Traits in any organism are not independent, but show considerable integration, observed in a form of couplings and trade-offs. Therefore, improvement in one trait may affect other traits, often in undesired direction. To account for this problem, crop breeding increasingly relies on multi-trait genomic prediction (MT-GP) approaches that leverage the availability of genetic markers from different populations along with advances in high-throughput precision phenotyping. While significant progress has been made to jointly model multiple traits using a variety of statistical and machine learning approaches, there is no systematic comparison of advantages and shortcomings of the existing classes of MT-GP models. Here, we fill this knowledge gap by first classifying the existing MT-GP models and briefly summarizing their general principles, modeling assumptions, and potential limitations. We then perform an extensive comparative analysis with 10 traits measured in an Oryza sativa diversity panel using cross-validation scenarios relevant in breeding practice. Finally, we discuss directions that can enable the building of next generation MT-GP models in addressing pressing challenges in crop breeding.

Despite extensive research efforts, reconstruction of gene regulatory networks (GRNs) from transcriptomics data remains a pressing challenge in systems biology. While non-linear approaches for reconstruction of GRNs show improved performance over simpler alternatives, we do not yet have understanding if joint modelling of multiple target genes may improve performance, even under linearity assumptions. To address this problem, we propose two novel approaches that cast the GRN reconstruction problem as a blend between regularized multivariate regression and graphical models that combine the L2,1-norm with classical regularization techniques. We used data and networks from the DREAM5 challenge to show that the proposed models provide consistently good performance in comparison to contenders whose performance varies with data sets from simulation and experiments from model unicellular organisms Escherichia coli and Saccharomyces cerevisiae. Since the models' formulation facilitates the prediction of master regulators, we also used the resulting findings to identify master regulators over all data sets as well as their plasticity across different environments. Our results demonstrate that the identified master regulators are in line with experimental evidence from the model bacterium E. coli. Together, our study demonstrates that simultaneous modelling of several target genes results in improved inference of GRNs and can be used as an alternative in different applications.

MOTIVATION: Genomic selection (GS) is currently deemed the most effective approach to speed up breeding of agricultural varieties. It has been recognized that consideration of multiple traits in GS can improve accuracy of prediction for traits of low heritability. However, since GS forgoes statistical testing with the idea of improving predictions, it does not facilitate mechanistic understanding of the contribution of particular single nucleotide polymorphisms (SNP). RESULTS: Here, we propose a L2,1-norm regularized multivariate regression model and devise a fast and efficient iterative optimization algorithm, called L2,1-joint, applicable in multi-trait GS. The usage of the L2,1-norm facilitates variable selection in a penalized multivariate regression that considers the relation between individuals, when the number of SNPs is much larger than the number of individuals. The capacity for variable selection allows us to define master regulators that can be used in a multi-trait GS setting to dissect the genetic architecture of the analyzed traits. Our comparative analyses demonstrate that the proposed model is a favorable candidate compared to existing state-of-the-art approaches. Prediction and variable selection with datasets from Brassica napus, wheat and Arabidopsis thaliana diversity panels are conducted to further showcase the performance of the proposed model. AVAILABILITY AND IMPLEMENTATION: : The model is implemented using R programming language and the code is freely available from https://github.com/alainmbebi/L21-norm-GS. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.