title: Technical note: Equivalent genomic models with a residual polygenic effect.
abstract: Routine genomic evaluations in animal breeding are usually based on either a BLUP with genomic relationship matrix (GBLUP) or single nucleotide polymorphism (SNP) BLUP model. For a multi-step genomic evaluation, these 2 alternative genomic models were proven to give equivalent predictions for genomic reference animals. The model equivalence was verified also for young genotyped animals without phenotypes. Due to incomplete linkage disequilibrium of SNP markers to genes or causal mutations responsible for genetic inheritance of quantitative traits, SNP markers cannot explain all the genetic variance. A residual polygenic effect is normally fitted in the genomic model to account for the incomplete linkage disequilibrium. In this study, we start by showing the proof that the multi-step GBLUP and SNP BLUP models are equivalent for the reference animals, when they have a residual polygenic effect included. Second, the equivalence of both multi-step genomic models with a residual polygenic effect was also verified for young genotyped animals without phenotypes. Additionally, we derived formulas to convert genomic estimated breeding values of the GBLUP model to its components, direct genomic values and residual polygenic effect. Third, we made a proof that the equivalence of these 2 genomic models with a residual polygenic effect holds also for single-step genomic evaluation. Both the single-step GBLUP and SNP BLUP models lead to equal prediction for genotyped animals with phenotypes (e.g., reference animals), as well as for (young) genotyped animals without phenotypes. Finally, these 2 single-step genomic models with a residual polygenic effect were proven to be equivalent for estimation of SNP effects, too.
authors.affiliation: VIT w.V., Heinrich-Schröder-Weg 1, D-27283 Verden, Germany. Electronic address: Zengting.Liu@vit.de.
authors.forename: Z
authors.initials: Z
authors.lastname: Liu
authors.affiliation: Dairy Futures Cooperative Research Centre, Bundoora, Melbourne 3083, VIC, Australia.
authors.forename: M E
authors.initials: ME
authors.lastname: Goddard
authors.affiliation: Dairy Futures Cooperative Research Centre, Bundoora, Melbourne 3083, VIC, Australia.
authors.forename: B J
authors.initials: BJ
authors.lastname: Hayes
authors.affiliation: VIT w.V., Heinrich-Schröder-Weg 1, D-27283 Verden, Germany.
authors.forename: F
authors.initials: F
authors.lastname: Reinhardt
authors.affiliation: VIT w.V., Heinrich-Schröder-Weg 1, D-27283 Verden, Germany.
authors.forename: R
authors.initials: R
authors.lastname: Reents
mesh_terms: D000818:Animals; D001947:Breeding; D016678:Genome; D023281:Genomics; D005838:Genotype; D015810:Linkage Disequilibrium; D008957:Models, Genetic; D020412:Multifactorial Inheritance; D010641:Phenotype; D020641:Polymorphism, Single Nucleotide; D012044:Regression Analysis
keywords: BLUP with genomic relationship matrix; SNP BLUP model; equivalent model; residual polygenic effect