Analysis of linear and non-linear genotype × environment interaction - Yang, Rong-Cai (Frontiers in Genetics, 2014)
The usual analysis of genotype × environment interaction (GxE) is based on the linear regression of genotypic performance on environmental changes (e.g., classic stability analysis). This linear model may often lead to lumping together of the nonlinear responses to the whole range of environmental changes from suboptimal and superoptimal conditions, thereby lowering the power of detecting GxE variation. On the other hand, the GxE is present when the magnitude of the genetic effect differs across the range of environmental conditions regardless of whether the response to environmental changes is linear or nonlinear. The objectives of this study are: (i) explore the use of four commonly used nonlinear functions (logistic, parabola, normal and Cauchy functions) for modeling nonlinear genotypic responses to environmental changes and (ii) to investigate the difference in the magnitude of estimated genetic effects under different environmental conditions. The use of nonlinear functions was illustrated through the analysis of one data set taken from barley cultivar trials in Alberta, Canada (Data A) and the examination of change in effect sizes is through the analysis another data set taken from the North America Barley Genome Mapping Project (Data B). The analysis of Data A showed that the Cauchy function captured an average of >40% of total GxE variation whereas the logistic function captured less GxE variation than the linear function. The analysis of Data B showed that genotypic responses were largely linear and that strong QTL × environment interaction existed as the positions, sizes and directions of QTL detected differed in poor vs. good environments. We conclude that (i) the nonlinear functions should be considered when analyzing multi-environmental trials with a wide range of environmental variation and (ii) QTL × environment interaction can arise from the difference in effect sizes across environments.