Differentiable breeding: Automatic differentiation enables efficient gradient-based optimization of breeding strategies
Authors: Hamazaki Kosuke , Iwata Hiroyoshi , Tsuda Koji 
Published: December 2024

Conventional breeding methods often require extensive time to develop new cultivars, hindering rapid adaptation to global challenges. While genomic selection has accelerated breeding, there remains substantial room for improvement. Recent studies have explored complex decision-making in breeding schemes using various optimization techniques such as black-box optimization. However, these methods are challenged by constraints in simultaneously optimizing multiple parameters necessary for achieving more efficient and flexible optimization. To address these limitations, this study implemented automatic differentiation of breeding schemes using PyTorch. By treating the entire breeding scheme as a differentiable computational graph, we enabled efficient gradient calculations for final genetic gains relative to progeny allocation parameters for each mating pair. We first validated our approaches by comparing automatic differentiation with analytical results in a simple gamete generation test case. Next, we used automatic differentiation to perform gradient-based optimization of progeny allocation strategies, aiming to maximize genetic gains in breeding schemes. The gradient-based strategy was then compared to black-box-based optimized and non-optimized strategies. Our framework successfully reduced the number of function evaluations needed for optimization compared to the black-box-based approach and outperformed the non-optimized strategy in terms of genetic gains. This demonstrates that our framework effectively harnessed gradient information via automatic differentiation. Integrating automatic differentiation into breeding strategy optimization is expected to enhance flexibility and lay the groundwork for future breeding optimization methods.

Author summary

Plant breeding plays a crucial role in addressing global challenges like population growth and climate change by developing more efficient and adaptable crop varieties. However, conventional breeding methods often require several years to produce new cultivars, making it difficult to keep pace with these challenges. Recent advancements in breeding techniques, such as genomic selection, have significantly enhanced selection accuracy and speed. Despite these improvements, substantial room for optimization remains in real breeding programs. This study explores the application of automatic differentiation to optimize breeding strategies, specifically focusing on the number of progenies allocated to each mating pair. Automatic differentiation enables efficient calculation of derivatives for complex functions, potentially accelerating the optimization process in breeding schemes. We implemented differentiable breeding schemes based on automatic differentiation using PyTorch, treating the entire breeding scheme as a differentiable computational graph. By integrating automatic differentiation into breeding strategy optimization, this approach is expected to enable more efficient exploration of optimal solutions while achieving more flexible optimization with a greater number of parameters. This novel method has the potential to significantly enhance the efficiency and flexibility of breeding optimization, ultimately contributing to the development of more adaptable and productive crop varieties to address global food challenges.