Extend Mixed Models to Multi-layer Neural Networks for Genomic Prediction Including Intermediate Omics Data

ABSTRACTWith the growing amount and diversity of intermediate omics data complementary to genomics (e.g., DNA methylation, gene expression, and protein abundance), there is a need to develop methods to incorporate intermediate omics data into conventional genomic evaluation. The omics data helps decode the multiple layers of regulation from genotypes to phenotypes, thus forms a connected multi-layer network naturally. We developed a new method named NN-LMM to model the multiple layers of regulation from genotypes to intermediate omics features, then to phenotypes, by extending conventional linear mixed models (“LMM”) to multi-layer artificial neural networks (“NN”). NN-LMM incorporates intermediate omics features by adding middle layers between genotypes and phenotypes. Linear mixed models (e.g., pedigree-based BLUP, GBLUP, Bayesian Alphabet, single-step GBLUP, or single-step Bayesian Alphabet) can be used to sample marker effects or genetic values on intermediate omics features, and activation functions in neural networks are used to capture the nonlinear relationships between intermediate omics features and phenotypes. NN-LMM had significantly better prediction performance than the recently proposed single-step approach for genomic prediction with intermediate omics data. Compared to the single-step approach, NN-LMM can handle various patterns of missing omics measures, and allows nonlinear relationships between intermediate omics features and phenotypes. NN-LMM has been implemented in an open-source package called “JWAS”.

Single-step genomic evaluation with metafounders for feed conversion ratio and average daily gain in Danish Landrace and Yorkshire pigs

Background The single-step genomic best linear unbiased prediction (SSGBLUP) method is a popular approach for genetic evaluation with high-density genotype data. To solve the problem that pedigree and genomic relationship matrices refer to different base populations, a single-step genomic method with metafounders (MF-SSGBLUP) was put forward. The aim of this study was to compare the predictive ability and bias of genomic evaluations obtained with MF-SSGBLUP and standard SSGBLUP. We examined feed conversion ratio (FCR) and average daily gain (ADG) in DanBred Landrace (LL) and Yorkshire (YY) pigs using both univariate and bivariate models, as well as the optimal weighting factors (ω), which represent the proportions of the genetic variance not captured by markers, for ADG and FCR in SSGBLUP and MF-SSGBLUP. Results In general, SSGBLUP and MF-SSGBLUP showed similar predictive abilities and bias of genomic estimated breeding values (GEBV). In the LL population, the predictive ability for ADG reached 0.36 using uni- or bi-variate SSGBLUP or MF-SSGBLUP, while the predictive ability for FCR was highest (0.20) for the bivariate model using MF-SSGBLUP, but differences between analyses were very small. In the YY population, predictive ability for ADG was similar for the four analyses (up to 0.35), while the predictive ability for FCR was highest (0.36) for the uni- and bi-variate MF-SSGBLUP analyses. SSGBLUP and MF-SSGBLUP exhibited nearly the same bias. In general, the bivariate models had lower bias than the univariate models. In the LL population, the optimal ω for ADG was ~ 0.2 in the univariate or bivariate models using SSGBLUP or MF-SSGBLUP, and the optimal ω for FCR was 0.70 and 0.55 for SSGBLUP and MF-SSGBLUP, respectively. In the YY population, the optimal ω ranged from 0.25 to 0. 35 for ADG across the four analyses and from 0.10 to 0.30 for FCR. Conclusions Our results indicate that MF-SSGBLUP performed slightly better than SSGBLUP for genomic evaluation. There was little difference in the optimal weighting factors (ω) between SSGBLUP and MF-SSGBLUP. Overall, the bivariate model using MF-SSGBLUP is recommended for single-step genomic evaluation of ADG and FCR in DanBred Landrace and Yorkshire pigs.

Application of Genomic Data for Reliability Improvement of Pig Breeding Value Estimates

Replacement pigs’ genomic prediction for reproduction (total number and born alive piglets in the first parity), meat, fatness and growth traits (muscle depth, days to 100 kg and backfat thickness over 6–7 rib) was tested using single-step genomic best linear unbiased prediction ssGBLUP methodology. These traits were selected as the most economically significant and different in terms of heritability. The heritability for meat, fatness and growth traits varied from 0.17 to 0.39 and for reproduction traits from 0.12 to 0.14. We confirm from our data that ssGBLUP is the most appropriate method of genomic evaluation. The validation of genomic predictions was performed by calculating the correlation between preliminary GEBV (based on pedigree and genomic data only) with high reliable conventional estimates (EBV) (based on pedigree, own phenotype and offspring records) of validating animals. Validation datasets include 151 and 110 individuals for reproduction, meat and fattening traits, respectively. The level of correlation (r) between EBV and GEBV scores varied from +0.44 to +0.55 for meat and fatness traits, and from +0.75 to +0.77 for reproduction traits. Average breeding value (EBV) of group selected on genomic evaluation basis exceeded the group selected on parental average estimates by 22, 24 and 66% for muscle depth, days to 100 kg and backfat thickness over 6–7 rib, respectively. Prediction based on SNP markers data and parental estimates showed a significant increase in the reliability of low heritable reproduction traits (about 40%), which is equivalent to including information about 10 additional descendants for sows and 20 additional descendants for boars in the evaluation dataset.