A new evaluation model for variety stability

Abstract

For a wide variation range, it could be admitted that the behaviour of a variety follows an exponential curve given by the E(Y_i) = K.A.^BXi model, that was replaced by a discontinuous bi-segmented model, with the following characteristics: Y_ij=b0_i+b1_it_j+b2_it_jZ_j+b3_iZ_j+d_ij+Î_ij for the l^st cultivar, where: b0 is the value of Y on spot, t_j = 0 of the first segment; b1 measures the slope of the first regression segment; b2 measures the difference in slope between the second and the first regression segments; b3 measures the discontinuity between both linear regression segments; d_ij is the model deviation; Î_ij is the error associated to the Y_ij estimator; t_j is the environmental effect; and Z_j = 1 if t_j > 0, and Z_j.=0 if £0. The efficiency of the model, when replacing the exponential curve, was more than 99%. By knowing the estimatives for b1, b2 and b3, it is possible to identify the relative position of any cultivar over the entire curve, and therefore identify its characteristics in order to compare it with other cultivars aiming to select it. A group of 33 maize cultivars evaluated in 19 localities of the State of Rio Grande do Sul were analysed.
Index terms: linear regression; exponential curve; environmental variation.