Beyond mean allelic effects: A locus at the major color gene MC1R associates also with differing levels of phenotypic and genetic (co)variance for coloration in barn owls

The mean phenotypic effects of a discovered variant help to predict major aspects of the evolution and inheritance of a phenotype. However, differences in the phenotypic variance associated to distinct genotypes are often overlooked despite being suggestive of processes that largely influence phenotypic evolution, such as interactions between the genotypes with the environment or the genetic background. We present empirical evidence for a mutation at the melanocortin‐1‐receptor gene, a major vertebrate coloration gene, affecting phenotypic variance in the barn owl, Tyto alba. The white MC1R allele, which associates with whiter plumage coloration, also associates with a pronounced phenotypic and additive genetic variance for distinct color traits. Contrarily, the rufous allele, associated with a rufous coloration, relates to a lower phenotypic and additive genetic variance, suggesting that this allele may be epistatic over other color loci. Variance differences between genotypes entailed differences in the strength of phenotypic and genetic associations between color traits, suggesting that differences in variance also alter the level of integration between traits. This study highlights that addressing variance differences of genotypes in wild populations provides interesting new insights into the evolutionary mechanisms and the genetic architecture underlying the phenotype.     

Effects on phenotypic variability of directional selection arising through genetic differences in residual variability

In standard models of quantitative traits, genotypes are assumed to differ in mean but not variance of the trait. Here we consider directional selection for a quantitative trait for which genotypes also confer differences in variability, viewed either as differences in residual phenotypic variance when individual loci are concerned or as differences in environmental variability when the whole genome is considered. At an individual locus with additive effects, the selective value of the increasing allele is given by ia/sigma + 1/2 ixb/sigma2, where i is the selection intensity, x is the standardized truncation point, sigma2 is the phenotypic variance, and a/sigma and b/sigma2 are the standardized differences in mean and variance respectively between genotypes at the locus. Assuming additive effects on mean and variance across loci, the response to selection on phenotype in mean is isigma2(Am)/sigma + 1/2 ixcov(Amv)/sigma2 and in variance is icov(Amv)/sigma + 1/2 ixsigma2(Av)/sigma2, where sigma2(Am) is the (usual) additive genetic variance of effects of genes on the mean, sigma2(Av) is the corresponding additive genetic variance of their effects on the variance, and cov(Amv) is the additive genetic covariance of their effects. Changes in variance also have to be corrected for any changes due to gene frequency change and for the Bulmer effect, and relevant formulae are given. It is shown that effects on variance are likely to be greatest when selection is intense and when selection is on individual phenotype or within family deviation rather than on family mean performance. The evidence for and implications of such variability in variance are discussed.     

Variance Heterogeneity in Saccharomyces cerevisiae Expression Data: Trans-Regulation and Epistasis

Here, we describe the results from the first variance heterogeneity Genome Wide Association Study (VGWAS) on yeast expression data. Using this forward genetics approach, we show that the genetic regulation of gene-expression in the budding yeast, Saccharomyces cerevisiae, includes mechanisms that can lead to variance heterogeneity in the expression between genotypes. Additionally, we performed a mean effect association study (GWAS). Comparing the mean and variance heterogeneity analyses, we find that the mean expression level is under genetic regulation from a larger absolute number of loci but that a higher proportion of the variance controlling loci were trans-regulated. Both mean and variance regulating loci cluster in regulatory hotspots that affect a large number of phenotypes; a single variance-controlling locus, mapping close to DIA2, was found to be involved in more than 10% of the significant associations. It has been suggested in the literature that variance-heterogeneity between the genotypes might be due to genetic interactions. We therefore screened the multi-locus genotype-phenotype maps for several traits where multiple associations were found, for indications of epistasis. Several examples of two and three locus genetic interactions were found to involve variance-controlling loci, with reports from the literature corroborating the functional connections between the loci. By using a new analytical approach to re-analyze a powerful existing dataset, we are thus able to both provide novel insights to the genetic mechanisms involved in the regulation of gene-expression in budding yeast and experimentally validate epistasis as an important mechanism underlying genetic variance-heterogeneity between genotypes.     

The Inheritance of Metabolic Flux: Expressions for the within-Sibship Mean and Variance Given the Parental Genotypes

Recent developments have related quantitative trait expression to metabolic flux. The present paper investigates some implications of this for statistical aspects of polygenic inheritance. Expressions are derived for the within-sibship genetic mean and genetic variance of metabolic flux given a pair of parental, diploid, n-locus genotypes. These are exact and hold for arbitrary numbers of gene loci, arbitrary allelic values at each locus, and for arbitrary recombination fractions between adjacent gene loci. The within-sibship, genetic variance is seen to be simply a measure of parental heterozygosity plus a measure of the degree of linkage coupling within the parental genotypes. Approximations are given for the within-sibship phenotypic mean and variance of metabolic flux. These results are applied to the problem of attaining adequate statistical power in a test of association between allozymic variation and inter-individual variation in metabolic flux. Simulations indicate that statistical power can be greatly increased by augmenting the data with predictions and observations on progeny statistics in relation to parental allozyme genotypes. Adequate power may thus be attainable at small sample sizes, and when allozymic variation is scored at a only small fraction of the total set of loci whose catalytic products determine the flux.     

The Multi-allelic Genetic Architecture of a Variance-Heterogeneity Locus for Molybdenum Concentration in Leaves Acts as a Source of Unexplained Additive Genetic Variance

Genome-wide association (GWA) analyses have generally been used to detect individual loci contributing to the phenotypic diversity in a population by the effects of these loci on the trait mean. More rarely, loci have also been detected based on variance differences between genotypes. Several hypotheses have been proposed to explain the possible genetic mechanisms leading to such variance signals. However, little is known about what causes these signals, or whether this genetic variance-heterogeneity reflects mechanisms of importance in natural populations. Previously, we identified a variance-heterogeneity GWA (vGWA) signal for leaf molybdenum concentrations in Arabidopsis thaliana. Here, fine-mapping of this association reveals that the vGWA emerges from the effects of three independent genetic polymorphisms that all are in strong LD with the markers displaying the genetic variance-heterogeneity. By revealing the genetic architecture underlying this vGWA signal, we uncovered the molecular source of a significant amount of hidden additive genetic variation or “missing heritability”. Two of the three polymorphisms underlying the genetic variance-heterogeneity are promoter variants for Molybdate transporter 1 (MOT1), and the third a variant located ~25 kb downstream of this gene. A fourth independent association was also detected ~600 kb upstream of MOT1. Use of a T-DNA knockout allele highlights Copper Transporter 6; COPT6 (AT2G26975) as a strong candidate gene for this association. Our results show that an extended LD across a complex locus including multiple functional alleles can lead to a variance-heterogeneity between genotypes in natural populations. Further, they provide novel insights into the genetic regulation of ion homeostasis in A. thaliana, and empirically confirm that variance-heterogeneity based GWA methods are a valuable tool to detect novel associations of biological importance in natural populations.     

Multipoint analysis of human quantitative genetic variation.

A unique method of partitioning human quantitative genetic variation into effects due to specific chromosomal regions is presented. This method is based on estimating the proportion of genetic material, R, shared identical by descent (IBD) by sibling pairs in a specified chromosomal region, on the basis of their marker genotypes at a set of marker loci spanning the region. The mean and variance of the distribution of R conditional on IBD status and recombination pattern between two marker loci are derived as a function of the distance between the two loci. The distribution of the estimates of R is exemplified using data on 22 loci on chromosome 7. A method of using the estimated R values and observed values of a quantitative trait in a set of sibships to estimate the proportion of total genetic variance explained by loci in the region of interest is presented. Monte Carlo simulation techniques are used to show that this method is more powerful than existing methods of quantitative linkage analysis based on sib pairs. It is also shown through simulation studies that the proposed method is sensitive to genetic variation arising from both a single locus of large effect as well as from several loosely linked loci of moderate phenotypic effect.     

Statistical epistasis is a generic feature of gene regulatory networks

Functional dependencies between genes are a defining characteristic of gene networks underlying quantitative traits. However, recent studies show that the proportion of the genetic variation that can be attributed to statistical epistasis varies from almost zero to very high. It is thus of fundamental as well as instrumental importance to better understand whether different functional dependency patterns among polymorphic genes give rise to distinct statistical interaction patterns or not. Here we address this issue by combining a quantitative genetic model approach with genotype-phenotype models capable of translating allelic variation and regulatory principles into phenotypic variation at the level of gene expression. We show that gene regulatory networks with and without feedback motifs can exhibit a wide range of possible statistical genetic architectures with regard to both type of effect explaining phenotypic variance and number of apparent loci underlying the observed phenotypic effect. Although all motifs are capable of harboring significant interactions, positive feedback gives rise to higher amounts and more types of statistical epistasis. The results also suggest that the inclusion of statistical interaction terms in genetic models will increase the chance to detect additional QTL as well as functional dependencies between genetic loci over a broad range of regulatory regimes. This article illustrates how statistical genetic methods can fruitfully be combined with nonlinear systems dynamics to elucidate biological issues beyond reach of each methodology in isolation.     

Evolution of pleiotropy: epistatic interaction pattern supports a mechanistic model underlying variation in genotype-phenotype map

The genotype-phenotype (GP) map consists of developmental and physiological mechanisms mapping genetic onto phenotypic variation. It determines the distribution of heritable phenotypic variance on which selection can act. Comparative studies of morphology as well as of gene regulatory networks show that the GP map itself evolves, yet little is known about the actual evolutionary mechanisms involved. The study of such mechanisms requires exploring the variation in GP maps at the population level, which presently is easier to quantify by statistical genetic methods rather than by regulatory network structures. We focus on the evolution of pleiotropy, a major structural aspect of the GP map. Pleiotropic genes affect multiple traits and underlie genetic covariance between traits, often causing evolutionary constraints. Previous quantitative genetic studies have demonstrated population-level variation in pleiotropy in the form of loci, at which genotypes differ in the genetic covariation between traits. This variation can potentially fuel evolution of the GP map under selection and/or drift. Here, we propose a developmental mechanism underlying population genetic variation in covariance and test its predictions. Specifically, the mechanism predicts that the loci identified as responsible for genetic variation in pleiotropy are involved in trait-specific epistatic interactions. We test this prediction for loci affecting allometric relationships between traits in an advanced intercross between inbred mouse strains. The results consistently support the prediction. We further find a high degree of sign epistasis in these interactions, which we interpret as an indication of adaptive gene complexes within the diverged parental lines.     

A Cladistic Analysis of Phenotype Associations with Haplotypes Inferred from Restriction Endonuclease Mapping. II. the Analysis of Natural Populations

Genes that code for products involved in the physiology of a phenotype are logical candidates for explaining interindividual variation in that phenotype. We present a methodology for discovering associations between genetic variation at such candidate loci (assayed through restriction endonuclease mapping) with phenotypic variation at the population level. We confine our analyses to DNA regions in which recombination is very rare. In this case, the genetic variation at the candiate locus can be organized into a cladogram that represents the evolutionary relationships between the observed haplotypes. Any mutation causing a significant phenotypic effect should be imbedded within the same historical structure defined by the cladogram. We showed, in the first paper of this series, how to use the cladogram to define a nested analysis of variance (NANOVA) that was very efficient at detecting and localizing phenotypically important mutations. However, the NANOVA of haplotype effects could only be applied to populations of homozygous genotypes. In this paper, we apply the quantitative genetic concept of average excess to evaluate the phenotypic effect of a haplotype or group of haplotypes stratified and contrasted according to the nested design defined by the cladogram. We also show how a permutational procedure can be used to make statistical inferences about the nested average excess values in populations containing heterozygous as well as homozygous genotypes. We provide two worked examples that investigate associations between genetic variation at or near the Alcohol dehydrogenase (Adh) locus and Adh activity in Drosophila melanogaster, and associations between genetic variation at or near some apolipoprotein loci and various lipid phenotypes in a human population.     

Effect of mass selection on the within-family genetic variance in finite populations

Summary The adequacy of an expression for the withinfamily genetic variance under pure random drift in an additive infinitesimal model was tested via simulation in populations undergoing mass selection. Two hundred or one thousand unlinked loci with two alleles at initial frequencies of 1/2 were considered. The size of the population was 100 (50 males and 50 females). Full-sib matings were carried out for 15 generations with only one male and one female chosen as parents each generation, either randomly or on an individual phenotypic value. In the unselected population, results obtained from 200 replicates were in agreement with predictions. With mass selection, within-family genetic variance was overpredicted by theory from the 12th and 4th generations for the 1,000 and 200 loci cases, respectively. Taking into account the observed change in gene frequencies in the algorithm led to a much better agreement with observed values. Results for the distribution of gene frequencies and the withinlocus genetic covariance are presented. It is concluded that the expression for the within-family genetic variance derived for pure random drift holds well for mass selection within the limits of an additive infinitesimal model.     

Genetic variants and underlying mechanisms influencing variance heterogeneity in maize

Traditional genetic studies focus on identifying genetic variants associated with the mean difference in a quantitative trait. Because genetic variants also influence phenotypic variation via heterogeneity, we conducted a variance‐heterogeneity genome‐wide association study to examine the contribution of variance heterogeneity to oil‐related quantitative traits. We identified 79 unique variance‐controlling single nucleotide polymorphisms (vSNPs) from the sequences of 77 candidate variance‐heterogeneity genes for 21 oil‐related traits using the Levene test (P < 1.0 × 10^?5). About 30% of the candidate genes encode enzymes that work in lipid metabolic pathways, most of which define clear expression variance quantitative trait loci. Of the vSNPs specifically associated with the genetic variance heterogeneity of oil concentration, 89% can be explained by additional linked mean‐effects genetic variants. Furthermore, we demonstrated that gene × gene interactions play important roles in the formation of variance heterogeneity for fatty acid compositional traits. The interaction pattern was validated for one gene pair (GRMZM2G035341 and GRMZM2G152328) using yeast two‐hybrid and bimolecular fluorescent complementation analyses. Our findings have implications for uncovering the genetic basis of hidden additive genetic effects and epistatic interaction effects, and we indicate opportunities to stabilize efficient breeding and selection of high‐oil maize (Zea mays L.).     

Evolution of robustness to noise and mutation in gene expression dynamics

Phenotype of biological systems needs to be robust against mutation in order to sustain themselves between generations. On the other hand, phenotype of an individual also needs to be robust against fluctuations of both internal and external origins that are encountered during growth and development. Is there a relationship between these two types of robustness, one during a single generation and the other during evolution? Could stochasticity in gene expression have any relevance to the evolution of these types of robustness? Robustness can be defined by the sharpness of the distribution of phenotype; the variance of phenotype distribution due to genetic variation gives a measure of 'genetic robustness', while that of isogenic individuals gives a measure of 'developmental robustness'. Through simulations of a simple stochastic gene expression network that undergoes mutation and selection, we show that in order for the network to acquire both types of robustness, the phenotypic variance induced by mutations must be smaller than that observed in an isogenic population. As the latter originates from noise in gene expression, this signifies that the genetic robustness evolves only when the noise strength in gene expression is larger than some threshold. In such a case, the two variances decrease throughout the evolutionary time course, indicating increase in robustness. The results reveal how noise that cells encounter during growth and development shapes networks' robustness to stochasticity in gene expression, which in turn shapes networks' robustness to mutation. The necessary condition for evolution of robustness, as well as the relationship between genetic and developmental robustness, is derived quantitatively through the variance of phenotypic fluctuations, which are directly measurable experimentally.     

Rare and common regulatory variation in population-scale sequenced human genomes

Population-scale genome sequencing allows the characterization of functional effects of a broad spectrum of genetic variants underlying human phenotypic variation. Here, we investigate the influence of rare and common genetic variants on gene expression patterns, using variants identified from sequencing data from the 1000 genomes project in an African and European population sample and gene expression data from lymphoblastoid cell lines. We detect comparable numbers of expression quantitative trait loci (eQTLs) when compared to genotypes obtained from HapMap 3, but as many as 80% of the top expression quantitative trait variants (eQTVs) discovered from 1000 genomes data are novel. The properties of the newly discovered variants suggest that mapping common causal regulatory variants is challenging even with full resequencing data; however, we observe significant enrichment of regulatory effects in splice-site and nonsense variants. Using RNA sequencing data, we show that 46.2% of nonsynonymous variants are differentially expressed in at least one individual in our sample, creating widespread potential for interactions between functional protein-coding and regulatory variants. We also use allele-specific expression to identify putative rare causal regulatory variants. Furthermore, we demonstrate that outlier expression values can be due to rare variant effects, and we approximate the number of such effects harboured in an individual by effect size. Our results demonstrate that integration of genomic and RNA sequencing analyses allows for the joint assessment of genome sequence and genome function.     

Competition can maintain genetic but not environmental variance in the presence of stabilizing selection

A population in which there is stabilizing selection acting on quantitative traits toward an intermediate optimum becomes monomorphic in the absence of mutation. Further, genotypes that show least environmental variation are also favored, such that selection is likely to reduce both genetic and environmental components of phenotypic variance. In contrast, intraspecific competition for resources is more severe between phenotypically similar individuals, such that those deviating from prevailing phenotypes have a selective advantage. It has been shown previously that polymorphism and phenotypic variance can be maintained if competition between individuals is "effectively" stronger than stabilizing selection. Environmental variance is generally observed in quantitative traits, so mechanisms to explain its maintenance are sought, but the impact of competition on its magnitude has not previously been studied. Here we assume that a quantitative trait is subject to selection for an optimal value and to selection due to competition. Further, we assume that both the mean and variance of the phenotypic value depend on genotype, such that both may be affected by selection. Theoretical analysis and numerical simulations reveal that environmental variance can be maintained only when the genetic variance (in mean phenotypic value) is constrained to a very low level. Environmental variance will be replaced entirely by genotypic variance if a range of genotypes that vary widely in mean phenotype are present or become so by mutation. The distribution of mean phenotypic values is discrete when competition is strong relative to stabilizing selection; but more genotypes segregate and the distribution can approach continuity as competition becomes extremely strong. If the magnitude of the environmental variance is not under genetic control, there is a complementary relationship between the levels of environmental and genetic variance such that the level of phenotypic variance is little affected.     

Quantifying the genetic component of phenotypic variation in unpedigreed wild plants: tailoring genomic scan for within-population use

The study of adaptive genetic variation in natural populations is central to evolutionary biology. Quantitative genetics methods, however, are hardly applicable to long-lived organisms, and current knowledge on adaptive genetic variation in wild plants mostly refers to annuals and short-lived perennials. Studies on long-lived species are essential to explore possible life-history correlates of genetic variation, selection, and trait heritability. In this paper, we propose a method based on molecular markers to quantify the genetic basis of individual phenotypic differences in wild plants under natural conditions. Rather than focusing on inferring individual relatedness to estimate the heritability of phenotypic traits, we directly estimate the proportion of observed phenotypic variance that is statistically accounted for by genotypic differences between individuals. This is achieved by (i) identifying loci that are correlated across individuals with the phenotypic trait of interest by means of an amplified fragment length polymorphism (AFLP)-based explorative genomic scan, and (ii) fitting multiple regression and linear random effect models to estimate the effects of genotype, environment and genotype × environment on phenotypes. We apply this method to estimate genotypic and environmental effects on cumulative maternal fecundity in a wild population of the long-lived Viola cazorlensis monitored for 20 years. Results show that between 56–63% (depending on estimation method) of phenotypic variance in fecundity is accounted for by genotypic differences in 11 AFLP loci that are significantly related to fecundity. Genotype × environment effects accounted for 38% of fecundity variance, which may help to explain the unexpectedly high levels of genetic variance for fecundity found.     

草鱼全同胞鱼苗不同个体甲基化位点的差异

本研究通过甲基化敏感扩增多态性(Methylation sensitive amplification polymorphism)对一对草鱼亲本的20个子代甲基化位点进行了研究。从20对引物组合中扩增出311个位点,其中甲基化位点236个,占总扩增位点的75.9%,表明草鱼水花期基因组甲基化水平已经很高,说明它们大部分组织分化基本完成;其中甲基化多态位点65个,占甲基化位点的27.5%,说明这些子代草鱼甲基化位点已经有相当的差异。对其他两对亲本的后代用六个引物组合扩增的结果表明,同一亲本的子代在甲基化模式上有差异可能是普遍现象。本研究结果说明,即使来自同一对草鱼亲本的不同子代个体在基因表达上也有较大的差异,因此很多性状在草鱼后代的分离和一些基因表达的改变有一定的关系。     

Phenotypic complexity, measurement bias, and poor phenotypic resolution contribute to the missing heritability problem in genetic association studies

Background

The variance explained by genetic variants as identified in (genome-wide) genetic association studies is typically small compared to family-based heritability estimates. Explanations of this ‘missing heritability’ have been mainly genetic, such as genetic heterogeneity and complex (epi-)genetic mechanisms.

Methodology

We used comprehensive simulation studies to show that three phenotypic measurement issues also provide viable explanations of the missing heritability: phenotypic complexity, measurement bias, and phenotypic resolution. We identify the circumstances in which the use of phenotypic sum-scores and the presence of measurement bias lower the power to detect genetic variants. In addition, we show how the differential resolution of psychometric instruments (i.e., whether the instrument includes items that resolve individual differences in the normal range or in the clinical range of a phenotype) affects the power to detect genetic variants.

Conclusion

We conclude that careful phenotypic data modelling can improve the genetic signal, and thus the statistical power to identify genetic variants by 20–99%.