New genotypic adaptability and stability analyses using Legendre polynomials and genotype-ideotype distances

Developing cultivars with superior performance in different cultivation environments is one of the main challenges of breeding programs. The current adaptability and stability analyses have limitations, especially when used with trials with genetic or statistical imbalances, heterogeneity of residual variances, and genetic covariance. Thus, adaptability and stability analyses based on mixed model approaches are an effective alternative in such cases. We propose a new methodology for genotypic adaptability and stability analyses, based on Legendre polynomials and genotype-ideotype distances aiming at greater precision when recommending cultivars. We applied the methodology to a set of common bean cultivars throughout a multi-environment trial. We used a set of 13 trials, where they were classified in unfavorable or favorable environments, depending on the average of the cultivars in these trials. The results showed that the methodology allows to predict the genotypic values of cultivars in environments where they were not evaluated with high accuracy values, therefore circumventing the imbalance of the experiments. From these values, it was possible to measure the genotypic adaptability according to ideotypes. The stability of the cultivars was quantified as the invariance of their behavior throughout the trials. The use of ideotypes based on real data allowed a better comparison of the performance of cultivars across environments.