Genomic prediction with epistasis models: on the marker-coding-dependent performance of the extended GBLUP and properties of the categorical epistasis model (CE)

Abstract

BackgroundEpistasis 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.ResultsWe 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.ConclusionBased 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.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-1439-1) contains supplementary material, which is available to authorized users.

A subfunctionalization epistasis model to evaluate homeologous gene interactions in allopolyploid wheat

“…Marker scores are typically assigned as either presence (or absence) of the reference, major, or minor allele, which may or may not be biologically relevant. While it has been noted that the two different marker encoding methods do not result in the same contrasts of genotypic classes (He et al ., 2015; Martini et al ., 2016, 2017), coding does not affect the least squares model fit (Zeng et al ., 2005; Álvarez-Castro and Carlborg, 2007). Álvarez-Castro and Carlborg (2007) show that there exists a linear transformation to shift between multiple parameterizations using a change-of-reference operation (see Appendix 3).…”

“…This transformation does not hold when marker effects are considered random, where the interaction effect is subject to differential shrinkage depending on the marker coding and orientation (Martini et al ., 2017, 2018). As such, orienting markers to capture functional allele relationships may be crucial for optimizing genomic prediction including epistasis.…”

MoBPS - Modular Breeding Program Simulator

“…This includes BGLR (Pérez and de los Campos 2014), sommer (Covarrubias-Pazaran 2016) and rrBLUP (Endelman 2011), as well as an efficient implementation for solving the mixed model (Henderson 1975) in the traditional GBLUP model (Meuwissen et al 2001; VanRaden 2008) that is assuming known heritability and is using the R-package RandomFieldsUtils (Schlather et al 2019b) for the matrix inversion. Inputs for these packages such as the different pedigree and genomic relationship matrices (VanRaden 2008; Legarra et al 2014; Martini et al 2017) can be derived via highly efficient and fully-parallelized bit-wise matrix multiplications (R-package miraculix (Schlather et al 2019a)). Non of the mentioned packages, however, is required to execute simulations in MoBPS.…”

A comparison of identity‐by‐descent and identity‐by‐state matrices that are used for genetic evaluation and estimation of variance components

“…Then, a small value is added to the diagonals of G to make it non‐singular (Vela‐Avitúa, Meuwissen, Luan, & Ødegård, ). It can be shown that centring the columns of M has no effect on the BLUPs of the substitution effects and thus will also not affect the BLUP of a i − (Martini et al., ; Strandén & Christensen, ) . Scaling on the other hand, results in a GARM that unequally weights the IBS matrices across the loci.…”