Abstract
Abstract: The objective of this work was to propose a weighting scheme for the additive main effects and multiplicative interactions (AMMI) model, as well as to assess the usefulness of this W-AMMI model in the study of genotype x environment interaction (GxE) and quantitative trait locus x environment interaction (QxE) for nonreplicated data. Data from the 'Harrington' x TR306 barley (Hordeum vulgare) mapping population, with 141 genotypes evaluated in 25 environments, were used to compare the results from the AMMI model with those of two proposed versions of the W-AMMI model: equal weights per row and equal weights per column. The proposed W-AMMI columns algorithm is viable to analyze data with heterogeneous variance, when there are no replicates available. The use of the AMMI and W-AMMI models, in the indicated cases, improves QTL detection, besides providing a sound interpretation of GxE and a better understanding of QxE, which allows obtaining valuable information on increasing productivities in different environments.
Highlights
The genotype x environment interaction (GxE) and the quantitative trait locus (QTL) x environment interaction (QxE) are common phenomena in multienvironmental trials (METs), and they represent a major challenge for breeders who intend to develop more adapted genotypes to different environmental conditions
The modelling strategies that have been used to understand GxE and quantitative trait locus x environment interaction (QxE) are based on fixed effect models, such as regression techniques (Rodrigues et al, 2011; Pereira et al, 2012a, 2012b), as well as on singular-value decomposition techniques (SVD) (Gauch Jr., 1992; Paderewski et al, 2011; Paderewski & Rodrigues, 2014), and on mixed effects models (Alimi et al, 2012)
When the error variance is heterogeneous throughout the environments, or when data are contaminated, the use of the AMMI model might not be appropriate (Rodrigues et al, 2014, 2016)
Summary
The genotype x environment interaction (GxE) and the quantitative trait locus (QTL) x environment interaction (QxE) are common phenomena in multienvironmental trials (METs), and they represent a major challenge for breeders who intend to develop more adapted genotypes to different environmental conditions. The modelling strategies that have been used to understand GxE and QxE are based on fixed effect models, such as regression techniques (Rodrigues et al, 2011; Pereira et al, 2012a, 2012b), as well as on singular-value decomposition techniques (SVD) (Gauch Jr., 1992; Paderewski et al, 2011; Paderewski & Rodrigues, 2014), and on mixed effects models (Alimi et al, 2012). The additive main effects and the multiplicative interaction (AMMI) (Gauch Jr., 1992) is the most widely used model to understand GxE and QxE.
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