human populations and one chimpanzee population. The estimated values of parameters suggest that there is a general tendency for microsatellite alleles to expand in size, because (1) each mutation has a slight tendency to cause size increase and (2) the mean size increase is larger than the mean size decrease for a mutation. Our estimates also suggest that most of these CA-repeat loci evolve according to multistep mutation models rather than single-step mutation models. We also introduced several quantities for measuring the quality of the estimation of ancestral allelic type, and it appears that the majority of the estimated ancestral allelic types are reasonably accurate. Implications of our analysis and potential extensions of the method are discussed.SINCE the discovery that a large number of loci with tandemly repeated sequences in human and many eukaryote species are highly polymorphic because of copy number variation of the repeats in different individuals (Jeffreys 1985; Litt and Luty 1989; Weber and May 1989), allele size data from such loci are rapidly becoming the dominant source of genetic markers for genome mapping, forensic testing, and population studies. Loci with repeat sequences longer than 5 bp are generally referred to as minisatellite or variable number tandem repeat loci, and those with repeat sequences between 2 to 5 bp are referred to as microsatellite or short tandem repeat loci (Tautz 1993). Because mutations change the copy number of such loci in a stepwise fashion, rapid accumulation of population samples from minisatellite and microsatellite loci has resurrected the interest of the stepwise mutation model (SMM), which was popular in the 1970s.     

GC-biased segregation of noncoding polymorphisms in Drosophila

The study of base composition evolution in Drosophila has been achieved mostly through the analysis of coding sequences. Third codon position GC content, however, is influenced by both neutral forces (e.g., mutation bias) and natural selection for codon usage optimization. In this article, large data sets of noncoding DNA sequence polymorphism in D. melanogaster and D. simulans were gathered from public databases to try to disentangle these two factors-noncoding sequences are not affected by selection for codon usage. Allele frequency analyses revealed an asymmetric pattern of AT vs. GC noncoding polymorphisms: AT --> GC mutations are less numerous, and tend to segregate at a higher frequency, than GC --> AT ones, especially at GC-rich loci. This is indicative of nonstationary evolution of base composition and/or of GC-biased allele transmission. Fitting population genetics models to the allele frequency spectra confirmed this result and favored the hypothesis of a biased transmission. These results, together with previous reports, suggest that GC-biased gene conversion has influenced base composition evolution in Drosophila and explain the correlation between intron and exon GC content.     

Polygenic Mutation in Drosophila Melanogaster: Genetic Interactions between Selection Lines and Candidate Quantitative Trait Loci

We have investigated genetic interactions between spontaneous mutations affecting abdominal and sternopleural bristle number that have accumulated in 12 long-term selection lines derived from an inbred strain, and mutations at 14 candidate bristle number quantitative trait loci. The quantitative test for complementation was to cross the selection lines to an inbred wild-type strain (the control cross) and to a derivative of the control strain into which the mutant allele at the candidate locus to be tested was substituted (the tester strain). Genetic interactions between spontaneous mutations affecting bristle number and the candidate locus mutations were common, and in several cases the interaction effects were different in males and females. Analyses of variance of the (tester - control) differences among and within groups of replicate lines selected in the same direction for the same trait showed significant group effects for several candidate loci. Genetically, the interactions could be caused by allelism of, and/or epistasis between, spontaneous mutations in the selection lines and the candidate locus mutations. It is possible that much of the response to selection was from new mutations at candidate bristle number quantitative trait loci, and that for some of these loci, mutation rates were high.     

On a genetic model of intraspecific competition and stabilizing selection

A genetic model is investigated in which two recombining loci determine the genotypic value of a quantitative trait additively. Two opposing evolutionary forces are assumed to act: stabilizing selection on the trait, which favors genotypes with an intermediate phenotype, and intraspecific competition mediated by that trait, which favors genotypes whose effect on the trait deviates most from that of the prevailing genotypes. Accordingly, fitnesses of genotypes have a frequency-independent component describing stabilizing selection and a frequency- and density-dependent component modeling competition. We study how the underlying genetics, in particular recombination rate and relative magnitude of allelic effects, interact with the conflicting selective forces and derive the resulting, surprisingly complex equilibrium patterns. We also investigate the conditions under which disruptive selection on the phenotypes can be observed and examine how much genetic variation can be maintained in such a model. We discovered a number of unexpected phenomena. For instance, we found that with little recombination the degree of stably maintained polymorphism and the equilibrium genetic variance can decrease as the strength of competition increases relative to the strength of stabilizing selection. In addition, we found that mean fitness at the stable equilibria is usually much lower than the maximum possible mean fitness and often even lower than the fitness at other, unstable equilibria. Thus, the evolutionary dynamics in this system are almost always nonadaptive.     

Selective sweeps in multilocus models of quantitative traits

We study the trajectory of an allele that affects a polygenic trait selected toward a phenotypic optimum. Furthermore, conditioning on this trajectory we analyze the effect of the selected mutation on linked neutral variation. We examine the well-characterized two-locus two-allele model but we also provide results for diallelic models with up to eight loci. First, when the optimum phenotype is that of the double heterozygote in a two-locus model, and there is no dominance or epistasis of effects on the trait, the trajectories of selected mutations rarely reach fixation; instead, a polymorphic equilibrium at both loci is approached. Whether a polymorphic equilibrium is reached (rather than fixation at both loci) depends on the intensity of selection and the relative distances to the optimum of the homozygotes at each locus. Furthermore, if both loci have similar effects on the trait, fixation of an allele at a given locus is less likely when it starts at low frequency and the other locus is polymorphic (with alleles at intermediate frequencies). Weaker selection increases the probability of fixation of the studied allele, as the polymorphic equilibrium is less stable in this case. When we do not require the double heterozygote to be at the optimum we find that the polymorphic equilibrium is more difficult to reach, and fixation becomes more likely. Second, increasing the number of loci decreases the probability of fixation, because adaptation to the optimum is possible by various combinations of alleles. Summaries of the genealogy (height, total length, and imbalance) and of sequence polymorphism (number of polymorphisms, frequency spectrum, and haplotype structure) next to a selected locus depend on the frequency that the selected mutation approaches at equilibrium. We conclude that multilocus response to selection may in some cases prevent selective sweeps from being completed, as described in previous studies, but that conditions causing this to happen strongly depend on the genetic architecture of the trait, and that fixation of selected mutations is likely in many instances.     

Detection of epistatic interactions between exotic alleles introgressed from wild barley (H. vulgare ssp. spontaneum)

The expression of a quantitative phenotype can be controlled through genotype, environment and genotype by environment interaction effects. Further, genotype effects can be attributed to major genes, quantitative trait loci (QTL) and gene by gene interactions, which are also termed epistatic interactions. The present study demonstrates that two-way epistatic interactions can play an important role for the expression of domestication-related traits like heading date, plant height and yield. In the BC₂DH population S42, carrying wild barley introgressions in the genetic background of the spring barley cultivar Scarlett, 13, 8 and 12 marker by marker interaction effects could be detected for the traits heading date, plant height and yield, respectively. Significant allelic combinations at interacting loci coincided for heading date, plant height and yield suggesting the presence of pleiotropic effects rather than several linked QTL. The mode of epistasis observed was primarily characterised by either (1) compensatory effects, where allelic combinations from the same genotype buffered the phenotype, or (2) augmented effects, where only the combination of the exotic allele at both interacting loci caused an altered phenotype. The present study shows that estimates of main effects of QTL can be confounded by interactions with background loci, suggesting that the identification of epistatic effects is important for gene cloning and marker-assisted selection. Furthermore, interaction effects between loci and putative candidate genes detected in the present study reveal potential functional relationships, which can be used to further elucidate gene networks in barley.     

Species range expansion by beneficial mutations

A species' range can be limited when there is no genetic variation for a trait that allows for adaptation to more extreme environments. We study how range expansion occurs by the establishment of a new mutation that affects a quantitative trait in a spatially continuous population. The optimal phenotype for the trait varies linearly in space. The survival probabilities of new mutations affecting the trait are found by simulation. Shallow environmental gradients favour mutations that arise nearer to the range margin and that have smaller phenotypic effects than do steep gradients. Mutations that become established in shallow environmental gradients typically result in proportionally larger range expansions than those that establish in steep gradients. Mutations that become established in populations with high maximum growth rates tend to originate nearer to the range edge and to cause relatively smaller range expansion than mutations that establish in populations with low maximum growth rates. Under plausible parameter values, mutations that allow for range expansion tend to have large phenotypic effects (more than one phenotypic standard deviation) and cause substantial range expansions (15% or more). Sexual reproduction allows for larger range expansions and adaptation to more extreme environments than asexual reproduction.     

Interchromosomal Biased Gene Conversion, Mutation and Selection in a Multigene Family

A mathematical model of the effects of interchromosomal biased gene conversion, mutation and natural selection on a multigene family is developed and analyzed. The model assumes two allelic states at each of n loci. The effects of genetic drift are ignored. The model is developed under the assumption of no recombination, but the analysis shows that, at equilibrium, there is no linkage disequilibrium, which implies that the conclusions are valid for arbitrary recombination among loci. At equilibrium, the balance between mutation, gene conversion and selection depends on the ratio of the mutation rates to the quantity [s + g(2α - 1)/ n], where s is the increment or decrement in relative fitness with each additional copy of one of the alleles, g is the conversion rate, and α is a measure of the bias in favor of one of the alleles. When this quantity is large relative to the mutation rates, the allele that has the net advantage, combining the effects of selection and conversion, will be nearly fixed in the multigene family. A comparison of these results with those from a comparable model of intrachromosomal biased conversion shows that biased interchromosomal conversion leads to approximately the same equilibrium copy number as does intrachromosomal conversion of the same strength. Interchromosomal conversion is much more effective in causing the substitution of one allele by another. The relative frequencies of interchromosomal and intrachromosomal conversion is indicated by the extent of the linkage disequilibrium among the loci in a multigene family.     

The relation between the genetic architecture of quantitative traits and long-term genetic response

The genetic architecture of a quantitative trait refers to the number of genetic variants, allele frequencies, and effect sizes of variants that affect a trait and their mode of gene action. This study was conducted to investigate the effect of four shapes of allelic frequency distributions (constant, uniform, L-shaped and U-shaped) and different number of trait-affecting loci (50, 100, 200, 500) on allelic frequency changes, long term genetic response, and maintaining genetic variance. To this end, a population of 440 individuals composed of 40 males and 400 females as well as a genome of 200 cM consisting of two chromosomes and with a mutation rate of 2.5?×?10^?5 per locus was simulated. Selection of superior animals was done using best linear unbiased prediction (BLUP) with assumption of infinitesimal model. Selection intensity was constant over 30 generations of selection. The highest genetic progress obtained when the allelic frequency had L-shaped distribution and number of trait-affecting loci was high (500). Although quantitative genetic theories predict the extinction of genetic variance due to artificial selection in long time, our results showed that under L- and U-shapped allelic frequency distributions, the additive genetic variance is persistent after 30 generations of selection. Further, presence or absence of selection limit can be an indication of low (<50) or high (>100) number of trait-affecting loci, respectively. It was concluded that the genetic architecture of complex traits is an important subject which should be considered in studies concerning long-term response to selection.     

Mutation-selection balance for environmental variance

The role of mutation-selection balance in maintaining environmental variance (V(E)) of quantitative traits is investigated under the assumption that genotypes differ in the magnitude of phenotypic variance, given genotypic value. Thus, V(E) can be regarded as a quantitative trait. As stabilizing selection on phenotype favors genotypes contributing low V(E), mutations that decrease V(E) are more likely to become fixed than those that increase it, and therefore V(E) should decline. If, however, essentially all mutants increase V(E) and overall selection is sufficiently strong that no mutants become fixed, then V(E) can be maintained. The heritability of the trait is determined by the relative sizes of mutational effects on phenotypic mean and residual variance and is independent of mutation rate and pleiotropic effects. This conclusion is not robust for small populations because some mutants may become fixed, which indicates that other selective forces must be involved, such as an intrinsic cost of homogeneity.     

Allele Frequencies at Microsatellite Loci: The Stepwise Mutation Model Revisited

We summarize available data on the frequencies of alleles at microsatellite loci in human populations and compare observed distributions of allele frequencies to those generated by a simulation of the stepwise mutation model. We show that observed frequency distributions at 108 loci are consistent with the results of the model under the assumption that mutations cause an increase or decrease in repeat number by one and under the condition that the product Nu, where N is the effective population size and u is the mutation rate, is larger than one. We show that the variance of the distribution of allele sizes is a useful estimator of Nu and performs much better than previously suggested estimators for the stepwise mutation model. In the data, there is no correlation between the mean and variance in allele size at a locus or between the number of alleles and mean allele size, which suggests that the mutation rate at these loci is independent of allele size.     

Heterogeneous selection at specific loci in natural environments in Arabidopsis thaliana

Genetic variation for quantitative traits is often greater than that expected to be maintained by mutation in the face of purifying natural selection. One possible explanation for this observed variation is the action of heterogeneous natural selection in the wild. Here we report that selection on quantitative trait loci (QTL) for fitness traits in the model plant species Arabidopsis thaliana differs among natural ecological settings and genetic backgrounds. At one QTL, the allele that enhanced the viability of fall-germinating seedlings in North Carolina reduced the fecundity of spring-germinating seedlings in Rhode Island. Several other QTL experienced strong directional selection, but only in one site and seasonal cohort. Thus, different loci were exposed to selection in different natural environments. Selection on allelic variation also depended upon the genetic background. The allelic fitness effects of two QTL reversed direction depending on the genotype at the other locus. Moreover, alternative alleles at each of these loci caused reversals in the allelic fitness effects of a QTL closely linked to TFL1, a candidate developmental gene displaying nucleotide sequence polymorphism consistent with balancing selection. Thus, both environmental heterogeneity and epistatic selection may maintain genetic variation for fitness in wild plant species.