Efficient Algorithms for Calculating Epistatic Genomic Relationship Matrices

Disentangling Multiple Sclerosis heterogeneity in the French territory among genetic and environmental factors via Bayesian heritability analysis

BACKGROUND

This study aimed to investigate the factors contributing to the variability of Multiple Sclerosis (MS) among individuals born and residing in France. Geographical variation in MS prevalence was observed in France, but the role of genetic and environmental factors in explaining this heterogeneity has not been yet elucidated.

METHODS

We employed a heritability analysis on a cohort of 403 trios with an MS-affected proband in the French population. This sample was retrieved from REFGENSEP register of MS cases collected in 23 French hospital centers from 1992 to 2017. Our objective was to quantify the proportion of MS liability variability explained by genetic variability, sex, shared environment effects, region of birth and year of birth. We further considered gene x environment (GxE) interaction effects between genetic variability and region of birth. We have implemented a Bayesian liability threshold model to obtain posterior distributions for the parameters of interest adjusting for ascertainment bias.

RESULTS

Our analysis revealed that GxE interaction effects between genetic variability and region of birth represent the primary significant explanatory factor for MS liability variability in French individuals (29 % [95 %CI: 5 %; 53 %]), suggesting that additive genetic effects are modified by environmental factors associated to the region of birth. The individual contributions of genetic variability and region of birth explained, respectively, ≈15 % and ≈16 % of MS variability, highlighting a significantly higher MS liability in individuals born in the Northern regions compared to the Southern region. Overall, the joint contribution of genetic variability, region of birth, and their interaction was then estimated to explain 65 % [95 %CI: 35 %; 92 %] of MS liability variability. The remaining proportion of MS variability is attributed to environmental exposures associated with the year of birth, shared within the same household, and specific to individuals.

CONCLUSION

Overall, our analysis highlighted the interaction between genetic variability and environmental exposures linked to the region of birth as the main factor explaining MS variability within individuals born and residing in France. Among the environmental exposures prevalent in the Northern regions, and potentially interacting with genetic variability, lower vitamin D levels due to reduced sun exposure, higher obesity prevalence and higher pollution levels represent the main risk factors in influencing MS risk. These findings emphasize the importance of accounting for environmental factors linked to geographical location in the investigation of MS risk factors, as well as to further explore the influence of GxE interactions in modifying genetic risk.

Genomic prediction for sugarcane diseases including hybrid Bayesian-machine learning approaches

Sugarcane smut and Pachymetra root rots are two serious diseases of sugarcane, with susceptible infected crops losing over 30% of yield. A heritable component to both diseases has been demonstrated, suggesting selection could improve disease resistance. Genomic selection could accelerate gains even further, enabling early selection of resistant seedlings for breeding and clonal propagation. In this study we evaluated four types of algorithms for genomic predictions of clonal performance for disease resistance. These algorithms were: Genomic best linear unbiased prediction (GBLUP), including extensions to model dominance and epistasis, Bayesian methods including BayesC and BayesR, Machine learning methods including random forest, multilayer perceptron (MLP), modified convolutional neural network (CNN) and attention networks designed to capture epistasis across the genome-wide markers. Simple hybrid methods, that first used BayesR/GWAS to identify a subset of 1000 markers with moderate to large marginal additive effects, then used attention networks to derive predictions from these effects and their interactions, were also developed and evaluated. The hypothesis for this approach was that using a subset of markers more likely to have an effect would enable better estimation of interaction effects than when there were an extremely large number of possible interactions, especially with our limited data set size. To evaluate the methods, we applied both random five-fold cross-validation and a structured PCA based cross-validation that separated 4702 sugarcane clones (that had disease phenotypes and genotyped for 26k genome wide SNP markers) by genomic relationship. The Bayesian methods (BayesR and BayesC) gave the highest accuracy of prediction, followed closely by hybrid methods with attention networks. The hybrid methods with attention networks gave the lowest variation in accuracy of prediction across validation folds (and lowest MSE), which may be a criteria worth considering in practical breeding programs. This suggests that hybrid methods incorporating the attention mechanism could be useful for genomic prediction of clonal performance, particularly where non-additive effects may be important.

Modeling within and between Sub-Genomes Epistasis of Synthetic Hexaploid Wheat for Genome-Enabled Prediction of Diseases

Common wheat (Triticum aestivum) is a hexaploid crop comprising three diploid sub-genomes labeled A, B, and D. The objective of this study is to investigate whether there is a discernible influence pattern from the D sub-genome with epistasis in genomic models for wheat diseases. Four genomic statistical models were employed; two models considered the linear genomic relationship of the lines. The first model (G) utilized all molecular markers, while the second model (ABD) utilized three matrices representing the A, B, and D sub-genomes. The remaining two models incorporated epistasis, one (GI) using all markers and the other (ABDI) considering markers in sub-genomes A, B, and D, including inter- and intra-sub-genome interactions. The data utilized pertained to three diseases: tan spot (TS), septoria nodorum blotch (SNB), and spot blotch (SB), for synthetic hexaploid wheat (SHW) lines. The results (variance components) indicate that epistasis makes a substantial contribution to explaining genomic variation, accounting for approximately 50% in SNB and SB and only 29% for TS. In this contribution of epistasis, the influence of intra- and inter-sub-genome interactions of the D sub-genome is crucial, being close to 50% in TS and higher in SNB (60%) and SB (60%). This increase in explaining genomic variation is reflected in an enhancement of predictive ability from the G model (additive) to the ABDI model (additive and epistasis) by 9%, 5%, and 1% for SNB, SB, and TS, respectively. These results, in line with other studies, underscore the significance of the D sub-genome in disease traits and suggest a potential application to be explored in the future regarding the selection of parental crosses based on sub-genomes.

Genomic prediction with machine learning in sugarcane, a complex highly polyploid clonally propagated crop with substantial non-additive variation for key traits

Sugarcane has a complex, highly polyploid genome with multi-species ancestry. Additive models for genomic prediction of clonal performance might not capture interactions between genes and alleles from different ploidies and ancestral species. As such, genomic prediction in sugarcane presents an interesting case for machine learning (ML) methods, which are purportedly able to deal with high levels of complexity in prediction. Here, we investigated deep learning (DL) neural networks, including multilayer networks (MLP) and convolution neural networks (CNN), and an ensemble machine learning approach, random forest (RF), for genomic prediction in sugarcane. The data set used was 2912 sugarcane clones, scored for 26,086 genome wide single nucleotide polymorphism markers, with final assessment trial data for total cane harvested (TCH), commercial cane sugar (CCS), and fiber content (Fiber). The clones in the latest trial (2017) were used as a validation set. We compared prediction accuracy of these methods to genomic best linear unbiased prediction (GBLUP) extended to include dominance and epistatic effects. The prediction accuracies from GBLUP models were up to 0.37 for TCH, 0.43 for CCS, and 0.48 for Fiber, while the optimized ML models had prediction accuracies of 0.35 for TCH, 0.38 for CCS, and 0.48 for Fiber. Both RF and DL neural network models have comparable predictive ability with the additive GBLUP model but are less accurate than the extended GBLUP model.

Comparison of the Accuracy of Epistasis and Haplotype Models for Genomic Prediction of Seven Human Phenotypes

The accuracy of predicting seven human phenotypes of 3657-7564 individuals using global epistasis effects was evaluated and compared to the accuracy of haplotype genomic prediction using 380,705 SNPs and 10-fold cross-validation studies. The seven human phenotypes were the normality transformed high density lipoproteins (HDL), low density lipoproteins (LDL), total cholesterol (TC), triglycerides (TG), weight (WT), and the original phenotypic observations of height (HTo) and body mass index (BMIo). Fourth-order epistasis effects virtually had no contribution to the phenotypic variances, and third-order epistasis effects did not affect the prediction accuracy. Without haplotype effects in the prediction model, pairwise epistasis effects improved the prediction accuracy over the SNP models for six traits, with accuracy increases of 2.41%, 3.85%, 0.70%, 0.97%, 0.62% and 0.93% for HDL, LDL, TC, HTo, WT and BMIo respectively. However, none of the epistasis models had higher prediction accuracy than the haplotype models we previously reported. The epistasis model for TG decreased the prediction accuracy by 2.35% relative to the accuracy of the SNP model. The integrated models with epistasis and haplotype effects had slightly higher prediction accuracy than the haplotype models for two traits, HDL and BMIo. These two traits were the only traits where additive × dominance effects increased the prediction accuracy. These results indicated that haplotype effects containing local high-order epistasis effects had a tendency to be more important than global pairwise epistasis effects for the seven human phenotypes, and that the genetic mechanism of HDL and BMIo was more complex than that of the other traits.

Genomic predictions to leverage phenotypic data across genebanks

Genome-wide prediction is a powerful tool in breeding. Initial results suggest that genome-wide approaches are also promising for enhancing the use of the genebank material: predicting the performance of plant genetic resources can unlock their hidden potential and fill the information gap in genebanks across the world and, hence, underpin prebreeding programs. As a proof of concept, we evaluated the power of across-genebank prediction for extensive germplasm collections relying on historical data on flowering/heading date, plant height, and thousand kernel weight of 9,344 barley (Hordeum vulgare L.) plant genetic resources from the German Federal Ex situ Genebank for Agricultural and Horticultural Crops (IPK) and of 1,089 accessions from the International Center for Agriculture Research in the Dry Areas (ICARDA) genebank. Based on prediction abilities for each trait, three scenarios for predictive characterization were compared: 1) a benchmark scenario, where test and training sets only contain ICARDA accessions, 2) across-genebank predictions using IPK as training and ICARDA as test set, and 3) integrated genebank predictions that include IPK with 30% of ICARDA accessions as a training set to predict the rest of ICARDA accessions. Within the population of ICARDA accessions, prediction abilities were low to moderate, which was presumably caused by a limited number of accessions used to train the model. Interestingly, ICARDA prediction abilities were boosted up to ninefold by using training sets composed of IPK plus 30% of ICARDA accessions. Pervasive genotype × environment interactions (GEIs) can become a potential obstacle to train robust genome-wide prediction models across genebanks. This suggests that the potential adverse effect of GEI on prediction ability was counterbalanced by the augmented training set with certain connectivity to the test set. Therefore, across-genebank predictions hold the promise to improve the curation of the world's genebank collections and contribute significantly to the long-term development of traditional genebanks toward biodigital resource centers.

Impact of epistasis effects on the accuracy of predicting phenotypic values of residual feed intake in U. S Holstein cows

The impact of genomic epistasis effects on the accuracy of predicting the phenotypic values of residual feed intake (RFI) in U.S. Holstein cows was evaluated using 6215 Holstein cows and 78,964 SNPs. Two SNP models and seven epistasis models were initially evaluated. Heritability estimates and the accuracy of predicting the RFI phenotypic values from 10-fold cross-validation studies identified the model with SNP additive effects and additive × additive (A×A) epistasis effects (A + A×A model) to be the best prediction model. Under the A + A×A model, additive heritability was 0.141, and A×A heritability was 0.263 that consisted of 0.260 inter-chromosome A×A heritability and 0.003 intra-chromosome A×A heritability, showing that inter-chromosome A×A effects were responsible for the accuracy increases due to A×A. Under the SNP additive model (A-only model), the additive heritability was 0.171. In the 10 validation populations, the average accuracy for predicting the RFI phenotypic values was 0.246 (with range 0.197-0.333) under A + A×A model and was 0.231 (with range of 0.188-0.319) under the A-only model. The average increase in the accuracy of predicting the RFI phenotypic values by the A + A×A model over the A-only model was 6.49% (with range of 3.02-14.29%). Results in this study showed A×A epistasis effects had a positive impact on the accuracy of predicting the RFI phenotypic values when combined with additive effects in the prediction model.

Multifactorial methods integrating haplotype and epistasis effects for genomic estimation and prediction of quantitative traits

The rapid growth in genomic selection data provides unprecedented opportunities to discover and utilize complex genetic effects for improving phenotypes, but the methodology is lacking. Epistasis effects are interaction effects, and haplotype effects may contain local high-order epistasis effects. Multifactorial methods with SNP, haplotype, and epistasis effects up to the third-order are developed to investigate the contributions of global low-order and local high-order epistasis effects to the phenotypic variance and the accuracy of genomic prediction of quantitative traits. These methods include genomic best linear unbiased prediction (GBLUP) with associated reliability for individuals with and without phenotypic observations, including a computationally efficient GBLUP method for large validation populations, and genomic restricted maximum estimation (GREML) of the variance and associated heritability using a combination of EM-REML and AI-REML iterative algorithms. These methods were developed for two models, Model-I with 10 effect types and Model-II with 13 effect types, including intra- and inter-chromosome pairwise epistasis effects that replace the pairwise epistasis effects of Model-I. GREML heritability estimate and GBLUP effect estimate for each effect of an effect type are derived, except for third-order epistasis effects. The multifactorial models evaluate each effect type based on the phenotypic values adjusted for the remaining effect types and can use more effect types than separate models of SNP, haplotype, and epistasis effects, providing a methodology capability to evaluate the contributions of complex genetic effects to the phenotypic variance and prediction accuracy and to discover and utilize complex genetic effects for improving the phenotypes of quantitative traits.

Genomic Prediction Methods Accounting for Nonadditive Genetic Effects

The use of genomic information for prediction of future phenotypes or breeding values for the candidates to selection has become a standard over the last decade. However, most procedures for genomic prediction only consider the additive (or substitution) effects associated with polymorphic markers. Nevertheless, the implementation of models that consider nonadditive genetic variation may be interesting because they (1) may increase the ability of prediction, (2) can be used to define mate allocation procedures in plant and animal breeding schemes, and (3) can be used to benefit from nonadditive genetic variation in crossbreeding or purebred breeding schemes. This study reviews the available methods for incorporating nonadditive effects into genomic prediction procedures and their potential applications in predicting future phenotypic performance, mate allocation, and crossbred and purebred selection. Finally, a brief outline of some future research lines is also proposed.

Incorporating Omics Data in Genomic Prediction

In this chapter, we discuss the motivation for integrating other types of omics data into genomic prediction methods. We give an overview of literature investigating the performance of omics-enhanced predictions, and highlight potential pitfalls when applying these methods in breeding. We emphasize that the statistical methods available for genomic data can be transferred to the general omics case. However, when using a framework of omic relationship matrices, the standardization of the variables may be more relevant than it is for a genomic relationship matrix based on single-nucleotide polymorphisms.

Accounting for epistasis improves genomic prediction of phenotypes with univariate and bivariate models across environments

The accuracy of genomic prediction of phenotypes can be increased by including the top-ranked pairwise SNP interactions into the prediction model. We compared the predictive ability of various prediction models for a maize dataset derived from 910 doubled haploid lines from two European landraces (Kemater Landmais Gelb and Petkuser Ferdinand Rot), which were tested at six locations in Germany and Spain. The compared models were Genomic Best Linear Unbiased Prediction (GBLUP) as an additive model, Epistatic Random Regression BLUP (ERRBLUP) accounting for all pairwise SNP interactions, and selective Epistatic Random Regression BLUP (sERRBLUP) accounting for a selected subset of pairwise SNP interactions. These models have been compared in both univariate and bivariate statistical settings for predictions within and across environments. Our results indicate that modeling all pairwise SNP interactions into the univariate/bivariate model (ERRBLUP) is not superior in predictive ability to the respective additive model (GBLUP). However, incorporating only a selected subset of interactions with the highest effect variances in univariate/bivariate sERRBLUP can increase predictive ability significantly compared to the univariate/bivariate GBLUP. Overall, bivariate models consistently outperform univariate models in predictive ability. Across all studied traits, locations and landraces, the increase in prediction accuracy from univariate GBLUP to univariate sERRBLUP ranged from 5.9 to 112.4 percent, with an average increase of 47 percent. For bivariate models, the change ranged from -0.3 to + 27.9 percent comparing the bivariate sERRBLUP to the bivariate GBLUP, with an average increase of 11 percent. This considerable increase in predictive ability achieved by sERRBLUP may be of interest for "sparse testing" approaches in which only a subset of the lines/hybrids of interest is observed at each location.

Fast and accurate exhaustive higher-order epistasis search with BitEpi

Complex genetic diseases may be modulated by a large number of epistatic interactions affecting a polygenic phenotype. Identifying these interactions is difficult due to computational complexity, especially in the case of higher-order interactions where more than two genomic variants are involved. In this paper, we present BitEpi, a fast and accurate method to test all possible combinations of up to four bi-allelic variants (i.e. Single Nucleotide Variant or SNV for short). BitEpi introduces a novel bitwise algorithm that is 1.7 and 56 times faster for 3-SNV and 4-SNV search, than established software. The novel entropy statistic used in BitEpi is 44% more accurate to identify interactive SNVs, incorporating a p-value-based significance testing. We demonstrate BitEpi on real world data of 4900 samples and 87,000 SNPs. We also present EpiExplorer to visualize the potentially large number of individual and interacting SNVs in an interactive Cytoscape graph. EpiExplorer uses various visual elements to facilitate the discovery of true biological events in a complex polygenic environment.

Genomic prediction with non-additive effects in beef cattle: stability of variance component and genetic effect estimates against population size

BACKGROUND

Genomic prediction is now an essential technology for genetic improvement in animal and plant breeding. Whereas emphasis has been placed on predicting the breeding values, the prediction of non-additive genetic effects has also been of interest. In this study, we assessed the potential of genomic prediction using non-additive effects for phenotypic prediction in Japanese Black, a beef cattle breed. In addition, we examined the stability of variance component and genetic effect estimates against population size by subsampling with different sample sizes.

RESULTS

Records of six carcass traits, namely, carcass weight, rib eye area, rib thickness, subcutaneous fat thickness, yield rate and beef marbling score, for 9850 animals were used for analyses. As the non-additive genetic effects, dominance, additive-by-additive, additive-by-dominance and dominance-by-dominance effects were considered. The covariance structures of these genetic effects were defined using genome-wide SNPs. Using single-trait animal models with different combinations of genetic effects, it was found that 12.6-19.5 % of phenotypic variance were occupied by the additive-by-additive variance, whereas little dominance variance was observed. In cross-validation, adding the additive-by-additive effects had little influence on predictive accuracy and bias. Subsampling analyses showed that estimation of the additive-by-additive effects was highly variable when phenotypes were not available. On the other hand, the estimates of the additive-by-additive variance components were less affected by reduction of the population size.

CONCLUSIONS

The six carcass traits of Japanese Black cattle showed moderate or relatively high levels of additive-by-additive variance components, although incorporating the additive-by-additive effects did not improve the predictive accuracy. Subsampling analysis suggested that estimation of the additive-by-additive effects was highly reliant on the phenotypic values of the animals to be estimated, as supported by low off-diagonal values of the relationship matrix. On the other hand, estimates of the additive-by-additive variance components were relatively stable against reduction of the population size compared with the estimates of the corresponding genetic effects.

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.