Response to mass selection when the genotype by environment interaction is modelled as a linear reaction norm

Abstract

-A breeding goal accounting for the effects of genotype by environment interaction (G × E) has to define not only traits but also the environment in which those traits are to be improved. The aim of this study was to predict the selection response in the coefficients of a linear reaction norm, and response in average phenotypic value in any environment, when mass selection is applied to a trait where G × E is modelled as a linear reaction norm. The optimum environment in which to test the selection candidates for a given breeding objective was derived. Optimisation of the selection environment can be used as a means to either maximise genetic progress in a certain response environment, to keep the change in environmental sensitivity at a desired rate, or to reduce the proportion of animals performing below an acceptance level. The results showed that the optimum selection environment is not always equal to the environment in which the response is to be realised, but depends on the degree of G × E (determined by the ratio of variances in slope and level of a linear reaction norm), the correlation between level and slope, and the heritability of the trait. mass selection / selection response / reaction norm / genotype by environment interaction INTRODUCTIONGenotype by environment interaction (G × E) is becoming increasingly important due to the globalisation of animal breeding. With G × E, the phenotypic expression of a trait in different environments, such as countries, climatic zones or production systems, is genetically not the same trait. In such cases, the breeding goal should define not only the traits but also the environment in which those traits are to be improved. * Corresponding author: Rebecka.Kolmodin@hgen.slu.se

Genotype by environment interactions in forest tree breeding: review of methodology and perspectives on research and application

“…For instance, a particularly steep reaction norm slope for a given genotype means that its phenotype is more sensitive to environments, and the genotype will contribute strongly to G×E. The level of G×E can also be expressed as the ratio of variances in the additive genetic slope (σ 2 a 1 ) to the additive genetic intercept (σ 2 a 0 ) (Kolmodin and Bijma 2004) Strandberg et al 2000). The reaction norm approach has been applied in forest trees (Gregorius and Kleinschmit 2001), including species that are widely distributed with clinal ranges, notably Norway spruce (Oleksyn et al 1998) and Scots pine (Abraitiene et al 2002) in Sweden, and lodgepole pine (Rehfeldt et al 1999;Wang et al 2006) and its hybrids (Wu and Ying 2001) in Canada.…”

“…The advantage of the reaction norm is that selection response can be predicted not only in the phenotypic expression in any environment but also in quantifying the environmental sensitivity of the trait through the slope of a linear reaction norm (robustness or responsiveness to changes in the environment) (Kolmodin and Bijma 2004). Disease exposure, stocking density and nutrient quality are thought to be included as environmental factors affecting livestock production when conducting reaction norm analysis (Rauw and Gomez-Raya 2015).…”

“…It is suitable for analysing data on traits that vary gradually and continuously over an environmental gradient (e.g. temperature) (Kolmodin and Bijma 2004). A linear reaction norm for a single trait has a model (Kolmodin and Bijma 2004;Strandberg et al 2000):…”

“…temperature) (Kolmodin and Bijma 2004). A linear reaction norm for a single trait has a model (Kolmodin and Bijma 2004;Strandberg et al 2000):…”

Genome-wide association analysis to identify genotype × environment interaction for milk protein yield and level of somatic cell score as environmental descriptors in German Holsteins

“…The correlation between intercept and slope depends on where the intersection point of the reaction norm model is placed. As recommended by Kolmodin and Bijma (2004), we placed it in the average environment. In this case, the intercept estimate can be interpreted as an estimate for average or general production and the slope as an estimate for the environmental sensitivity.…”