Genetic architecture affecting maize agronomic traits identified by variance heterogeneity association mapping.

Conventional genome-wide association studies (GWAS) focused on the phenotypic mean differences (mGWAS) but often ignored genetic variants influencing differences in the variance between genotypes. In this study, we performed variance heterogeneity GWAS (vGWAS) analysis for 13 previously measured agronomic traits in a maize population. We discovered a total of 129 significant SNPs. We demonstrated that the genetic loci influencing mean differences and variance heterogeneity formed distinct groups, suggesting that breeders were able to independently select for phenotype mean and variance values. Moreover, vGWAS served as a tractable approach to effectively identify 214 epistatic interaction pairs. In addition, we documented four agronomic traits with decreasing phenotype variance during modern maize breeding history and identified the potential genetic variants influencing this process. In summary, we discovered additional non-additive effects contributing to missing heritability and valuable genetic variants used for breeding varieties with desired phenotypic variance.

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.).

Score tests for scale effects, with application to genomic analysis.

Tests for variance or scale effects due to covariates are used in many areas and recently, in genomic and genetic association studies. We study score tests based on location-scale models with arbitrary error distributions that allow incorporation of additional adjustment covariates. Tests based on Gaussian and Laplacian double generalized linear models are examined in some detail. Numerical properties of the tests under Gaussian and other error distributions are examined. Our results show that the use of model-based asymptotic distributions with score tests for scale effects does not control type 1 error well in many settings of practical relevance. We consider simple statistics based on permutation distribution approximations, which correspond to well-known statistics derived by another approach. They are shown to give good type 1 error control under different error distributions and under covariate distribution imbalance. The methods are illustrated through a differential gene expression analysis involving breast cancer tumor samples.

Analytical strategies to include the X-chromosome in variance heterogeneity analyses: Evidence for trait-specific polygenic variance structure.

Genotype-stratified variance of a quantitative trait could differ in the presence of gene-gene or gene-environment interactions. Genetic markers associated with phenotypic variance are thus considered promising candidates for follow-up interaction or joint location-scale analyses. However, as in studies of main effects, the X-chromosome is routinely excluded from "whole-genome" scans due to analytical challenges. Specifically, as males carry only one copy of the X-chromosome, the inherent sex-genotype dependency could bias the trait-genotype association, through sexual dimorphism in quantitative traits with sex-specific means or variances. Here we investigate phenotypic variance heterogeneity associated with X-chromosome single nucleotide polymorphisms (SNPs) and propose valid and powerful strategies. Among those, a generalized Levene's test has adequate power and remains robust to sexual dimorphism. An alternative approach is a sex-stratified analysis but at the cost of slightly reduced power and modeling flexibility. We applied both methods to an Estonian study of gene expression quantitative trait loci (eQTL; n = 841), and two complex trait studies of height, hip, and waist circumferences, and body mass index from Multi-Ethnic Study of Atherosclerosis (MESA; n = 2,073) and UK Biobank (UKB; n = 327,393). Consistent with previous eQTL findings on mean, we found some but no conclusive evidence for cis regulators being enriched for variance association. SNP rs2681646 is associated with variance of waist circumference (p = 9.5E-07) at X-chromosome-wide significance in UKB, with a suggestive female-specific effect in MESA (p = 0.048). Collectively, an enrichment analysis using permutated UKB (p < 0.1) and MESA (p < 0.01) datasets, suggests a possible polygenic structure for the variance of human height.

Beyond the traditional simulation design for evaluating type 1 error control: From the "theoretical" null to "empirical" null.

When evaluating a newly developed statistical test, an important step is to check its type 1 error (T1E) control using simulations. This is often achieved by the standard simulation design S0 under the so-called "theoretical" null of no association. In practice, the whole-genome association analyses scan through a large number of genetic markers ( G s) for the ones associated with an outcome of interest ( Y ), where Y comes from an alternative while the majority of G s are not associated with Y ; the Y - G relationships are under the "empirical" null. This reality can be better represented by two other simulation designs, where design S1.1 simulates Y from analternative model based on G , then evaluates its association with independently generated G n e w ; while design S1.2 evaluates the association between permutated Y and G . More than a decade ago, Efron (2004) has noted the important distinction between the "theoretical" and "empirical" null in false discovery rate control. Using scale tests for variance heterogeneity, direct univariate, and multivariate interaction tests as examples, here we show that not all null simulation designs are equal. In examining the accuracy of a likelihood ratio test, while simulation design S0 suggested the method being accurate, designs S1.1 and S1.2 revealed its increased empirical T1E rate if applied in real data setting. The inflation becomes more severe at the tail and does not diminish as sample size increases. This is an important observation that calls for new practices for methods evaluation and T1E control interpretation.

Simulating variance heterogeneity in quantitative genome wide association studies.

BACKGROUND: Analyzing Variance heterogeneity in genome wide association studies (vGWAS) is an emerging approach for detecting genetic loci involved in gene-gene and gene-environment interactions. vGWAS analysis detects variability in phenotype values across genotypes, as opposed to typical GWAS analysis, which detects variations in the mean phenotype value. RESULTS: A handful of vGWAS analysis methods have been recently introduced in the literature. However, very little work has been done for evaluating these methods. To enable the development of better vGWAS analysis methods, this work presents the first quantitative vGWAS simulation procedure. To that end, we describe the mathematical framework and algorithm for generating quantitative vGWAS phenotype data from genotype profiles. Our simulation model accounts for both haploid and diploid genotypes under different modes of dominance. Our model is also able to simulate any number of genetic loci causing mean and variance heterogeneity. CONCLUSIONS: We demonstrate the utility of our simulation procedure through generating a variety of genetic loci types to evaluate common GWAS and vGWAS analysis methods. The results of this evaluation highlight the challenges current tools face in detecting GWAS and vGWAS loci.

Detecting Gene-Environment Interactions for a Quantitative Trait in a Genome-Wide Association Study.

A genome-wide association study (GWAS) typically is focused on detecting marginal genetic effects. However, many complex traits are likely to be the result of the interplay of genes and environmental factors. These SNPs may have a weak marginal effect and thus unlikely to be detected from a scan of marginal effects, but may be detectable in a gene-environment (G × E) interaction analysis. However, a genome-wide interaction scan (GWIS) using a standard test of G × E interaction is known to have low power, particularly when one corrects for testing multiple SNPs. Two 2-step methods for GWIS have been previously proposed, aimed at improving efficiency by prioritizing SNPs most likely to be involved in a G × E interaction using a screening step. For a quantitative trait, these include a method that screens on marginal effects [Kooperberg and Leblanc, 2008] and a method that screens on variance heterogeneity by genotype [Paré et al., 2010] In this paper, we show that the Paré et al. approach has an inflated false-positive rate in the presence of an environmental marginal effect, and we propose an alternative that remains valid. We also propose a novel 2-step approach that combines the two screening approaches, and provide simulations demonstrating that the new method can outperform other GWIS approaches. Application of this method to a G × Hispanic-ethnicity scan for childhood lung function reveals a SNP near the MARCO locus that was not identified by previous marginal-effect scans.

On the relationship between epistasis and genetic variance heterogeneity.

Epistasis and genetic variance heterogeneity are two non-additive genetic inheritance patterns that are often, but not always, related. Here we use theoretical examples and empirical results from earlier analyses of experimental data to illustrate the connection between the two. This includes an introduction to the relationship between epistatic gene action, statistical epistasis, and genetic variance heterogeneity, and a brief discussion about how genetic processes other than epistasis can also give rise to genetic variance heterogeneity.

Putting the Genome in Context: Gene-Environment Interactions in Type 2 Diabetes.

The genome is often the conduit through which environmental exposures convey their effects on health and disease. Whilst not all diseases act by directly perturbing the genome, the phenotypic responses are often genetically determined. Hence, whilst diseases are often defined has having differing degrees of genetic determination, genetic and environmental factors are, with few exceptions, inseparable features of most diseases, not least type 2 diabetes. It follows that to optimize diabetes, prevention and treatment will require that the etiological roles of genetic and environmental risk factors be jointly considered. As we discuss here, studies focused on quantifying gene-environment and gene-treatment interactions are gathering momentum and may eventually yield data that helps guide health-related choices and medical interventions for type 2 diabetes and other complex diseases.

A family-based joint test for mean and variance heterogeneity for quantitative traits.

Traditional quantitative trait locus (QTL) analysis focuses on identifying loci associated with mean heterogeneity. Recent research has discovered loci associated with phenotype variance heterogeneity (vQTL), which is important in studying genetic association with complex traits, especially for identifying gene-gene and gene-environment interactions. While several tests have been proposed to detect vQTL for unrelated individuals, there are no tests for related individuals, commonly seen in family-based genetic studies. Here we introduce a likelihood ratio test (LRT) for identifying mean and variance heterogeneity simultaneously or for either effect alone, adjusting for covariates and family relatedness using a linear mixed effect model approach. The LRT test statistic for normally distributed quantitative traits approximately follows χ(2)-distributions. To correct for inflated Type I error for non-normally distributed quantitative traits, we propose a parametric bootstrap-based LRT that removes the best linear unbiased prediction (BLUP) of family random effect. Simulation studies show that our family-based test controls Type I error and has good power, while Type I error inflation is observed when family relatedness is ignored. We demonstrate the utility and efficiency gains of the proposed method using data from the Framingham Heart Study to detect loci associated with body mass index (BMI) variability.

Scoring the Icecap-a capability instrument. Estimation of a UK general population tariff.

This paper reports the results of a best-worst scaling (BWS) study to value the Investigating Choice Experiments Capability Measure for Adults (ICECAP-A), a new capability measure among adults, in a UK setting. A main effects plan plus its foldover was used to estimate weights for each of the four levels of all five attributes. The BWS study was administered to 413 randomly sampled individuals, together with sociodemographic and other questions. Scale-adjusted latent class analyses identified two preference and two (variance) scale classes. Ability to characterize preference and scale heterogeneity was limited, but data quality was good, and the final model exhibited a high pseudo-r-squared. After adjusting for heterogeneity, a population tariff was estimated. This showed that 'attachment' and 'stability' each account for around 22% of the space, and 'autonomy', 'achievement' and 'enjoyment' account for around 18% each. Across all attributes, greater value was placed on the difference between the lowest levels of capability than between the highest. This tariff will enable ICECAP-A to be used in economic evaluation both within the field of health and across public policy generally.

Genetic architecture of trait variance in craniofacial morphology.

The genetic architecture of trait variance has long been of interest in genetics and evolution. One of the earliest attempts to understand this architecture was presented in Lerner's Genetic Homeostasis (1954). Lerner proposed that heterozygotes should be better able to tolerate environmental perturbations because of functional differences between the alleles at a given locus, with each allele optimal for slightly different environments. This greater robustness to environmental variance, he argued, would result in smaller trait variance for heterozygotes. The evidence for Lerner's hypothesis has been inconclusive. To address this question using modern genomic methods, we mapped loci associated with differences in trait variance (vQTL) on 1,101 individuals from the F34 of an advanced intercross between LG/J and SM/J mice. We also mapped epistatic interactions for these vQTL in order to understand the influence of epistasis for the architecture of trait variance. We did not find evidence supporting Lerner's hypothesis, that heterozygotes tend to have smaller trait variances than homozygotes. We further show that the effects of most mapped loci on trait variance are produced by epistasis affecting trait means and that those epistatic effects account for about a half of the differences in genotypic-specific trait variances. Finally, we propose a model where the different interactions between the additive and dominance effects of the vQTL and their epistatic partners can explain Lerner's original observations but can also be extended to include other conditions where heterozygotes are not the least variable genotype.

The Relevance of the Expected Value of the Proportion of Arabian Genes in Genetic Evaluations for Eventing Competitions.

The Arabian horse is a generally reliable sport horse, and continues to be a remarkable endurance horse, so the relevance of the expected value of the proportion of Arabian genes (EV%AG) in horses participating in eventing could be a relevant factor. A total of 1089 horses participating in eventing (8866 records) were used. A GLM revealed that the EV%AG was significant in dressage, show jumping and cross-country. A BLUP genetic evaluation was computed with five genetic models (without the EV%AG (0) using as a covariate (A), as a fixed effect (B), with variance heterogeneity, and in genetic groups without (C) and with (D)). Dressage heritability ranged from 0.103 to 0.210, show jumping ranged from 0.117 to 0.203 and cross-country ranged from 0.070 to 0.099. The lowest DIC value was used as a criterion of fitness. The best fits (those which included variance heterogeneity) showed fewer than two points of difference in DIC values. The highest average estimated breeding value in dressage, show jumping and cross-country was found for horses with an expected value of the proportion of Arabian genes of 0%, ≥1% to <25%, and 100%, respectively. Therefore, the best way to model the EV%AG effect seems to be by considering the variance heterogeneity.

A taxonomy of multiple regression methods for immunologists.

Multiple regression is a powerful tool in the immunologist's toolbox. This paper defines multiple regression, discusses availability and accessibility, provides some additional helpful definitions, treats the topics of transformation and extreme value screening, and establishes the paper's scope and philosophy. Then eleven methods of multiple regression are detailed, giving strengths and limitations. Throughout an emphasis is placed on application to immunological assays. A flowchart to guide selection of multiple regression methods is provided.

Basal Reactivity Evaluated by Infrared Thermography in the "Caballo de Deporte Español" Horse Breed According to Its Coat Color.

Horses have been valued for their diversity of coat color since prehistoric times. In particular, the pleiotropic effect that coat color genes have on behavior determines the way the horse perceives and reacts to its environment. The primary aim of this study was to evaluate the influence of coat color on basal reactivity assessed with infrared thermography as eye temperature at rest (ETR), determine their relation with the results obtained by these horses in Show Jumping competitions and to estimate the genetic parameters for this variable to test its suitability for genetic selection. A General Linear Model (GLM) and Duncan post-hoc analysis indicated differences in ETR due to coat color, sex, age, location, and breed-group factors. A Spearman's rank correlation of 0.11 (p < 0.05) was found with ranking, indicating that less reactive horses were more likely to achieve better rankings. Heritability values ranged from 0.17 to 0.22 and were computed with a model with genetic groups and a model with residual variance heterogeneity. Breeding values were higher with the last genetic model, thus demonstrating the pleiotropic effect of coat color. These results indicate that ETR has a suitable genetic basis to be used in the breeding program to select for basal reactivity due to coat color.

gJLS2: an R package for generalized joint location and scale analysis in X-inclusive genome-wide association studies.

A joint analysis of location and scale can be a powerful tool in genome-wide association studies to uncover previously overlooked markers that influence a quantitative trait through both mean and variance, as well as to prioritize candidates for gene-environment interactions. This approach has recently been generalized to handle related samples, dosage data, and the analytically challenging X-chromosome. We disseminate the latest advances in methodology through a user-friendly R software package with added functionalities to support genome-wide analysis on individual-level or summary-level data. The implemented R package can be called from PLINK or directly in a scripting environment, to enable a streamlined genome-wide analysis for biobank-scale data. Application results on individual-level and summary-level data highlight the advantage of the joint test to discover more genome-wide signals as compared to a location or scale test alone. We hope the availability of gJLS2 software package will encourage more scale and/or joint analyses in large-scale datasets, and promote the standardized reporting of their P-values to be shared with the scientific community.

A statistical measure for the skewness of X chromosome inactivation for quantitative traits and its application to the MCTFR data.

BACKGROUND: X chromosome inactivation (XCI) is that one of two chromosomes in mammalian females is silenced during early development of embryos. There has been a statistical measure for the degree of the skewness of XCI for qualitative traits. However, no method is available for such task at quantitative trait loci. RESULTS: In this article, we extend the existing statistical measure for the skewness of XCI for qualitative traits, and the likelihood ratio, Fieller's and delta methods for constructing the corresponding confidence intervals, and make them accommodate quantitative traits. The proposed measure is a ratio of two linear regression coefficients when association exists. Noting that XCI may cause variance heterogeneity of the traits across different genotypes in females, we obtain the point estimate and confidence intervals of the measure by incorporating such information. The hypothesis testing of the proposed methods is also investigated. We conduct extensive simulation studies to assess the performance of the proposed methods. Simulation results demonstrate that the median of the point estimates of the measure is very close to the pre-specified true value. The likelihood ratio and Fieller's methods control the size well, and have the similar test power and accurate coverage probability, which perform better than the delta method. So far, we are not aware of any association study for the X-chromosomal loci in the Minnesota Center for Twin and Family Research data. So, we apply our proposed methods to these data for their practical use and find that only the rs792959 locus, which is simultaneously associated with the illicit drug composite score and behavioral disinhibition composite score, may undergo XCI skewing. However, this needs to be confirmed by molecular genetics. CONCLUSIONS: We recommend the Fieller's method in practical use because it is a non-iterative procedure and has the similar performance to the likelihood ratio method.

Ambient air pollution and depression: A systematic review with meta-analysis up to 2019.

Although epidemiological studies have evaluated the associations of ambient air pollution with depression, the results remained mixed. To clarify the nature of the association, we performed a comprehensive systematic review and meta-analysis with the Inverse Variance Heterogeneity (IVhet) model to estimate the effect of ambient air pollution on depression. Three English and four Chinese databases were searched for epidemiologic studies investigating associations of ambient particulate (diameter ≤ 2.5 µm (PM2.5), ≤10 µm (PM10)) and gaseous (nitric oxide (NO), nitrogen dioxide (NO2), carbon monoxide (CO), sulfur dioxide (SO2) and ozone (O3)) air pollutants with depression. Odds ratios (OR) and corresponding 95% confidence intervals (CI) were calculated to evaluate the strength of the associations. We identified 22 eligible studies from 10 countries of the world. Under the IVhet model, per 10 µg/m3 increase in long-term exposure to PM2.5 (OR: 1.12, 95% CI: 0.97-1.29, I2: 51.6), PM10 (OR: 1.04, 95% CI: 0.88-1.25, I2: 85.7), and NO2 (OR: 1.05, 95% CI: 0.83-1.34, I2: 83.6), as well as short-term exposure to PM2.5 (OR: 1.01, 95% CI: 0.99-1.04, I2: 51.6), PM10 (OR: 1.01, 95% CI: 0.98-1.04, I2: 86.7), SO2 (OR: 1.03, 95% CI: 0.99-1.07, I2: 71.2), and O3 (OR: 1.01, 95% CI: 0.99-1.03, I2: 82.2) was not significantly associated with depression. However, we observed significant association between short-term NO2 exposure (per 10 µg/m3 increase) and depression (OR: 1.02, 95% CI: 1.00-1.04, I2: 65.4). However, the heterogeneity was high for all of the pooled estimates, which reduced credibility of the cumulative evidence. Additionally, publication bias was detected for six of eight meta-estimates. In conclusion, short-term exposure to NO2, but not other air pollutants, was significantly associated with depression. Given the limitations, a larger meta-analysis incorporating future well-designed longitudinal studies, and investigations into potential biologic mechanisms, will be necessary for a more definitive result.

vqtl: An R Package for Mean-Variance QTL Mapping.

We present vqtl, an R package for mean-variance QTL mapping. This QTL mapping approach tests for genetic loci that influence the mean of the phenotype, termed mean QTL, the variance of the phenotype, termed variance QTL, or some combination of the two, termed mean-variance QTL. It is unique in its ability to correct for variance heterogeneity arising not only from the QTL itself but also from nuisance factors, such as sex, batch, or housing. This package provides functions to conduct genome scans, run permutations to assess the statistical significance, and make informative plots to communicate results. Because it is inter-operable with the popular qtl package and uses many of the same data structures and input patterns, it will be straightforward for geneticists to analyze future experiments with vqtl as well as re-analyze past experiments, possibly discovering new QTL.