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CROP BREEDING, GENETICS & CYTOLOGY

Likelihood-Based Analysis of Genotype–Environment Interactions

Alberta Agriculture, Food and Rural Development, #301, 7000-113 Street, Edmonton, AB, Canada T6H 5T6 and Dep. of Agricultural, Food and Nutritional Science, Univ. of Alberta, Edmonton, AB, Canada T6G 2P5

* Corresponding author (rongcai.yang{at}gov.ab.ca)

Variation of genotype–environment interactions can be divided to determine whether or not the interactions involve change in genotype or cultivar ranks across environments. However, no sound statistical tests are available for such determination. In this study, the restricted maximum likelihood (REML) analysis based on the mixed models theory was used to estimate genetic parameters and to test statistically for causes of genotype–environment interactions in two wheat (Triticum aestivum L.) crosses, Potam x Ingal and RL4137 x Ingal. The data with each cross consisted of the measurements of five quantitative traits for 144 F₃-derived F₅ and F₆ lines from 48 F₂ families evaluated at Saskatoon in 1986 and 1987, respectively. The causes of family x year or line x year interactions were tested by comparing log likelihoods of reduced and full models (i.e., the family or line covariance structures with and without constraints). The REML estimation guaranteed that an estimated family or line covariance matrix was positive definite. Significant line x year interactions were detected in three traits in RL4137 x Ingal only and none involved rank changes. Significant family x year interactions were found in seven of 10 cross-trait cases, but four of those seven cases involved change in family ranks across the 2 yr. The REML analysis allows the development of sound statistical tests for the different causes of interactions and constraining estimated genetic variances and covariances within acceptable ranges, thereby effectively removing the deficiencies with the conventional multivariate analysis of variance method.

Abbreviations: LR, likelihood ratio • MANOVA, multivariate analysis of variance • REML, restricted maximum likelihood • WLS, weighted least squares

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