The usual analysis of genotype × environment interaction (G × E) 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 non-linear responses to the whole range of environmental changes from suboptimal and super optimal conditions, thereby lowering the power of detecting G × E variation. On the other hand, the G × E 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 non-linear. The objectives of this study are: (i) explore the use of four commonly used non-linear functions (logistic, parabola, normal and Cauchy functions) for modeling non-linear 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 non-linear 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 G × E variation whereas the logistic function captured less G × E 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 non-linear 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.
Keywords: barley, environmental index, estimation, genotype × environment interaction, non-linear functions, quantitative trait loci
Citation: Yang R-C (2014) Analysis of linear and non-linear genotype × environment interaction. Front. Genet. 5:227. doi: 10.3389/fgene.2014.00227
Received: 19 May 2014; Accepted: 30 June 2014;
Published online: 22 July 2014.
Edited by:José M. Álvarez-Castro, Universidade de Santiago de Compostela, Spain
Reviewed by:Keyan Zhao, University of California, Los Angeles, USA
Copyright © 2014 Yang. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Rong-Cai Yang, Department of Agricultural, Food and Nutritional Science, University of Alberta, 410 Agriculture/Forestry Centre, Edmonton, Alberta T6G 2P5, Canada e-mail: email@example.com