The objective of this work was to obtain the theoretical derivation of the bivariate extension to the methods proposed by Annicchiarico (1992) and Annicchiarico et al. (1995) for studing phenotypic stability. Considering assays with <img src="/img/revistas/cagro/v28n5/a11res01.gif" align=texttop>genotypes in <img src="/img/revistas/cagro/v28n5/a11res02.gif" align=texttop>environments and two variates, every genotype had the response of each variate (k = 1, 2) standardized. This standardization has been made using the environment means as follows: Wijk = Yijk/<img src="/img/revistas/cagro/v28n5/a11res03.gif" align=top>×100 ; where Wijk represents the ith genotype standard value in the jth environment for the kth variate; <img src="/img/revistas/cagro/v28n5/a11res04.gif" align=top>represents the observed mean of the ith genotype, in jth environment for the kth variate e <img src="/img/revistas/cagro/v28n5/a11res07.gif" align=texttop>the overall genotypes means for jth environment to kth variate. Considering the standardized values, the genotypes mean vector and covariance matrix were estimated. The theoretical derivation of the bivariate reliability index (Ii) of Annicchiarico was wasked out and a second risk index was proposed based on the bivariate probabilities (Prb i); the two indexes proposed has shown good agreement to the results in an example with melon genotypes.
Reliability index; bivariate normal distribution; principal components
