SNP-SNP Interaction Analysis on Soybean Oil Content under Multi-Environments

Quantitative Trait Locus (QTLs) Mapping for Quality Traits of Wheat Based on High Density Genetic Map Combined With Bulked Segregant Analysis RNA-seq (BSR-Seq) Indicates That the Basic 7S Globulin Gene Is Related to Falling Number

Numerous quantitative trait loci (QTLs) have been identified for wheat quality; however, most are confined to low-density genetic maps. In this study, based on specific-locus amplified fragment sequencing (SLAF-seq), a high-density genetic map was constructed with 193 recombinant inbred lines derived from Chuanmai 42 and Chuanmai 39. In total, 30 QTLs with phenotypic variance explained (PVE) up to 47.99% were identified for falling number (FN), grain protein content (GPC), grain hardness (GH), and starch pasting properties across three environments. Five NAM genes closely adjacent to QGPC.cib-4A probably have effects on GPC. QGH.cib-5D was the only one detected for GH with high PVE of 33.31-47.99% across the three environments and was assumed to be related to the nearest pina-D1 and pinb-D1genes. Three QTLs were identified for FN in at least two environments, of which QFN.cib-3D had relatively higher PVE of 16.58-25.74%. The positive effect of QFN.cib-3D for high FN was verified in a double-haploid population derived from Chuanmai 42 × Kechengmai 4. The combination of these QTLs has a considerable effect on increasing FN. The transcript levels of Basic 7S globulin and Basic 7S globulin 2 in QFN.cib-3D were significantly different between low FN and high FN bulks, as observed through bulk segregant RNA-seq (BSR). These QTLs and candidate genes based on the high-density genetic map would be beneficial for further understanding of the genetic mechanism of quality traits and molecular breeding of wheat.

Lost in Translation: On the Problem of Data Coding in Penalized Whole Genome Regression with Interactions

Mixed models can be considered as a type of penalized regression and are everyday tools in statistical genetics. The standard mixed model for whole genome regression (WGR) is ridge regression best linear unbiased prediction (RRBLUP) which is based on an additive marker effect model. Many publications have extended the additive WGR approach by incorporating interactions between loci or between genes and environment. In this context of penalized regressions with interactions, it has been reported that translating the coding of single nucleotide polymorphisms -for instance from -1,0,1 to 0,1,2- has an impact on the prediction of genetic values and interaction effects. In this work, we identify the reason for the relevance of variable coding in the general context of penalized polynomial regression. We show that in many cases, predictions of the genetic values are not invariant to translations of the variable coding, with an exception when only the sizes of the coefficients of monomials of highest total degree are penalized. The invariance of RRBLUP can be considered as a special case of this setting, with a polynomial of total degree 1, penalizing additive effects (total degree 1) but not the fixed effect (total degree 0). The extended RRBLUP (eRRBLUP), which includes interactions, is not invariant to translations because it does not only penalize interactions (total degree 2), but also additive effects (total degree 1). This observation implies that translation-invariance can be maintained in a pair-wise epistatic WGR if only interaction effects are penalized, but not the additive effects. In this regard, approaches of pre-selecting loci may not only reduce computation time, but can also help to avoid the variable coding issue. To illustrate the practical relevance, we compare different regressions on a publicly available wheat data set. We show that for an eRRBLUP, the relevance of the marker coding for interaction effect estimates increases with the number of variables included in the model. A biological interpretation of estimated interaction effects may therefore become more difficult. Consequently, comparing reproducing kernel Hilbert space (RKHS) approaches to WGR approaches modeling effects explicitly, the supposed advantage of an increased interpretability of the latter may not be real. Our theoretical results are generally valid for penalized regressions, for instance also for the least absolute shrinkage and selection operator (LASSO). Moreover, they apply to any type of interaction modeled by products of predictor variables in a penalized regression approach or by Hadamard products of covariance matrices in a mixed model.