Augmented Monte Carlo AI-REML for (co)variance component estimation in single-step models

Abstract

Accurate (co)variance component estimation (VCE) is essential for reliable genetic evaluation. Analytical restricted maximum likelihood (REML) estimation in single-step genomic models is often computationally demanding because mixed model equations (MME) have dense genomic relationship blocks. In this study, we extended the augmented AI-REML to an augmented Monte Carlo (MC) AI-REML approach, in which MC sampling was used to approximate the trace terms required for REML, thereby avoiding explicit inversion of the coefficient matrix of MME. The method was implemented for three single-step models: ssGBLUP, ssGTABLUP, and ssSNPBLUP. Data were simulated for 44,280 individuals over 20 generations, with 9,000 markers and three scenarios comprising 10,000, 20,000, or 30,000 genotyped individuals. Variance component estimates were consistent across single-step models and genotyping scenarios. The augmented MC AI-REML converged within 11-18 REML iterations. Computing time increased with the number of genotyped individuals for all models. Based on the current datasets, ssGBLUP was the fastest in all scenarios but showed a substantial increase in memory requirements as the number of genotyped individuals increased. ssSNPBLUP required the longest computing time. ssGTABLUP showed intermediate computing times with substantially lower memory requirements than ssGBLUP. Overall, augmented MC AI-REML provides an efficient approach for VCE in single-step models and has potential for application to large-scale genomic datasets.