Dominic L. Waters, Julius H. J. van der Werf, Hannah Robinson, Lee T. Hickey & Sam A. Clark

Theoretical and Applied Genetics May 2023; vol. 136, Article number: 99

Key message

The reaction norm analysis of stability can be enhanced by partitioning the contribution of different types of G × E to the variation in slope.

Abstract

The slope of regression in a reaction norm model, where the performance of a genotype is regressed over an environmental covariable, is often used as a measure of stability of genotype performance. This method could be developed further by partitioning variation in the slope of regression into the two sources of genotype-by-environment interaction (G × E) which cause it: scale-type G × E (heterogeneity of variance) and rank-type G × E (heterogeneity of correlation). Because the two types of G × E have very different properties, separating their effect would enable a clearer understanding of stability. The aim of this paper was to demonstrate two methods which seek to achieve this in reaction norm models. Reaction norm models were fit to yield data from a multi-environment trial in Barley (Hordeum vulgare), with the adjusted mean yield from each environment used as the environmental covariable. Stability estimated from factor-analytic models, which can disentangle the two types of G × E and estimate stability based on rank-type G × E, was used for comparison. Adjusting the reaction norm slope to account for scale-type G × E using a genetic regression more than tripled the correlation with factor-analytic estimates of stability (0.24–0.26 to 0.80–0.85), indicating that it removed variation in the reaction norm slope that originated from scale-type G × E. A standardisation procedure had a more modest increase (055–0.59) but could be useful when curvilinear reaction norms are required. Analyses which use reaction norms to explore the stability of genotypes could gain additional insight into the mechanisms of stability by applying the methods outlined in this study.

See https://link.springer.com/article/10.1007/s00122-023-04319-9

Fig.1: Schematic example of the regression of four genotypes (coloured lines) across a common factor, ‘x’ in a FA model. The vertical black lines represent the variation in GEBVs for the common factor ‘x’ at the average of the positive and negative loadings (or average contrasts). In a, the average negative and positive loading are − 0.15 and 0.7 units, respectively, and in b, − 0.7 and 0.7 units respectively.