Genetic gain & Inbreeding

Leveraging Price equation to generalise breeding value definition and predicting response to selection on additive and non-additive genetic variation

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Abstract

Response to selection is a fundamental concept in quantitative genetics and animal breeding, where it is traditionally examined through the Breeder's equation. This equation predicts change in trait means due to selection on additive genetic variation and is as such closely connected to the concept of additive genetic value. Due to this connection, additive genetic values are called as breeding values. In evolutionary biology, change due to selection is examined through the Price equation. This equation is a more general description of the change in trait means between generations. The generality comes from the exact decomposition of change in trait means into i) a covariance between individual trait values and relative reproductive success (describing change due to selection) and ii) the expectation of change in trait values weighted by relative reproductive success (describing change due to transmission). The Price equation is described as a mathematical identity and its generality comes from the minimal assumptions required: it does not assume additive genetic variation, or simple inheritance, or random mating, which is why it can accommodate varying genetic architecture, modes of inheritance and population structure. As a result, it can encompass a wider range of scenarios-including non-additive genetic effects, but also environmental trends, transmission biases, even epigenetic and cultural inheritance. This evolutionary theory indicates that the standard definition of the breeding value is lacking a generalised definition. In this work, we use the Price equation to study the definition of breeding value and response to selection in animal breeding scenarios with additive, dominance, and imprinting effects under random and non-random mating. Derivations show that breeding value can be generally expressed as individual's expected genetic contribution to genetic values of its progeny given a mating pool of selection candidates. This reformulation decomposes the expected response to selection into the population mean, the paternal and maternal linear contributions to progeny genetic value, and a deviation term that captures the non-linear component of the response. The resulting equation accommodates scenarios involving dominance, non-random mating, imprinting, and other parent-of-origin or epigenetic effects, thereby relaxing the focus on additive genetic variation only. Under this framework, the variance of breeding values can differ from the additive genetic variance, yielding a prospective/inheritance/realised definition of heritability. Moreover, the deviation term is proportional to the average dominance effect, providing direct insight into the presence and magnitude of directional dominance. The theory was further applied to a real dataset from the Pirenaica beef cattle population, revealing for carcass weight a systematic change associated with directional dominance, with an estimated magnitude of approximately 0.8 kg. This work provides a theoretical foundation that bridges quantitative and evolutionary genetics, offering a flexible and biologically grounded framework for analysing selection responses beyond the additive genetic paradigm.

Keywords: 2026

How to Cite:

López-Carbonell, D., Varona, L., Gaynor, C. & Gorjanc, G., (2026) “Leveraging Price equation to generalise breeding value definition and predicting response to selection on additive and non-additive genetic variation”, World Congress on Genetics Applied to Livestock Production Digital Archive 2026(1): 2285655. doi: https://doi.org/10.31274/wcgalp.23769

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