title: Genomic prediction with epistasis models: on the marker-coding-dependent performance of the extended GBLUP and properties of the categorical epistasis model (CE).
abstract: BACKGROUND
  Epistasis marker effect models incorporating products of marker values as predictor variables in a linear regression approach (extended GBLUP, EGBLUP) have been assessed as potentially beneficial for genomic prediction, but their performance depends on marker coding. Although this fact has been recognized in literature, the nature of the problem has not been thoroughly investigated so far.
  
  
  RESULTS
  We illustrate how the choice of marker coding implicitly specifies the model of how effects of certain allele combinations at different loci contribute to the phenotype, and investigate coding-dependent properties of EGBLUP. Moreover, we discuss an alternative categorical epistasis model (CE) eliminating undesired properties of EGBLUP and show that the CE model can improve predictive ability. Finally, we demonstrate that the coding-dependent performance of EGBLUP offers the possibility to incorporate prior experimental information into the prediction method by adapting the coding to already available phenotypic records on other traits.
  
  
  CONCLUSIONS
  Based on our results, for EGBLUP, a symmetric coding {-1,1} or {-1,0,1} should be preferred, whereas a standardization using allele frequencies should be avoided. Moreover, CE can be a valuable alternative since it does not possess the undesired theoretical properties of EGBLUP. However, which model performs best will depend on characteristics of the data and available prior information. Data from previous experiments can for instance be incorporated into the marker coding of EGBLUP.
authors.affiliation: Department of Animal Sciences, Georg-August University, Albrecht Thaer-Weg 3, Göttingen, Germany. jmartin2@gwdg.de.
authors.forename: Johannes W R
authors.initials: JW
authors.lastname: Martini
authors.affiliation: Department of Animal Sciences, Georg-August University, Albrecht Thaer-Weg 3, Göttingen, Germany.|National Engineering Research Center for Breeding Swine Industry, Guangdong Provincial Key Lab of Agro-animal Genomics and Molecular Breeding, College of Animal Science, South China Agricultural University, Guangzhou, China.
authors.forename: Ning
authors.initials: N
authors.lastname: Gao
authors.affiliation: Department of Animal Sciences, Georg-August University, Albrecht Thaer-Weg 3, Göttingen, Germany.|Departamento de Zootecnia, São Paulo State University, São Paulo, Brazil.
authors.forename: Diercles F
authors.initials: DF
authors.lastname: Cardoso
authors.affiliation: KWS SAAT SE, Einbeck, Germany.
authors.forename: Valentin
authors.initials: V
authors.lastname: Wimmer
authors.affiliation: Department of Animal Sciences, Georg-August University, Albrecht Thaer-Weg 3, Göttingen, Germany.|Institute for Animal Breeding, Bavarian State Research Centre for Agriculture, Grub, Germany.
authors.forename: Malena
authors.initials: M
authors.lastname: Erbe
authors.affiliation: Department of Animal Production, University of Buenos Aires, INPA-CONICET, Buenos Aires, Argentina.
authors.forename: Rodolfo J C
authors.initials: RJ
authors.lastname: Cantet
authors.affiliation: Department of Animal Sciences, Georg-August University, Albrecht Thaer-Weg 3, Göttingen, Germany.
authors.forename: Henner
authors.initials: H
authors.lastname: Simianer
mesh_terms: D000483:Alleles; D000818:Animals; D004843:Epistasis, Genetic; D051379:Mice; D008957:Models, Genetic; D020641:Polymorphism, Single Nucleotide; D040641:Quantitative Trait Loci; D014908:Triticum / Q000235:genetics
keywords: Epistasis model; Genomic prediction; Interaction