GWAS & Selection signatures

A Method to Compute Genomic Window Variances for a Multiple-Regression Model Using Posterior Samples of Effects from an Equivalent Dimension-Reduced Model

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Abstract

Advances in high-throughput genotyping have resulted in high-dimensional single nucleotide polymorphism (SNP) marker data used for research and applications in animal and plant breeding. Bayesian multiple-regression models that fit all markers simultaneously have been used for genomic prediction and genome-wide association studies. To reduce the computational burden of these analyses, dimension-reducing transformations have been used to greatly reduce the number of covariates that are fitted in the model, e.g., orthogonalization of genotype covariates when the number of SNPs is greater than the number of genotyped individuals. Estimated effects (β) from the reduced model can be back-transformed to obtain SNP effect estimates (α = Vβ) from the original model, where V is a known matrix that is related to the transformation. However, because of linkage disequilibrium, inferences from estimates of these individual SNP effects may not be very meaningful, and thus, inferences on variances contributed by each genomic window have been proposed, using Bayesian methods. In these methods, samples are obtained from the posterior distribution of SNP effects and are used to compute sampled breeding values of individuals for each genomic window. Using these sampled breeding values, the genomic variance for each window can be calculated. However, if sampled SNP effects are obtained by back-transformation from a reduced-dimension model, the resulting genomic window variances are not invariant to the transformation used. Denoting the breeding value for a genomic window as k'α, where k is an arbitrary vector and α is obtained as Vβ, k'α depends on the transformation used. Now suppose that k' = k'p + k'r, where k'p is the projection of k' onto the row space of the genotype covariate matrix and kr = k - kp. We can show that k'pα is invariant to the transformation and that k'rα does not depend on the phenotypic data. Therefore, we propose to sample the breeding values for a genomic window as k'pα1 + k'rα2, where α1 is obtained as Vβ and α2 is sampled from its prior distribution, since it does not depend on the data. A numerical example is used to illustrate the method. We observe that as the window size becomes smaller, the contribution from the prior (k'rα2) to the sampled genomic window variance increases and the contribution from the data becomes smaller.

Keywords: 2026

How to Cite:

Yu, H., Godinho, R., Dekkers, J. & Fernando, R., (2026) “A Method to Compute Genomic Window Variances for a Multiple-Regression Model Using Posterior Samples of Effects from an Equivalent Dimension-Reduced Model”, World Congress on Genetics Applied to Livestock Production Digital Archive 2026(1): 2285892. doi: https://doi.org/10.31274/wcgalp.23815

Rights: 1