Construction of optimum index to maximize overall response across countries in the presence of genotype x environment interaction

Sire effect is partitioned into two parts: constant effect unaffected by environments and interaction effect specific to each environment and responsible for genotype x environment (GE) interaction. Response to selection for constant effect is the same across environments, thus increasing genetic stability, whereas response to selection for interaction effect would vary depending upon environments. The conventional measure of GE interaction based on genetic correlation (gammaG) considers both constant and interaction components even though the constant component plays no role in GE interaction. In contrast, the proposed measure of GE interaction based on interaction correlation (gammaI) deals only with interaction component responsible for GE interaction and thus indicates the intensity of GE interaction generated by responsible genes. Constant and interaction effects with different economic weights were combined into optimum index to improve both genetic stability and overall response across countries (countries represent environments). Optimum index was more efficient than the unpartitioned index which was more efficient than selection in a single country except when economic weights between constant and interaction effects were equal. Optimum index and unpartitioned index were the same when these economic weights were equal. The advantage of optimum index over the other selection methods increases as the intensity of GE interaction increases. When the relative economic weights are equivalent among countries and between constant and interaction effects, selection in a country with a larger sire variance is more effective than selection in a country with a smaller sire variance.