Reviving the Desired Gains Index: An optimal solution for parent selection in public plant breeding programs

The Desired Gains Index is an optimal solution for parent selection in public plant breeding programs. It enables breeders to quantify their breeding objectives in terms of desired genetic gains and facilitates the efficient simultaneous improvement of multiple quantitative traits in a breeding population without the need for economic weights. We deliberately chose the term "optimal" here, which is typically associated with the profit-oriented selection indices commonly used in animal breeding, such as the Smith-Hazel Index. Our intention is to refute the perception that the Desired Gains Index is less efficient than the Smith-Hazel Index since both approaches maximise expected genetic gains in proportion to the breeding objective. To achieve this, we first review the relationship between the Desired Gains Index and the Smith-Hazel Index to show that desired gains are actually a form of economic weighting expressed as an improvement ratio for the traits under selection. We then present a general form of the Desired Gains Index to leverage best linear unbiased prediction (BLUP), which enables seamless integration of pedigree or genomic relationship information (e.g., genomic estimated breeding values) between the selection candidates and other related individuals. Finally, using stochastic simulation, we compare the performance of different parent selection strategies, including index selection, independent culling, and selection of extreme genotypes. The objective of these demonstrations is to convey the potential impact and benefits of the Desired Gains Index to a broader audience without the need for a deep understanding of selection theory and the equations presented here.