Genotype ✕ Environment Interactions for Cane and Sugar Yield and Their Implications in Sugarcane Breeding1

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Abstract
Genotype ✕ environment (GE) interactions limit the effectiveness of selection when selection is based only on mean yields. This study evaluated three methods of partitioning GE interaction into stability‐variance components assignable to each cultivar in sugarcane (Saccharum spp.) cultivar evaluation tests. An unbiased stability‐variance parameter (σ̂21) developed by Shukla and an ecovalence stability index (w) developed by Wricke were calculated separately for plant‐cane and ratoon crops for Brix (%), grams of sugar per kilogram of cane, and tons per hectare of cane and of sugar for 11 cultivars. A cultivar ✕ location component of variance (σ̂2c1) proposed by Plaisted and Peterson was also calculated. Within each crop, σ̂21 and w had identical cultivar rankings (rs = 1.00**) (**, Significant at the 0.01 level.) for each of the four traits studied. We propose that w sum of squares for each cultivar be expressed as w mean square and the latter be tested for significance in the same manner as σ̂21. Those cultivars with a significant mean square were judged to be unstable. Shukla's method allowed use of a covariate of fertility and cultural practices at different locations to remove heterogeneity variance (nonadditivity) from the GE interaction, and partitioning of the remainder of variance assignable to each cultivar (ŝ21). Certain cultivars were judged stable after the covariate adjustment, indicating that the instability Was introduced by the linear effect of the covariate. Methodology for computing the σ̂2CL component is cumbersome and would have little application when a large number of genotypes are evaluated. Repeatability of stability‐variance parameters between crops (individual repeatability) was relatively low for the four traits studied.