A rapid epistatic mixed-model association analysis by linear retransformations of genomic estimated values

FastBiCmrMLM: a fast and powerful compressed variance component mixed logistic model for big genomic case-control genome-wide association study

Large sample datasets have been regarded as the primary basis for innovative discoveries and the solution to missing heritability in genome-wide association studies. However, their computational complexity cannot consider all comprehensive effects and all polygenic backgrounds, which reduces the effectiveness of large datasets. To address these challenges, we included all effects and polygenic backgrounds in a mixed logistic model for binary traits and compressed four variance components into two. The compressed model combined three computational algorithms to develop an innovative method, called FastBiCmrMLM, for large data analysis. These algorithms were tailored to sample size, computational speed, and reduced memory requirements. To mine additional genes, linkage disequilibrium markers were replaced by bin-based haplotypes, which are analyzed by FastBiCmrMLM, named FastBiCmrMLM-Hap. Simulation studies highlighted the superiority of FastBiCmrMLM over GMMAT, SAIGE and fastGWA-GLMM in identifying dominant, small α (allele substitution effect), and rare variants. In the UK Biobank-scale dataset, we demonstrated that FastBiCmrMLM could detect variants as small as 0.03% and with α ≈ 0. In re-analyses of seven diseases in the WTCCC datasets, 29 candidate genes, with both functional and TWAS evidence, around 36 variants identified only by the new methods, strongly validated the new methods. These methods offer a new way to decipher the genetic architecture of binary traits and address the challenges outlined above.

Whole-Genome Resequencing Reveals Genetic Diversity and Wool Trait-Related Genes in Liangshan Semi-Fine-Wool Sheep

Understanding the genetic makeup of local sheep breeds is essential for their scientific conservation and sustainable utilization. The Liangshan semi-fine-wool sheep (LSS), a Chinese semi-fine-wool breed renowned for its soft wool, was analyzed using whole-genome sequencing data including 35 LSS, 84 sheep from other domestic breeds, and 20 Asiatic mouflons. We investigated the genetic composition of LSS by conducting analyses of the population structure, runs of homozygosity, genomic inbreeding coefficients, and selection signature. Our findings indicated that LSS shares greater genetic similarity with Border Leicester and Romney sheep than with Tibetan (TIB), Yunnan (YNS), and Chinese Merino sheep. Genomic analysis indicated low to moderate inbreeding coefficients, ranging from 0.014 to 0.154. In identifying selection signals across the LSS genome, we pinpointed 195 candidate regions housing 74 annotated genes (e.g., IRF2BP2, BVES, and ALOX5). We also found the overlaps between the candidate regions and several known quantitative trait loci related to wool traits, such as the wool staple length and wool fiber diameter. A selective sweep region, marked by the highest value of cross-population extended haplotype homozygosity, encompassed IRF2BP2-an influential candidate gene affecting fleece fiber traits. Furthermore, notable differences in genotype frequency at a mutation site (c.1051 + 46T > C, Chr25: 6,784,190 bp) within IRF2BP2 were observed between LSS and TIB and YNS sheep (Fisher's exact test, p < 2.2 × 10-16). Taken together, these findings offer insights crucial for the conservation and breeding enhancement of LSS.

Compressed variance component mixed model reveals epistasis associated with flowering in Arabidopsis

Introduction

Epistasis is currently a topic of great interest in molecular and quantitative genetics. Arabidopsis thaliana, as a model organism, plays a crucial role in studying the fundamental biology of diverse plant species. However, there have been limited reports about identification of epistasis related to flowering in genome-wide association studies (GWAS). Therefore, it is of utmost importance to conduct epistasis in Arabidopsis.

Method

In this study, we employed Levene's test and compressed variance component mixed model in GWAS to detect quantitative trait nucleotides (QTNs) and QTN-by-QTN interactions (QQIs) for 11 flowering-related traits of 199 Arabidopsis accessions with 216,130 markers.

Results

Our analysis detected 89 QTNs and 130 pairs of QQIs. Around these loci, 34 known genes previously reported in Arabidopsis were confirmed to be associated with flowering-related traits, such as SPA4, which is involved in regulating photoperiodic flowering, and interacts with PAP1 and PAP2, affecting growth of Arabidopsis under light conditions. Then, we observed significant and differential expression of 35 genes in response to variations in temperature, photoperiod, and vernalization treatments out of unreported genes. Functional enrichment analysis revealed that 26 of these genes were associated with various biological processes. Finally, the haplotype and phenotypic difference analysis revealed 20 candidate genes exhibiting significant phenotypic variations across gene haplotypes, of which the candidate genes AT1G12990 and AT1G09950 around QQIs might have interaction effect to flowering time regulation in Arabidopsis.

Discussion

These findings may offer valuable insights for the identification and exploration of genes and gene-by-gene interactions associated with flowering-related traits in Arabidopsis, that may even provide valuable reference and guidance for the research of epistasis in other species.

Dissecting Complex Traits Using Omics Data: A Review on the Linear Mixed Models and Their Application in GWAS

Genome-wide association study (GWAS) is the most popular approach to dissecting complex traits in plants, humans, and animals. Numerous methods and tools have been proposed to discover the causal variants for GWAS data analysis. Among them, linear mixed models (LMMs) are widely used statistical methods for regulating confounding factors, including population structure, resulting in increased computational proficiency and statistical power in GWAS studies. Recently more attention has been paid to pleiotropy, multi-trait, gene-gene interaction, gene-environment interaction, and multi-locus methods with the growing availability of large-scale GWAS data and relevant phenotype samples. In this review, we have demonstrated all possible LMMs-based methods available in the literature for GWAS. We briefly discuss the different LMM methods, software packages, and available open-source applications in GWAS. Then, we include the advantages and weaknesses of the LMMs in GWAS. Finally, we discuss the future perspective and conclusion. The present review paper would be helpful to the researchers for selecting appropriate LMM models and methods quickly for GWAS data analysis and would benefit the scientific society.

Genetic Dissection of Epistatic Interactions Contributing Yield-Related Agronomic Traits in Rice Using the Compressed Mixed Model

Rice (Oryza sativa) is one of the most important cereal crops in the world, and yield-related agronomic traits, including plant height (PH), panicle length (PL), and protein content (PC), are prerequisites for attaining the desired yield and quality in breeding programs. Meanwhile, the main effects and epistatic effects of quantitative trait nucleotides (QTNs) are all important genetic components for yield-related quantitative traits. In this study, we conducted genome-wide association studies (GWAS) for 413 rice germplasm resources, with 36,901 single nucleotide polymorphisms (SNPs), to identify QTNs, QTN-by-QTN interaction (QQI), and their candidate genes, using a multi-locus compressed variance component mixed model, 3VmrMLM. As a result, two significant QTNs and 56 paired QQIs were detected, amongst 5219 genes of these QTNs, and 26 genes were identified as the yield-related confirmed genes, such as LCRN1, OsSPL3, and OsVOZ1 for PH, and LOG and QsBZR1 for PL. To reveal the substantial contributions related to the variation of yield-related agronomic traits in rice, we further implemented an enrichment analysis and expression analysis. As the results showed, 114 genes, nearly all significant QQIs, were involved in 37 GO terms; for example, the macromolecule metabolic process (GO:0043170), intracellular part (GO:0044424), and binding (GO:0005488). It was revealed that most of the QQIs and the candidate genes were significantly involved in the biological process, molecular function, and cellular component of the target traits. The demonstrated genetic interactions play a critical role in yield-related agronomic traits of rice, and such epistatic interactions contributed to large portions of the missing heritability in GWAS. These results help us to understand the genetic basis underlying the inheritance of the three yield-related agronomic traits and provide implications for rice improvement.

A compressed variance component mixed model for detecting QTNs and QTN-by-environment and QTN-by-QTN interactions in genome-wide association studies

Although genome-wide association studies are widely used to mine genes for quantitative traits, the effects to be estimated are confounded, and the methodologies for detecting interactions are imperfect. To address these issues, the mixed model proposed here first estimates the genotypic effects for AA, Aa, and aa, and the genotypic polygenic background replaces additive and dominance polygenic backgrounds. Then, the estimated genotypic effects are partitioned into additive and dominance effects using a one-way analysis of variance model. This strategy was further expanded to cover QTN-by-environment interactions (QEIs) and QTN-by-QTN interactions (QQIs) using the same mixed-model framework. Thus, a three-variance-component mixed model was integrated with our multi-locus random-SNP-effect mixed linear model (mrMLM) method to establish a new methodological framework, 3VmrMLM, that detects all types of loci and estimates their effects. In Monte Carlo studies, 3VmrMLM correctly detected all types of loci and almost unbiasedly estimated their effects, with high powers and accuracies and a low false positive rate. In re-analyses of 10 traits in 1439 rice hybrids, detection of 269 known genes, 45 known gene-by-environment interactions, and 20 known gene-by-gene interactions strongly validated 3VmrMLM. Further analyses of known genes showed more small (67.49%), minor-allele-frequency (35.52%), and pleiotropic (30.54%) genes, with higher repeatability across datasets (54.36%) and more dominance loci. In addition, a heteroscedasticity mixed model in multiple environments and dimension reduction methods in quite a number of environments were developed to detect QEIs, and variable selection under a polygenic background was proposed for QQI detection. This study provides a new approach for revealing the genetic architecture of quantitative traits.

Effects of kinship correction on inflation of genetic interaction statistics in commonly used mouse populations

It is well understood that variation in relatedness among individuals, or kinship, can lead to false genetic associations. Multiple methods have been developed to adjust for kinship while maintaining power to detect true associations. However, relatively unstudied are the effects of kinship on genetic interaction test statistics. Here, we performed a survey of kinship effects on studies of six commonly used mouse populations. We measured inflation of main effect test statistics, genetic interaction test statistics, and interaction test statistics reparametrized by the Combined Analysis of Pleiotropy and Epistasis (CAPE). We also performed linear mixed model (LMM) kinship corrections using two types of kinship matrix: an overall kinship matrix calculated from the full set of genotyped markers, and a reduced kinship matrix, which left out markers on the chromosome(s) being tested. We found that test statistic inflation varied across populations and was driven largely by linkage disequilibrium. In contrast, there was no observable inflation in the genetic interaction test statistics. CAPE statistics were inflated at a level in between that of the main effects and the interaction effects. The overall kinship matrix overcorrected the inflation of main effect statistics relative to the reduced kinship matrix. The two types of kinship matrices had similar effects on the interaction statistics and CAPE statistics, although the overall kinship matrix trended toward a more severe correction. In conclusion, we recommend using an LMM kinship correction for both main effects and genetic interactions and further recommend that the kinship matrix be calculated from a reduced set of markers in which the chromosomes being tested are omitted from the calculation. This is particularly important in populations with substantial population structure, such as recombinant inbred lines in which genomic replicates are used.

On the use of GBLUP and its extension for GWAS with additive and epistatic effects

Genomic best linear unbiased prediction (GBLUP) is the most widely used model for genome-wide predictions. Interestingly, it is also possible to perform genome-wide association studies (GWAS) based on GBLUP. Although the estimated marker effects in GBLUP are shrunken and the conventional test based on such effects has low power, it was observed that a modified test statistic can be produced and the result of test was identical to a standard GWAS model. Later, a mathematical proof was given for the special case that there is no fixed covariate in GBLUP. Since then, the new approach has been called “GWAS by GBLUP”. Nevertheless, covariates such as environmental and subpopulation effects are very common in GBLUP. Thus, it is necessary to confirm the equivalence in the general case. Recently, the concept was generalized to GWAS for epistatic effects and the new approach was termed rapid epistatic mixed-model association analysis (REMMA) because it greatly improved the computational efficiency. However, the relationship between REMMA and the standard GWAS model has not been investigated. In this study, we first provided a general mathematical proof of the equivalence between “GWAS by GBLUP” and the standard GWAS model for additive effects. Then, we compared REMMA with the standard GWAS model for epistatic effects by a theoretical investigation and by empirical data analyses. We hypothesized that the similarity of the two models is influenced by the relative contribution of additive and epistatic effects to the phenotypic variance, which was verified by empirical and simulation studies.

Rapid epistatic mixed-model association studies by controlling multiple polygenic effects

SUMMARY

We have developed a rapid mixed model algorithm for exhaustive genome-wide epistatic association analysis by controlling multiple polygenic effects. Our model can simultaneously handle additive by additive epistasis, dominance by dominance epistasis and additive by dominance epistasis, and account for intrasubject fluctuations due to individuals with repeated records. Furthermore, we suggest a simple but efficient approximate algorithm, which allows the examination of all pairwise interactions in a remarkably fast manner of linear with population size. Simulation studies are performed to investigate the properties of REMMAX. Application to publicly available yeast and human data has showed that our mixed model-based method has similar performance with simple linear model on computational efficiency. It took less than 40 h for the pairwise analysis of 5000 individuals genotyped with roughly 350 000 SNPs with five threads on Intel Xeon E5 2.6 GHz CPU.

AVAILABILITY AND IMPLEMENTATION

Source codes are freely available at https://github.com/chaoning/GMAT.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Deshrinking ridge regression for genome-wide association studies

MOTIVATION

Genome-wide association studies (GWAS) are still the primary steps toward gene discovery. The urgency is more obvious in the big data era when GWAS are conducted simultaneously for thousand traits, e.g. transcriptomic and metabolomic traits. Efficient mixed model association (EMMA) and genome-wide efficient mixed model association (GEMMA) are the widely used methods for GWAS. An algorithm with high computational efficiency is badly needed. It is interesting to note that the test statistics of the ordinary ridge regression (ORR) have the same patterns across the genome as those obtained from the EMMA method. However, ORR has never been used for GWAS due to its severe shrinkage on the estimated effects and the test statistics.

RESULTS

We introduce a degree of freedom for each marker effect obtained from ORR and use it to deshrink both the estimated effect and the standard error so that the Wald test of ORR is brought back to the same level as that of EMMA. The new method is called deshrinking ridge regression (DRR). By evaluating the methods under three different model sizes (small, medium and large), we demonstrate that DRR is more generalized for all model sizes than EMMA, which only works for medium and large models. Furthermore, DRR detect all markers in a simultaneous manner instead of scanning one marker at a time. As a result, the computational time complexity of DRR is much simpler than EMMA and about m (number of genetic variants) times simpler than that of GEMMA when the sample size is way smaller than the number of markers.

CONTACT

shizhong.xu@ucr.edu.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Efficient Algorithms for Calculating Epistatic Genomic Relationship Matrices

The genomic relationship matrix plays a key role in the analysis of genetic diversity, genomic prediction, and genome-wide association studies. The epistatic genomic relationship matrix is a natural generalization of the classic genomic relationship matrix in the sense that it implicitly models the epistatic effects among all markers. Calculating the exact form of the epistatic relationship matrix requires high computational load, and is hence not feasible when the number of markers is large, or when high-degree of epistasis is in consideration. Currently, many studies use the Hadamard product of the classic genomic relationship matrix as an approximation. However, the quality of the approximation is difficult to investigate in the strict mathematical sense. In this study, we derived iterative formulas for the precise form of the epistatic genomic relationship matrix for arbitrary degree of epistasis including both additive and dominance interactions. The key to our theoretical results is the observation of an interesting link between the elements in the genomic relationship matrix and symmetric polynomials, which motivated the application of the corresponding mathematical theory. Based on the iterative formulas, efficient recursive algorithms were implemented. Compared with the approximation by the Hadamard product, our algorithms provided a complete solution to the problem of calculating the exact epistatic genomic relationship matrix. As an application, we showed that our new algorithms easily relieved the computational burden in a previous study on the approximation behavior of two limit models.

ADDO: a comprehensive toolkit to detect, classify and visualize additive and non-additive quantitative trait loci

MOTIVATION

During the past decade, genome-wide association studies (GWAS) have been used to map quantitative trait loci (QTLs) underlying complex traits. However, most GWAS focus on additive genetic effects while ignoring non-additive effects, on the assumption that most QTL act additively. Consequently, QTLs driven by dominance and other non-additive effects could be overlooked.

RESULTS

We developed ADDO, a highly efficient tool to detect, classify and visualize QTLs with additive and non-additive effects. ADDO implements a mixed-model transformation to control for population structure and unequal relatedness that accounts for both additive and dominant genetic covariance among individuals, and decomposes single-nucleotide polymorphism effects as either additive, partial dominant, dominant or over-dominant. A matrix multiplication approach is used to accelerate the computation: a genome scan on 13 million markers from 900 individuals takes about 5 h with 10 CPUs. Analysis of simulated data confirms ADDO's performance on traits with different additive and dominance genetic variance components. We showed two real examples in outbred rat where ADDO identified significant dominant QTL that were not detectable by an additive model. ADDO provides a systematic pipeline to characterize additive and non-additive QTL in whole genome sequence data, which complements current mainstream GWAS software for additive genetic effects.

AVAILABILITY AND IMPLEMENTATION

ADDO is customizable and convenient to install and provides extensive analytics and visualizations. The package is freely available online at https://github.com/LeileiCui/ADDO.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Short communication: Replication of genome-wide association studies for milk production traits in Chinese Holstein by an efficient rotated linear mixed model

Milk is regarded as an important nutrient for humans, and Chinese Holstein cows provide high-quality milk for billions of Chinese people. Therefore, detecting quantitative trait nucleotides (QTN) or candidate genes for milk production traits in Chinese Holstein is important. In this study, we performed genome-wide association studies (GWAS) in a Chinese Holstein population of 6,675 cows and 71,633 SNP using deregressed proofs (DRP) as phenotypes to replicate our previous study in a population of 1,815 cows and 39,163 SNP using estimated breeding values (EBV) as phenotypes. The associations between 3 milk production traits-milk yield (MY), fat percentage (FP), and protein percentage (PP)-and the SNP were determined by using an efficient rotated linear mixed model, which benefits from linear transformations of genomic estimated values and Eigen decomposition of the genomic relationship matrix algorithm. In total, we detected 94 SNP that were significantly associated with one or more milk production traits, including 7 SNP for MY, 76 for FP, and 36 for PP; 87% of these SNP were distributed across Bos taurus autosomes 14 and 20. In total, 83 SNP were found to be located within the reported quantitative trait loci (QTL) regions, and one novel segment (between 1.41 and 1.49 Mb) on chromosome 14 was significantly associated with FP, which could be an important candidate QTL region. In addition, the detected intervals were narrowed down from the reported regions harboring causal variants. The top significant SNP for the 3 traits was ARS-BFGL-NGS-4939, which is located within the DGAT1 gene. Five detected genes (CYHR1, FOXH1, OPLAH, PLEC, VPS28) have effects on all 3 traits. Our study provides a suite of QTN, candidate genes, and a novel QTL associated with milk production traits, and thus forms a solid basis for genomic selection and molecular breeding for milk production traits in Chinese Holstein.

Converging phenomics and genomics to study natural variation in plant photosynthetic efficiency

In recent years developments in plant phenomic approaches and facilities have gradually caught up with genomic approaches. An opportunity lies ahead to dissect complex, quantitative traits when both genotype and phenotype can be assessed at a high level of detail. This is especially true for the study of natural variation in photosynthetic efficiency, for which forward genetics studies have yielded only a little progress in our understanding of the genetic layout of the trait. High-throughput phenotyping, primarily from chlorophyll fluorescence imaging, should help to dissect the genetics of photosynthesis at the different levels of both plant physiology and development. Specific emphasis should be directed towards understanding the acclimation of the photosynthetic machinery in fluctuating environments, which may be crucial for the identification of genetic variation for relevant traits in food crops. Facilities should preferably be designed to accommodate phenotyping of photosynthesis-related traits in such environments. The use of forward genetics to study the genetic architecture of photosynthesis is likely to lead to the discovery of novel traits and/or genes that may be targeted in breeding or bio-engineering approaches to improve crop photosynthetic efficiency. In the near future, big data approaches will play a pivotal role in data processing and streamlining the phenotype-to-gene identification pipeline.