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STATISTICS

Interpreting Treatment x Environment Interaction in Agronomy Trials

^a Universidad Autónoma de Chapingo, Km 38.5 Carretera México-Texcoco, Chapingo, Mexico and Biometrics and Statistics Unit, CIMMYT, Apdo. Postal 6-641, 06600 Mexico D.F., Mexico
^b Biometrics and Statistics Unit, CIMMYT, Apdo. Postal 6-641, 06600 Mexico D.F., Mexico
^c Wheat Progr., CIMMYT, Apdo. Postal 6-641, 06600 Mexico D.F., Mexico
^d Dep. of Plant Sci., Lab. of Plant Breeding, Wageningen Univ., P.O. Box 386, 6700 AJ Wageningen, the Netherlands

* Corresponding author (j.crossa{at}cgiar.org)

Received for publication August 7, 2000. Multienvironment trials are important in agronomy because the effects of agronomic treatments can change differentially in relation to environmental changes, producing a treatment x environment interaction (T x E). The aim of this study was to find a parsimonious description of the T x E existing in the 24 agronomic treatments evaluated during 10 consecutive years by (i) investigating the factorial structure of the treatments to reduce the number of treatment terms in the interaction and (ii) using quantitative year covariables to replace the qualitative variable year. Multiple factorial regression (MFR) for specific T x E terms was performed using standard forward selection procedures for finding year covariables that could replace the factor year in those T x E terms. Subsequently, we compared the results of the final MFR with those of a partial least squares based analysis to achieve extra insight in both the T x E and final MFR model. The MFR model with a stepwise procedure used in this study for describing the T x E showed that the most important interaction with year was that due to different N fertilizer levels and the most important environmental variables that explained year x N interaction were minimum temperatures in January, February, and March and maximum temperature in April. Evaporation in December and April were important covariables for describing year x tillage and year x summer crop interactions, whereas precipitation in December and sun hours in February were important for explaining the year x manure interaction. We also discuss the parallels with extended additive main effect and multiplicative interaction analysis. Biological interpretation of the results are provided.

Abbreviations: A, April • AMMI, additive main effect and multiplicative interaction • D, December • EV, total monthly evaporation • F, February • FR, factorial regression • G x E, genotype x environment interaction • J, January • M, March • MFR, multiple factorial regression • mT, mean minimum temperature sheltered • MT, mean maximum temperature sheltered • mTU, mean minimum temperature unsheltered • N_L, linear N effects • N_Q, quadratic N effects • PLS, partial least squares • PR, total monthly precipitation • SH, mean sun hours per day • T x E, treatment x environment interaction