Genomic Heritability: A Ragged Diagonal Between Bias and Variance

Many important traits in plants, animals, and microbes are polygenic and are therefore difficult to improve through traditional marker?assisted selection. Genomic prediction addresses this by enabling the inclusion of all genetic data in a mixed model framework. The main method for predicting breeding values is genomic best linear unbiased prediction (GBLUP), which uses the realized genomic relationship or kinship matrix (K) to connect genotype to phenotype. The use of relationship matrices allows information to be shared for estimating the genetic values for observed entries and predicting genetic values for unobserved entries. One of the key parameters of such models is genomic heritability (h2g), or the variance of a trait associated with a genome-wide sample of DNA polymorphisms. Here we discuss the relationship between several common methods for calculating the genomic relationship matrix and propose a new matrix based on the average semivariance that yields accurate estimates of genomic variance in the observed population regardless of the focal population quality as well as accurate breeding value predictions in unobserved samples. Notably, our proposed method is highly similar to the approach presented by Legarra (2016) despite different mathematical derivations and statistical perspectives and only deviates from the classic approach presented in VanRaden (2008) by a scaling factor. With current approaches, we found that the genomic heritability tends to be either over- or underestimated depending on the scaling and centering applied to the marker matrix (Z), the value of the average diagonal element of K, and the assortment of alleles and heterozygosity (H) in the observed population and that, unlike its predecessors, our newly proposed kinship matrix KASV yields accurate estimates of h2g in the observed population, generalizes to larger populations, and produces BLUPs equivalent to common methods in plants and animals.

Optimal Genomic Control in Large-scale Genetic Associations for Binary Diseases

Complex computation and approximate solution hinder the application of generalized linear mixed models (GLMM) into genome-wide association studies. We extended GRAMMAR to handle binary diseases by considering genomic breeding values (GBVs) estimated in advance as a known predictor in genomic logit regression, and then controlled polygenic effects by regulating downward genomic heritability. Using simulations and case analyses, we showed in optimizing GRAMMAR, polygenic effects and genomic controls could be evaluated using the fewer sampling markers, which extremely simplified GLMM-based association analysis in large-scale data. In addition, joint analysis for quantitative trait nucleotide (QTN) candidates chosen by multiple testing offered significant improved statistical power to detect QTNs over existing methods.

A Shortcut Approach for Large-scale Mixed Model Associations with Binary Traits

Generalized linear mixed models exhibit computationally intensive and biasness in mapping quantitative trait nucleotides for binary diseases. In genomic logit regression, we consider genomic breeding values estimated in advance as a known predictor, and then correct the deflated association test statistics by using genomic control, thereby successfully extending GRAMMAR-Lambda to analyze binary diseases in a complex structured population. Because there is no need to estimate genomic heritability and genomic breeding values can be estimated by a small number of sampling markers, the generalized mixed-model association analysis has been extremely simplified to handle large-scale data. With almost perfect genomic control, joint analysis for the candidate quantitative trait nucleotides chosen by multiple testing offered a significant improvement in statistical power.

A Shortcut Approach for Large-scale Mixed Model Associations with Binary Traits

Generalized linear mixed models exhibit computationally intensive and biasness in mapping quantitative trait nucleotides for binary diseases. In genomic logit regression, we consider genomic breeding values estimated in advance as a known predictor, and then correct the deflated association test statistics by using genomic control, thereby successfully extending GRAMMAR-Lambda to analyze binary diseases in a complex structured population. Because there is no need to estimate genomic heritability and genomic breeding values can be estimated by a small number of sampling markers, the generalized mixed-model association analysis has been extremely simplified to handle large-scale data. With almost perfect genomic control, joint analysis for the candidate quantitative trait nucleotides chosen by multiple testing offered a significant improvement in statistical power.

Efficient Genomic Control for Mixed Model Associations in Large-scale Population

Among linear mixed model-based association methods, GRAMMAR has the lowest computing complexity for association tests, but it produces a high false-negative rate due to the deflation of test statistics for complex population structure. Here, we present an optimized GRAMMAR method by efficient genomic control, Optim-GRAMMAR, that estimates the phenotype residuals by regulating downward genomic heritability in the genomic best linear unbiased prediction. Even though using the fewer sampling markers to evaluate genomic relationship matrices and genomic controls, Optim-GRAMMAR retains a similar statistical power to the exact mixed model association analysis, which infers an extremely efficient approach to handle large-scale data. Moreover, joint association analysis significantly improved statistical power over existing methods.

Optimal Genomic Control in Large-scale Genetic Associations for Binary Diseases

Complex computation and approximate solution hinder the application of generalized linear mixed models (GLMM) into genome-wide association studies. We extended GRAMMAR to handle binary diseases by considering genomic breeding values (GBVs) estimated in advance as a known predictor in genomic logit regression, and then controlled polygenic effects by regulating downward genomic heritability. Using simulations and case analyses, we showed in optimizing GRAMMAR, polygenic effects and genomic controls could be evaluated using the fewer sampling markers, which extremely simplified GLMM-based association analysis in large-scale data. In addition, joint analysis for quantitative trait nucleotide (QTN) candidates chosen by multiple testing offered significant improved statistical power to detect QTNs over existing methods.

GRAMMAR-Lambda: An Extreme Simplification for Genome-wide Mixed Model Association Analysis

A highly efficient genome-wide association method, GRAMMAR-Lambda is proposed to make simple genomic control for the test statistics deflated by GRAMMAR, producing statistical power as high as exact mixed model association method. Using the simulated and real phenotypes, we show that at a moderate or above genomic heritability, polygenic effects can be estimated using a small number of randomly selected markers, which extremely simplify genome-wide association analysis with an approximate computational complexity to naïve method in large-scale complex population. Upon a test at once, joint association analysis offers significant increase in statistical power over existing methods.

Genetic regulation and heritability of miRNA and mRNA expression link to phosphorus utilization and gut microbiome

Improved utilization of phytates and mineral phosphorus (P) in monogastric animals contributes significantly to preserving the finite resource of mineral P and mitigating environmental pollution. In order to identify pathways and to prioritize candidate genes related to P utilization (PU), the genomic heritability of 77 and 80 trait-dependent expressed miRNAs and mRNAs in 482 Japanese quail were estimated and eQTL (expression quantitative trait loci) were detected. In total, 104 miR-eQTL (microRNA expression quantitative traits loci) were associated with SNP markers (false discovery rate less than 10%) including 41 eQTL of eight miRNAs. Similarly, 944 mRNA-eQTL were identified at the 5% False discovery rate threshold, with 573 being cis-eQTL of 36 mRNAs. High heritabilities of miRNA and mRNA expression coincide with highly significant eQTL. Integration of phenotypic data with transcriptome and microbiome data of the same animals revealed genetic regulated mRNA and miRNA transcripts (SMAD3, CAV1, ENNPP6, ATP2B4, miR-148a-3p, miR-146b-5p, miR-16-5p, miR-194, miR-215-5p, miR-199-3p, miR-1388a-3p) and microbes ( Candidatus Arthromitus , Enterococcus ) that are associated with PU. The results reveal novel insights into the role of mRNAs and miRNAs in host gut tissue functions, which are involved in PU and other related traits, in terms of the genetic regulation and inheritance of their expression and in association with microbiota components.