Selection index theory for populations under directional and stabilizing selection

Abstract

Background The purpose of a selection index is that its use to select animals for breeding maximizes the profit of a breed in future generations. The profit of a breed is in general a quantity that predicts the satisfaction of future owners with their breed, and the satisfaction of the consumers with the products that are produced by the breed. Many traits, such as conformation traits and product quality traits have intermediate optima. Traditional selection index theory applies only to directional selection and cannot achieve any further improvement once the trait means have reached their optima. A well-founded theory is needed that extends the established selection index theory to cover directional as well as stabilizing selection as limiting cases, and that can be applied to maximize the profit of a breed in both situations. Results The optimum selection index shifts the trait means towards the optima and, in the case of stabilizing selection, decreases the phenotypic variance, which causes the phenotypes to be closer to the optimum. The optimum index depends not only on the breeding values, but also on the squared breeding values, the allele contents of major quantitative trait loci (QTL), the QTL heterozygosities, the inbreeding coefficient of the animal, and the kinship of the animal with the population. Conclusion The optimum selection index drives the alleles of major QTL to fixation when the trait mean approaches the optimum because decreasing the phenotypic variance shifts the trait values closer to the optimum, which increases the profit of the breed. The index weight on the kinship coefficient balances the increased genetic gain that can be achieved in future generations by outcrossing, and the increased genetic gain that can be achieved under stabilizing selection by reducing the phenotypic variance. In a model with dominance variance, it can also account for the effect of inbreeding depression. The combining ability between potential mating partners, which predicts the total merit of their offspring, could become an important parameter for mate allocation that could be used to further shift the phenotypes towards their optimum values.

Defining valid breeding goals for animal breeds

“…where the sum is taken over the relevant performance and behaviour traits. Wellmann [10] shows how merit functions with this functional form can be integrated for deriving selection indices. The weights ω ek of the traits could be determined by expert assessment or by discrete choice experiments [21].…”

“…The selection index can then be computed with the desired gain approach [8]. The more general case that the phenotypic covariance matrix changes over time is considered in [10]. The proposed optimization process outlined above consists of three steps, which are model development, parameter Fig.…”

“…The vector with desired gains equals µ = μi b − µ c b , where µ c b is the vector of current trait means. The approach could be further improved by discounting future genetic gains [9], or by relaxing simplistic assumptions about the trait architecture [10], which is, however, rarely done in practice.…”

Genomic-inferred cross-selection metrics for multi-trait improvement in a recurrent selection breeding program

“…In general, these metrics and others are typically evaluated based on individual traits. However, in practice, potential parents often possess multiple traits of economic and agronomic significance (Cerón-Rojas & Crossa, 2022; Wellmann, 2023). These traits have attributes linked to productive performance, adaptability, and production stability.…”

“…The Smith and Hazel selection index, which integrates genetic correlation with economic weights, has gained wide traction in animal breeding (Bernardo, 2020;Cerón-Rojas & Crossa, 2022;Wellmann, 2023). Determining suitable weights for different agronomic and quality traits remains a significant challenge, limiting the widespread adoption of this index in plant breeding.…”