Reducing computational demands of restricted maximum likelihood estimation with genomic relationship matrices

Area of Science:

• Animal Breeding and Genetics
• Quantitative Genetics
• Bioinformatics

Background:

• Restricted maximum likelihood (REML) estimation using genomic relationship matrices (GRMs) is computationally intensive compared to pedigree-based methods.
• The computational burden arises from the dense nature of GRMs and their inverses, posing challenges for large datasets.

Purpose of the Study:

• To present a reparameterization of the multivariate linear mixed model using principal components.
• To demonstrate the impact of this reparameterization on the sparsity of the coefficient matrix in mixed model equations.
• To reduce the computational time for REML estimation in genomic analyses.

Main Methods:

• Reparameterization of the multivariate linear mixed model to principal components.
• Analysis of the resulting sparsity pattern in the mixed model equations' coefficient matrix.
• Application of the 'average information' algorithm for REML estimation on two real datasets.

Main Results:

• The reparameterization significantly reduces computing time per iteration of the average information REML algorithm.
• On the principal component scale, derivatives of the coefficient matrix are independent of the individual-based relationship matrix.
• This independence mitigates the computational cost associated with dense genomic relationships.

Conclusions:

• Reparameterizing the mixed model to principal components offers a computationally efficient alternative for REML estimation with genomic data.
• This approach substantially lowers the burden of genomic relationship matrices in genetic parameter estimation.
• The method holds promise for accelerating large-scale genomic analyses in animal breeding and quantitative genetics.