Gene action,genetic variation,and GWAS: A user-friendly web tool

Fisher’s partitioning of genotypic values and genetic variance is highly relevant in the current era of genome-wide association studies (GWASs). However, despite being more than a century old, a number of persistent misconceptions related to nonadditive genetic effects remain. We developed a user-friendly web tool, the Falconer ShinyApp, to show how the combination of gene action and allele frequencies at causal loci translate to genetic variance and genetic variance components for a complex trait. The app can be used to demonstrate the relationship between a SNP effect size estimated from GWAS and the variation the SNP generates in the population, i.e., how locus-specific effects lead to individual differences in traits. In addition, it can also be used to demonstrate how within and between locus interactions (dominance and epistasis, respectively) usually do not lead to a large amount of nonadditive variance relative to additive variance, and therefore, that these interactions usually do not explain individual differences in a population.     

The Nature of Genetic Variation for Complex Traits Revealed by GWAS and Regional Heritability Mapping Analyses

We use computer simulations to investigate the amount of genetic variation for complex traits that can be revealed by single-SNP genome-wide association studies (GWAS) or regional heritability mapping (RHM) analyses based on full genome sequence data or SNP chips. We model a large population subject to mutation, recombination, selection, and drift, assuming a pleiotropic model of mutations sampled from a bivariate distribution of effects of mutations on a quantitative trait and fitness. The pleiotropic model investigated, in contrast to previous models, implies that common mutations of large effect are responsible for most of the genetic variation for quantitative traits, except when the trait is fitness itself. We show that GWAS applied to the full sequence increases the number of QTL detected by as much as 50% compared to the number found with SNP chips but only modestly increases the amount of additive genetic variance explained. Even with full sequence data, the total amount of additive variance explained is generally below 50%. Using RHM on the full sequence data, a slightly larger number of QTL are detected than by GWAS if the same probability threshold is assumed, but these QTL explain a slightly smaller amount of genetic variance. Our results also suggest that most of the missing heritability is due to the inability to detect variants of moderate effect (∼0.03–0.3 phenotypic SDs) segregating at substantial frequencies. Very rare variants, which are more difficult to detect by GWAS, are expected to contribute little genetic variation, so their eventual detection is less relevant for resolving the missing heritability problem.     

Application of genome-wide SNP data for uncovering pairwise relationships and quantitative trait loci

The genetic analysis of quantitative traits in humans is changing as a result of the availability of whole-genome SNP data. Heritability analysis can make use of actual genetic sharing between pairs of individuals estimated from the genotype data, rather than the expected genetic sharing implied by their family relationship. This could provide more accurate heritability estimates and help to overcome the equal environment assumption. Quantitative trait locus (QTL) linkage mapping can make use of local genetic sharing inferred from very dense local genotype data from pedigree members or individuals not previously known to be related. This approach may be particularly suited for detecting loci that contain rare variants with major effect on the phenotype. Finally, whole-genome SNP data can be used to measure the genetic similarity between individuals to provide matched sets for association studies, in order to avoid spurious association from population stratification.     

The strength of the selection barrier between populations

Genetic differences among populations exposed to selection form barriers against genetic exchange by mortality among hybrids. The strength of such a selection barrier, with which one (recipient) population reacts against immigration from another (donor) population, may be measured as the cumulative mean fitness of hybrids and their descendants relative to the fitness of the recipient population. Previous work analysed a case of weak selection with pairwise epistatic interactions by assuming small genetic distance between two populations in contact. The present study allows large genetic difference between the donor and recipient populations and considers weak multilocus selection with arbitrary epistatic interactions between two or more linked loci. An approximate analytical expression for the barrier strength is obtained as an expansion in which the strength of selection plays the role of a small parameter. It is shown that allele frequencies and gametic linkage disequilibria contribute in different ways to the strength of the selection barrier.     

Epistatic interaction is an important genetic basis of grain yield and its components in maize

A population of 294 recombinant inbred lines (RIL) derived from Yuyu22, an elite maize hybrid extending broadly in China, has been constructed to investigate the genetic basis of grain yield, and associated yield components in maize. The main-effect quantitative trait loci (QTL), digenic epistatic interactions, and their interactions with the environment for grain yield and its three components were identified by using the mixed linear model approach. Thirty-two main-effect QTL and forty-four pairs of digenic epistatic interactions were detected for the four measured traits in four environments. Our results suggest that both additive effects and epistasis (additive × additive) effects are important genetic bases of grain yield and its components in the RIL population. Only 30.4% of main-effect QTL for ear length were involved in epistatic interactions. This implies that many loci in epistatic interactions may not have significant effects for traits alone but may affect trait expression by epistatic interaction with the other loci.     

Indirect genetic effects from ecological interactions in Arabidopsis thaliana

Indirect genetic effects arise when genes expressed in one individual affect the expression of traits in other individuals. The importance of indirect genetic effects has been recognized for a diversity of evolutionary processes including kin selection, sexual selection, community structure and multilevel selection, but data regarding their genetic architecture and prevalence throughout the genome remain scarce, especially for interactions between unrelated individuals. Using a set of 411 Bay-0 x Shahdara Arabidopsis recombinant inbred lines grown with Landsberg neighbours, we examined quantitative trait loci (QTL) having direct and indirect effects on size, developmental, and fitness related traits. Using an interval mapping approach, we identified 15 QTL with direct effects and found that 13 of these QTL had significant indirect effects on trait expression in neighbouring plants. These results suggest widespread pleiotropy, as nearly all direct effect QTL have associated pleiotropic indirect effects. Paradoxically, most indirect effects were of the same sign as direct effects, creating a pattern of nearly universal positive pleiotropy that makes most covariances between direct and indirect effects positive. These results are consistent with a complex genetic basis for intraspecific interactions, but suggest that interactions between neighbouring plants are largely positive, rather than negative as would be expected for competition. In addition to their evolutionary and ecological importance, these pleiotropic relationships between DGE and IGE loci have implications for quantitative genetic studies of natural populations as well as experimental design considerations. Additionally, studies that ignore IGEs may over- or underestimate quantitative genetic parameters, as well as the effect of and variance contributed by QTL.     

High-Resolution Mapping of Complex Traits with a Four-Parent Advanced Intercross Yeast Population

A large fraction of human complex trait heritability is due to a high number of variants with small marginal effects and their interactions with genotype and environment. Such alleles are more easily studied in model organisms, where environment, genetic makeup, and allele frequencies can be controlled. Here, we examine the effect of natural genetic variation on heritable traits in a very large pool of baker’s yeast from a multiparent 12th generation intercross. We selected four representative founder strains to produce the Saccharomyces Genome Resequencing Project (SGRP)-4X mapping population and sequenced 192 segregants to generate an accurate genetic map. Using these individuals, we mapped 25 loci linked to growth traits under heat stress, arsenite, and paraquat, the majority of which were best explained by a diverging phenotype caused by a single allele in one condition. By sequencing pooled DNA from millions of segregants grown under heat stress, we further identified 34 and 39 regions selected in haploid and diploid pools, respectively, with most of the selection against a single allele. While the most parsimonious model for the majority of loci mapped using either approach was the effect of an allele private to one founder, we could validate examples of pleiotropic effects and complex allelic series at a locus. SGRP-4X is a deeply characterized resource that provides a framework for powerful and high-resolution genetic analysis of yeast phenotypes and serves as a test bed for testing avenues to attack human complex traits.     

Weighted Interaction SNP Hub (WISH) network method for building genetic networks for complex diseases and traits using whole genome genotype data

Background

High-throughput genotype (HTG) data has been used primarily in genome-wide association (GWA) studies; however, GWA results explain only a limited part of the complete genetic variation of traits. In systems genetics, network approaches have been shown to be able to identify pathways and their underlying causal genes to unravel the biological and genetic background of complex diseases and traits, e.g., the Weighted Gene Co-expression Network Analysis (WGCNA) method based on microarray gene expression data. The main objective of this study was to develop a scale-free weighted genetic interaction network method using whole genome HTG data in order to detect biologically relevant pathways and potential genetic biomarkers for complex diseases and traits.

Results

We developed the Weighted Interaction SNP Hub (WISH) network method that uses HTG data to detect genome-wide interactions between single nucleotide polymorphism (SNPs) and its relationship with complex traits. Data dimensionality reduction was achieved by selecting SNPs based on its: 1) degree of genome-wide significance and 2) degree of genetic variation in a population. Network construction was based on pairwise Pearson's correlation between SNP genotypes or the epistatic interaction effect between SNP pairs. To identify modules the Topological Overlap Measure (TOM) was calculated, reflecting the degree of overlap in shared neighbours between SNP pairs. Modules, clusters of highly interconnected SNPs, were defined using a tree-cutting algorithm on the SNP dendrogram created from the dissimilarity TOM (1-TOM). Modules were selected for functional annotation based on their association with the trait of interest, defined by the Genome-wide Module Association Test (GMAT). We successfully tested the established WISH network method using simulated and real SNP interaction data and GWA study results for carcass weight in a pig resource population; this resulted in detecting modules and key functional and biological pathways related to carcass weight.

Conclusions

We developed the WISH network method which is a novel 'systems genetics' approach to study genetic networks underlying complex trait variation. The WISH network method reduces data dimensionality and statistical complexity in associating genotypes with phenotypes in GWA studies and enables researchers to identify biologically relevant pathways and potential genetic biomarkers for any complex trait of interest.

     

Genetic variation maintained in multilocus models of additive quantitative traits under stabilizing selection.

Stabilizing selection for an intermediate optimum is generally considered to deplete genetic variation in quantitative traits. However, conflicting results from various types of models have been obtained. While classical analyses assuming a large number of independent additive loci with individually small effects indicated that no genetic variation is preserved under stabilizing selection, several analyses of two-locus models showed the contrary. We perform a complete analysis of a generalization of Wright's two-locus quadratic-optimum model and investigate numerically the ability of quadratic stabilizing selection to maintain genetic variation in additive quantitative traits controlled by up to five loci. A statistical approach is employed by choosing randomly 4000 parameter sets (allelic effects, recombination rates, and strength of selection) for a given number of loci. For each parameter set we iterate the recursion equations that describe the dynamics of gamete frequencies starting from 20 randomly chosen initial conditions until an equilibrium is reached, record the quantities of interest, and calculate their corresponding mean values. As the number of loci increases from two to five, the fraction of the genome expected to be polymorphic declines surprisingly rapidly, and the loci that are polymorphic increasingly are those with small effects on the trait. As a result, the genetic variance expected to be maintained under stabilizing selection decreases very rapidly with increased number of loci. The equilibrium structure expected under stabilizing selection on an additive trait differs markedly from that expected under selection with no constraints on genotypic fitness values. The expected genetic variance, the expected polymorphic fraction of the genome, as well as other quantities of interest, are only weakly dependent on the selection intensity and the level of recombination.     

Assessing the degree of stratification between closely related Holstein-Friesian populations

Genomic information is an important part of the routine evaluation of dairy cattle and provides the wide availability of animals genotyped using single nucleotide polymorphism (SNP) microarrays. We analyzed 2243 Polish and 2294 German Holstein-Friesian bulls genotyped using the Illumina BovineSNP50 BeadChip. For each bull, estimated breeding values (EBVs) calculated from national routine genetic evaluation were available for production traits and for somatic cell score (SCS). Separately for each population, we estimated SNP haplotypes, pairwise linkage disequilibrium (LD), and SNP effects. The SNP genetic covariance between both populations was estimated using a bivariate mixed model. The average LD was lower in the Polish than in the German population and, with increasing genomic distance, LD decays 1.7 times more rapidly in German than in Polish cattle. The comparison of SNP allele frequencies for base populations estimated separately using Polish and German data revealed a very good agreement. The comparison of genetic effects corresponding to various window lengths defined in bp emerged a systematic pattern: regardless of the length of the compared region, few significant differences were found for production traits, while many were observed for SCS. For each trait, the German population had much higher SNP variances than the Polish population and the genetic covariance estimates were all positive. Depending on traits’ inheritance mode, the additive genetic variation can be stored in many genes following the infinitesimal model (like for SCS) or distributed between genes with high effects and the polygenic “background” (like for production traits). Accounting for those differences has implications on the prospective international genomic evaluation.     

Heritability of interpack aggression in a wild pedigreed population of North American grey wolves

Aggression is a quantitative trait deeply entwined with individual fitness. Mapping the genomic architecture underlying such traits is complicated by complex inheritance patterns, social structure, pedigree information and gene pleiotropy. Here, we leveraged the pedigree of a reintroduced population of grey wolves (Canis lupus) in Yellowstone National Park, Wyoming, USA, to examine the heritability of and the genetic variation associated with aggression. Since their reintroduction, many ecological and behavioural aspects have been documented, providing unmatched records of aggressive behaviour across multiple generations of a wild population of wolves. Using a linear mixed model, a robust genetic relationship matrix, 12,288 single nucleotide polymorphisms (SNPs) and 111 wolves, we estimated the SNP‐based heritability of aggression to be 37% and an additional 14% of the phenotypic variation explained by shared environmental exposures. We identified 598 SNP genotypes from 425 grey wolves to resolve a consensus pedigree that was included in a heritability analysis of 141 individuals with SNP genotype, metadata and aggression data. The pedigree‐based heritability estimate for aggression is 14%, and an additional 16% of the phenotypic variation was explained by shared environmental exposures. We find strong effects of breeding status and relative pack size on aggression. Through an integrative approach, these results provide a framework for understanding the genetic architecture of a complex trait that influences individual fitness, with linkages to reproduction, in a social carnivore. Along with a few other studies, we show here the incredible utility of a pedigreed natural population for dissecting a complex, fitness‐related behavioural trait.     

Towards genetic markers in animal populations as biomonitors for human-induced environmental change

Genetic markers provide potentially sensitive indicators of changes in environmental conditions because the genetic constitution of populations is normally altered well before populations become extinct. Genetic indicators in populations include overall genetic diversity, genetic changes in traits measured at the phenotypic level, and evolution at specific loci under selection. While overall genetic diversity has rarely been successfully related to environmental conditions, genetically based changes in traits have now been linked to the presence of toxins and both local and global temperature shifts. Candidate loci for monitoring stressors are emerging from information on how specific genes influence traits, and from screens of random loci across environmental gradients. Drosophila research suggests that chromosomal regions under recent intense selection can be identified from patterns of molecular variation and a high frequency of transposable element insertions. Allele frequency changes at candidate loci have been linked to pesticides, pollutants and climate change. Nevertheless, there are challenges in interpreting allele frequencies in populations, particularly when a large number of loci control a trait and when interactions between alleles influence trait expression. To meet these challenges, population samples should be collected for longitudinal studies, and experimental programmes should be undertaken to link variation at candidate genes to ecological processes.     

Simultaneous mapping of epistatic QTL in DU6i × DBA/2 mice

We have mapped epistatic quantitative trait loci (QTL) in an F₂ cross between DU6i × DBA/2 mice. By including these epistatic QTL and their interaction parameters in the genetic model, we were able to increase the genetic variance explained substantially (8.8%–128.3%) for several growth and body composition traits. We used an analysis method based on a simultaneous search for epistatic QTL pairs without assuming that the QTL had any effect individually. We were able to detect several QTL that could not be detected in a search for marginal QTL effects because the epistasis cancelled out the individual effects of the QTL. In total, 23 genomic regions were found to contain QTL affecting one or several of the traits and eight of these QTL did not have significant individual effects. We identified 44 QTL pairs with significant effects on the traits, and, for 28 of the pairs, an epistatic QTL model fit the data significantly better than a model without interactions. The epistatic pairs were classified by the significance of the epistatic parameters in the genetic model, and visual inspection of the two-locus genotype means identified six types of related genotype–phenotype patterns among the pairs. Five of these patterns resembled previously published patterns of QTL interactions.     

Epistasis Is a Major Determinant of the Additive Genetic Variance in Mimulus guttatus

The influence of genetic interactions (epistasis) on the genetic variance of quantitative traits is a major unresolved problem relevant to medical, agricultural, and evolutionary genetics. The additive genetic component is typically a high proportion of the total genetic variance in quantitative traits, despite that underlying genes must interact to determine phenotype. This study estimates direct and interaction effects for 11 pairs of Quantitative Trait Loci (QTLs) affecting floral traits within a single population of Mimulus guttatus. With estimates of all 9 genotypes for each QTL pair, we are able to map from QTL effects to variance components as a function of population allele frequencies, and thus predict changes in variance components as allele frequencies change. This mapping requires an analytical framework that properly accounts for bias introduced by estimation errors. We find that even with abundant interactions between QTLs, most of the genetic variance is likely to be additive. However, the strong dependency of allelic average effects on genetic background implies that epistasis is a major determinant of the additive genetic variance, and thus, the population’s ability to respond to selection.     

Genome-Wide Association Analysis of Adaptation Using Environmentally Predicted Traits

Current methods for studying the genetic basis of adaptation evaluate genetic associations with ecologically relevant traits or single environmental variables, under the implicit assumption that natural selection imposes correlations between phenotypes, environments and genotypes. In practice, observed trait and environmental data are manifestations of unknown selective forces and are only indirectly associated with adaptive genetic variation. In theory, improved estimation of these forces could enable more powerful detection of loci under selection. Here we present an approach in which we approximate adaptive variation by modeling phenotypes as a function of the environment and using the predicted trait in multivariate and univariate genome-wide association analysis (GWAS). Based on computer simulations and published flowering time data from the model plant Arabidopsis thaliana, we find that environmentally predicted traits lead to higher recovery of functional loci in multivariate GWAS and are more strongly correlated to allele frequencies at adaptive loci than individual environmental variables. Our results provide an example of the use of environmental data to obtain independent and meaningful information on adaptive genetic variation.     

The genetic basis of adaptive population differentiation: a quantitative trait locus analysis of fitness traits in two wild barley populations from contrasting habitats

We used a quantitative trait locus (QTL) approach to study the genetic basis of population differentiation in wild barley, Hordeum spontaneum. Several ecotypes are recognized in this model species, and population genetic studies and reciprocal transplant experiments have indicated the role of local adaptation in shaping population differences. We derived a mapping population from a cross between a coastal Mediterranean population and a steppe inland population from Israel and assessed F3 progeny fitness in the natural growing environments of the two parental populations. Dilution of the local gene pool, estimated as the proportion of native alleles at 96 marker loci in the recombinant lines, negatively affected fitness traits at both sites. QTLs for fitness traits tended to differ in the magnitude but not in the direction of their effects across sites, with beneficial alleles generally conferring a greater fitness advantage at their native site. Several QTLs showed fitness effects at one site only, but no opposite selection on individual QTLs was observed across the sites. In a common-garden experiment, we explored the hypothesis that the two populations have adapted to divergent nutrient availabilities. In the different nutrient environments of this experiment, but not under field conditions, fitness of the F3 progeny lines increased with the number of heterozygous marker loci. Comparison of QTL-effects that underlie genotype x nutrient interaction in the common-garden experiment and genotype x site interaction in the field suggested that population differentiation at the field sites may have been driven by divergent nutrient availabilities to a limited extent. Also in this experiment no QTLs were observed with opposite fitness effects in contrasting environments. Our data are consistent with the view that adaptive differentiation can be based on selection on multiple traits changing gradually along ecological gradients. This can occur without QTLs showing opposite fitness effects in the different environments, that is, in the absence of genetic trade-offs in performance between environments.     

Statistical Mechanics and the Evolution of Polygenic Quantitative Traits

The evolution of quantitative characters depends on the frequencies of the alleles involved, yet these frequencies cannot usually be measured. Previous groups have proposed an approximation to the dynamics of quantitative traits, based on an analogy with statistical mechanics. We present a modified version of that approach, which makes the analogy more precise and applies quite generally to describe the evolution of allele frequencies. We calculate explicitly how the macroscopic quantities (i.e., quantities that depend on the quantitative trait) depend on evolutionary forces, in a way that is independent of the microscopic details. We first show that the stationary distribution of allele frequencies under drift, selection, and mutation maximizes a certain measure of entropy, subject to constraints on the expectation of observable quantities. We then approximate the dynamical changes in these expectations, assuming that the distribution of allele frequencies always maximizes entropy, conditional on the expected values. When applied to directional selection on an additive trait, this gives a very good approximation to the evolution of the trait mean and the genetic variance, when the number of mutations per generation is sufficiently high (4Nμ > 1). We show how the method can be modified for small mutation rates (4Nμ → 0). We outline how this method describes epistatic interactions as, for example, with stabilizing selection.     

A Direct Assessment of the Role of Genetic Drift in Determining Allele Frequency Variation in Populations of EUPHYDRYAS EDITHA

Estimates of allele frequencies at six polymorphic loci were collected over eight generations in two populations of Euphydryas editha. We have estimated, in addition, the effective population size for each generation for both populations with results from mark-recapture and other field data. The variation in allele frequencies generated by random genetic drift was then studied using computer simulations and our direct estimates of effective population size. Substantial differences between observed values and computer-generated expected values assuming drift alone were found for three loci (Got, Hk, Pgi) in one population. These observations are consistent with natural selection in a variable environment.