High-dimensional multi-omics microbiome data play an important role in elucidating microbial community interactions with their hosts and environment in critical diseases and ecological changes. Although Bayesian clustering methods have recently been used for the integrated analysis of multi-omics data, no method designed to analyze multi-omics microbiome data has been proposed. In this study, we propose a novel framework called integrative stochastic variational variable selection (I-SVVS), which is an extension of stochastic variational variable selection for high-dimensional microbiome data. The I-SVVS approach addresses a specific Bayesian mixture model for each type of omics data, such as an infinite Dirichlet multinomial mixture model for microbiome data and an infinite Gaussian mixture model for metabolomic data. This approach is expected to reduce the computational time of the clustering process and improve the accuracy of the clustering results. Additionally, I-SVVS identifies a critical set of representative variables in multi-omics microbiome data. Three datasets from soybean, mice, and humans (each set integrated microbiome and metabolome) were used to demonstrate the potential of I-SVVS. The results indicate that I-SVVS achieved improved accuracy and faster computation compared to existing methods across all test datasets. It effectively identified key microbiome species and metabolites characterizing each cluster. For instance, the computational analysis of the soybean dataset, including 377 samples with 16 943 microbiome species and 265 metabolome features, was completed in 2.18 hours using I-SVVS, compared to 2.35 days with Clusternomics and 1.12 days with iClusterPlus. The software for this analysis, written in Python, is freely available at https://github.com/tungtokyo1108/I-SVVS.

MOTIVATION: Differentiable programming frameworks like PyTorch and JAX revolutionized biological modeling. A foremost merit is that multiple components programmed separately can be put together so that the parameters are jointly optimized. Despite its proven value in agricultural applications, existing breeding simulators are non-differentiable, hindering integration into general deep learning systems. RESULTS: In this paper, we present DiffBreed, a differentiable breeding simulator. Its performance was evaluated in gradient-based optimization of a progeny allocation strategy that maximizes the genetic gain. By utilizing gradient-based optimization, DiffBreed refined progeny allocation strategies, achieving superior genetic gains compared to a non-optimized equal allocation approach. These findings highlight DiffBreed's capacity to properly calculate gradient information through automatic differentiation. With its innovative design, DiffBreed is expected to transform future breeding optimization by integrating into modern deep learning workflows. AVAILABILITY AND IMPLEMENTATION: The proposed automatic differentiation framework was implemented as the Python module "DiffBreed." This module and all the scripts used in this study, including the gradient-based optimization, are available from the "KosukeHamazaki/GORA-PT" repository on GitHub, https://github.com/KosukeHamazaki/GORA-PT. While the simulated datasets in the present study are available from the same repository, the optimized results by PyTorch were not shared in this repository due to the file sizes. Instead, all datasets, including the optimized ones, will be shared in the repository on Zenodo, https://doi.org/10.5281/zenodo.14046522.

The evaluation of plant and animal growth, separately for genetic and environmental effects, is necessary for genetic understanding and genetic improvement of environmental responses of plants and animals. We propose to extend an existing approach that combines nonlinear mixed-effects model (NLMEM) and the stochastic approximation of the Expectation-Maximization algorithm (SAEM) to analyze genetic and environmental effects on plant growth. These tools are widely used in many fields but very rarely in plant biology. During model formulation, a nonlinear function describes the shape of growth, and random effects describe genetic and environmental effects and their variability. Genetic relationships among the varieties were also integrated into the model using a genetic relationship matrix. The SAEM algorithm was chosen as an efficient alternative to MCMC methods, which are more commonly used in the domain. It was implemented to infer the expected growth patterns in the analyzed population and the expected curves for each variety through a maximum-likelihood and a maximum-a-posteriori approaches, respectively. The obtained estimates can be used to predict the growth curves for each variety. We illustrate the strengths of the proposed approach using simulated data and soybean plant growth data obtained from a soybean cultivation experiment conducted at the Arid Land Research Center, Tottori University. In this experiment, plant height was measured daily using drones, and the growth was monitored for approximately 200 soybean cultivars for which whole-genome sequence data were available. The NLMEM approach improved our understanding of the determinants of soybean growth and can be successfully used for the genomic prediction of growth pattern characteristics.

Genomic selection (GS) is expected to accelerate plant and animal breeding. During the last decade, genome-wide polymorphism data have increased, which has raised concerns about storage cost and computational time. Several individual studies have attempted to compress the genome data and predict phenotypes. However, compression models lack adequate quality of data after compression, and prediction models are time consuming and use original data to predict the phenotype. Therefore, a combined application of compression and genomic prediction modeling using deep learning could resolve these limitations. A Deep Learning Compression-based Genomic Prediction (DeepCGP) model that can compress genome-wide polymorphism data and predict phenotypes of a target trait from compressed information was proposed. The DeepCGP model contained two parts: (i) an autoencoder model based on deep neural networks to compress genome-wide polymorphism data, and (ii) regression models based on random forests (RF), genomic best linear unbiased prediction (GBLUP), and Bayesian variable selection (BayesB) to predict phenotypes from compressed information. Two datasets with genome-wide marker genotypes and target trait phenotypes in rice were applied. The DeepCGP model obtained up to 99% prediction accuracy to the maximum for a trait after 98% compression. BayesB required extensive computational time among the three methods, and showed the highest accuracy; however, BayesB could only be used with compressed data. Overall, DeepCGP outperformed state-of-the-art methods in terms of both compression and prediction. Our code and data are available at https://github.com/tanzilamohita/DeepCGP.

Difficulty in detecting rare variants is one of the problems in conventional genome-wide association studies (GWAS). The problem is closely related to the complex gene compositions comprising multiple alleles, such as haplotypes. Several single nucleotide polymorphism (SNP) set approaches have been proposed to solve this problem. These methods, however, have been rarely discussed in connection with haplotypes. In this study, we developed a novel SNP-set method named "RAINBOW" and applied the method to haplotype-based GWAS by regarding a haplotype block as a SNP-set. Combining haplotype block estimation and SNP-set GWAS, haplotype-based GWAS can be conducted without prior information of haplotypes. We prepared 100 datasets of simulated phenotypic data and real marker genotype data of Oryza sativa subsp. indica, and performed GWAS of the datasets. We compared the power of our method, the conventional single-SNP GWAS, the conventional haplotype-based GWAS, and the conventional SNP-set GWAS. Our proposed method was shown to be superior to these in three aspects: (1) controlling false positives; (2) in detecting causal variants without relying on the linkage disequilibrium if causal variants were genotyped in the dataset; and (3) it showed greater power than the other methods, i.e., it was able to detect causal variants that were not detected by the others, primarily when the causal variants were located very close to each other, and the directions of their effects were opposite. By using the SNP-set approach as in this study, we expect that detecting not only rare variants but also genes with complex mechanisms, such as genes with multiple causal variants, can be realized. RAINBOW was implemented as an R package named "RAINBOWR" and is available from CRAN (https://cran.r-project.org/web/packages/RAINBOWR/index.html) and GitHub (https://github.com/KosukeHamazaki/RAINBOWR).

BACKGROUND: Genomic selection is an effective tool for animal and plant breeding, allowing effective individual selection without phenotypic records through the prediction of genomic breeding value (GBV). To date, genomic selection has focused on a single trait. However, actual breeding often targets multiple correlated traits, and, therefore, joint analysis taking into consideration the correlation between traits, which might result in more accurate GBV prediction than analyzing each trait separately, is suitable for multi-trait genomic selection. This would require an extension of the prediction model for single-trait GBV to multi-trait case. As the computational burden of multi-trait analysis is even higher than that of single-trait analysis, an effective computational method for constructing a multi-trait prediction model is also needed. RESULTS: We described a Bayesian regression model incorporating variable selection for jointly predicting GBVs of multiple traits and devised both an MCMC iteration and variational approximation for Bayesian estimation of parameters in this multi-trait model. The proposed Bayesian procedures with MCMC iteration and variational approximation were referred to as MCBayes and varBayes, respectively. Using simulated datasets of SNP genotypes and phenotypes for three traits with high and low heritabilities, we compared the accuracy in predicting GBVs between multi-trait and single-trait analyses as well as between MCBayes and varBayes. The results showed that, compared to single-trait analysis, multi-trait analysis enabled much more accurate GBV prediction for low-heritability traits correlated with high-heritability traits, by utilizing the correlation structure between traits, while the prediction accuracy for uncorrelated low-heritability traits was comparable or less with multi-trait analysis in comparison with single-trait analysis depending on the setting for prior probability that a SNP has zero effect. Although the prediction accuracy with varBayes was generally lower than with MCBayes, the loss in accuracy was slight. The computational time was greatly reduced with varBayes. CONCLUSIONS: In genomic selection for multiple correlated traits, multi-trait analysis was more beneficial than single-trait analysis and varBayes was much advantageous over MCBayes in computational time, which would outweigh the loss of prediction accuracy caused by the approximation procedure, and is thus considered a practical method of choice.