Analysis of Genotype × Environment Interaction by Stability Estimates

Genotype × environmental interaction (GEI) is an important consideration in plant breeding programs because it reduces the progress from selection in any one environment (Hill, 1975). Significant GEI results from the changes in the magnitude of differences between genotypes in different environments or changes in the relative ranking of the genotypes. Consistent performances across different sites and/or years are referred to as stability. Partitioning GEI into stability statistics assignable to each genotype evaluated across a range of environments is useful in selecting stable genotypes. Different stability estimates are proposed to measure the stability of genotypes tested under a wide range of environments (Fernandez et al., 1989; Hill, 1975; Pritts and Luby, 1990). The most popular methods (Eberhart and Russell, 1966; Finlay and Wilkinson, 1963) have used analysis of variance combined with joint regression analysis to determine whether GEI is a linear function of the additive environment. Genotypes having unit slope (Finlay and Wilkinson, 1963), insignificant deviation from regression (Eberhart and Russell, 1966), and a large coefficient of determination (r2) (Pinthus, 1973) are considered averagely stable. One of the essential features in developing this regression technique was the estimation of the environmental index (EI), an independent variable, which is obtained by subtracting the environmental mean from the grand mean. Although joint regression analysis (Eberhart and Russell, 1966) has been extensively used to study stability, the statistical validity of this method has been questioned because genotypic means are not statistically independent of the EI on which they are regressed (Hill, 1975; Shukla, 1972). However, Hardwick and Wood (1972) claimed that when many genotypes are included in the experiment and the environmental range is such that the betweenenvironments mean square is significantly greater than error mean square, any bias that results should not prove serious in practice. Freeman (1973) also agreed that this regression procedure is perfectly valid provided the