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.

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).