Optimising desired gain indices to maximise selection response.

Introduction: In plant breeding, we often aim to improve multiple traits at once. However, without knowing the economic value of each trait, it is hard to decide which traits to focus on. This is where "desired gain selection indices" come in handy, which can yield optimal gains in each trait based on the breeder's prioritisation of desired improvements when economic weights are not available. However, they lack the ability to maximise the selection response and determine the correlation between the index and net genetic merit.

Methods: Here, we report the development of an iterative desired gain selection index method that optimises the sampling of the desired gain values to achieve a targeted or a user-specified selection response for multiple traits. This targeted selection response can be constrained or unconstrained for either a subset or all the studied traits.

Results: We tested the method using genomic estimated breeding values (GEBVs) for seven traits in a bread wheat () reference breeding population comprising 3,331 lines and achieved prediction accuracies ranging between 0.29 and 0.47 across the seven traits. The indices were validated using 3,005 double haploid lines that were derived from crosses between parents selected from the reference population. We tested three user-specified response scenarios: a constrained equal weight (INDEX1), a constrained yield dominant weight (INDEX2), and an unconstrained weight (INDEX3). Our method achieved an equivalent response to the user-specified selection response when constraining a set of traits, and this response was much better than the response of the traditional desired gain selection indices method without iteration. Interestingly, when using unconstrained weight, our iterative method maximised the selection response and shifted the average GEBVs of the selection candidates towards the desired direction.

Discussion: Our results show that the method is an optimal choice not only when economic weights are unavailable, but also when constraining the selection response is an unfavourable option.