The large number of markers in genome-wide prediction demands the use of methods with regularization and model comparison based on some hold-out test prediction error measure. In quantitative genetics, it is common practice to calculate the Pearson correlation coefficient (r²) as a standardized measure of the predictive accuracy of a model. Based on arguments from the bias–variance trade-off theory in statistical learning, we show that shrinkage of the regression coefficients (i.e., QTL effects) reduces the prediction mean squared error (MSE) by introducing model bias compared with the ordinary least squares method. We also show that the LASSO and the adaptive LASSO (ALASSO) can reduce the model bias and prediction MSE by adding model variance. In an application of ridge regression, the LASSO and ALASSO to a simulated example based on results for 9,723 SNPs and 3,226 individuals, the best model selected was with the LASSO when r² was used as a measure. However, when model selection was based on test MSE and coefficient of determination R² the ALASSO proved to be the best method. Hence, use of r² may lead to selection of the wrong model and therefore also nonoptimal ranking of phenotype predictions and genomic breeding values. Instead, we propose use of the test MSE for model selection and R² as a standardized measure of the accuracy.

Genome-wide marker data are used both in phenotypic genome-wide association studies (GWAS) and genome-wide prediction (GWP). Typically, such studies include high-dimensional data with thousands to millions of single nucleotide polymorphisms (SNPs) recorded in hundreds to a few thousands individuals. Different machine-learning approaches have been used in GWAS and GWP effectively, but the use of neural networks (NN) and deep-learning is still scarce. This study presents a NN model for genomic SNP data. We show, using both simulated and real pig data, that regularization is obtained using weight decay and dropout, and results in an approximate Bayesian (ABNN) model that can be used to obtain model averaged posterior predictions. The ABNN model is implemented in mxnet and shown to yield better prediction accuracy than genomic best linear unbiased prediction and Bayesian LASSO. The mean squared error was reduced by at least 6.5% in the simulated data and by at least 1% in the real data. Moreover, by comparing NN of different complexities, our results confirm that a shallow model with one layer, one neuron, one-hot encoding and a linear activation function performs better than more complex models. The ABNN model provides a computationally efficient approach with good prediction performance and in which the weight components can also provide information on the importance of the SNPs. Hence, ABNN is suitable for both GWP and GWAS.

The goal of genome-wide prediction (GWP) is to predict phenotypes based on marker genotypes, often obtained through single nucleotide polymorphism (SNP) chips. The major problem with GWP is high-dimensional data from many thousands of SNPs scored on several thousands of individuals. A large number of methods have been developed for GWP, which are mostly parametric methods that assume statistical linearity and only additive genetic effects. The Bayesian additive regression trees (BART) method was recently proposed and is based on the sum of nonparametric regression trees with the priors being used to regularize the parameters. Each regression tree is based on a recursive binary partitioning of the predictor space that approximates an unknown function, which will automatically model nonlinearities within SNPs (dominance) and interactions between SNPs (epistasis). In this study, we introduced BART and compared its predictive performance with that of the LASSO, Bayesian LASSO (BLASSO), genomic best linear unbiased prediction (GBLUP), reproducing kernel Hilbert space (RKHS) regression and random forest (RF) methods. Tests on the QTLMAS2010 simulated data, which are mainly based on additive genetic effects, show that cross-validated optimization of BART provides a smaller prediction error than the RF, BLASSO, GBLUP and RKHS methods, and is almost as accurate as the LASSO method. If dominance and epistasis effects are added to the QTLMAS2010 data, the accuracy of BART relative to the other methods was increased. We also showed that BART can produce importance measures on the SNPs through variable inclusion proportions. In evaluations using real data on pigs, the prediction error was smaller with BART than with the other methods. BART was shown to be an accurate method for GWP, in which the regression trees guarantee a very sparse representation of additive and complex non-additive genetic effects. Moreover, the Markov chain Monte Carlo algorithm with Bayesian back-fitting provides a computationally efficient procedure that is suitable for high-dimensional genomic data.

Genome-wide prediction (GWP) has become the state-of-the art method in artificial selection. Data sets often comprise number of genomic markers and individuals in ranges from a few thousands to millions. Hence, computational efficiency is important and various machine learning methods have successfully been used in GWP. Neural networks (NN) and deep learning (DL) are very flexible methods that usually show outstanding prediction properties on complex structured data, but their use in GWP is nevertheless rare and debated. This study describes a powerful NN method for genomic marker data that can easily be extended. It is shown that a one-dimensional convolutional neural network (CNN) can be used to incorporate the ordinal information between markers and, together with pooling and ℓ₁-norm regularization, provides a sparse and computationally efficient approach for GWP. The method, denoted CNNGWP, is implemented in the deep learning software Keras, and hyper-parameters of the NN are tuned with Bayesian optimization. Model averaged ensemble predictions further reduce prediction error. Evaluations show that CNNGWP improves prediction error by more than 25% on simulated data and around 3% on real pig data compared with results obtained with GBLUP and the LASSO. In conclusion, the CNNGWP provides a promising approach for GWP, but the magnitude of improvement depends on the genetic architecture and the heritability.

Runs of homozygosity (ROH) islands are stretches of homozygous sequence in the genome of a large proportion of individuals in a population. Algorithms for the detection of ROH depend on the similarity of haplotypes. Coverage gaps and copy number variants (CNV) may result in incorrect identification of such similarity, leading to the detection of ROH islands where none exists. Misidentified hemizygous regions will also appear as homozygous based on sequence variation alone. Our aim was to identify ROH islands influenced by marker coverage gaps or CNV, using Illumina BovineHD BeadChip (777 K) single nucleotide polymorphism (SNP) data for Austrian Brown Swiss, Tyrol Grey and Pinzgauer cattle. ROH were detected using clustering, and ROH islands were determined from population inbreeding levels for each marker. CNV were detected using a multivariate copy number analysis method and a hidden Markov model. SNP coverage gaps were defined as genomic regions with intermarker distances on average longer than 9.24 kb. ROH islands that overlapped CNV regions (CNVR) or SNP coverage gaps were considered as potential artefacts. Permutation tests were used to determine if overlaps between CNVR with copy losses and ROH islands were due to chance. Diversity of the haplotypes in the ROH islands was assessed by haplotype analyses. In Brown Swiss, Tyrol Grey and Pinzgauer, we identified 13, 22, and 24 ROH islands covering 26.6, 389.0 and 35.8 Mb, respectively, and we detected 30, 50 and 71 CNVR derived from CNV by using both algorithms, respectively. Overlaps between ROH islands, CNVR or coverage gaps occurred for 7, 14 and 16 ROH islands, respectively. About 37, 44 and 52% of the ROH islands coverage in Brown Swiss, Tyrol Grey and Pinzgauer, respectively, were affected by copy loss. Intersections between ROH islands and CNVR were small, but significantly larger compared to ROH islands at random locations across the genome, implying an association between ROH islands and CNVR. Haplotype diversity for reliable ROH islands was lower than for ROH islands that intersected with copy loss CNVR. Our findings show that a significant proportion of the ROH islands in the bovine genome are artefacts due to CNV or SNP coverage gaps.

Purpose: More accurate prediction of phenotype traits can increase the success of genomic selection in both plant and animal breeding studies and provide more reliable disease risk prediction in humans. Traditional approaches typically use regression models based on linear assumptions between the genetic markers and the traits of interest. Non-linear models have been considered as an alternative tool for modeling genomic interactions (i.e. non-additive effects) and other subtle non-linear patterns between markers and phenotype. Deep learning has become a state-of-the-art non-linear prediction method for sound, image and language data. However, genomic data is better represented in a tabular format. The existing literature on deep learning for tabular data proposes a wide range of novel architectures and reports successful results on various datasets. Tabular deep learning applications in genome-wide prediction (GWP) are still rare. In this work, we perform an overview of the main families of recent deep learning architectures for tabular data and apply them to multi-trait regression and multi-class classification for GWP on real gene datasets. Methods: The study involves an extensive overview of recent deep learning architectures for tabular data learning: NODE, TabNet, TabR, TabTransformer, FT-Transformer, AutoInt, GANDALF, SAINT and LassoNet. These architectures are applied to multi-trait GWP. Comprehensive benchmarks of various tabular deep learning methods are conducted to identify best practices and determine their effectiveness compared to traditional methods. Results: Extensive experimental results on several genomic datasets (three for multi-trait regression and two for multi-class classification) highlight LassoNet as a standout performer, surpassing both other tabular deep learning models and the highly efficient tree based LightGBM method in terms of both best prediction accuracy and computing efficiency. Conclusion: Through series of evaluations on real-world genomic datasets, the study identifies LassoNet as a standout performer, surpassing decision tree methods like LightGBM and other tabular deep learning architectures in terms of both predictive accuracy and computing efficiency. Moreover, the inherent variable selection property of LassoNet provides a systematic way to find important genetic markers that contribute to phenotype expression.