specific adaptability to favorable (requires a high level of technology) or unfavorable (requires 58 a low level of technology) environments, methodologies that are based on linear regression 59 models have shown promise [4][5][6][7]. Some of the previous methods to determine the adaptability 60 and stability included the ideotype concept [8][9][10][11], and resulted in an improved understanding 61 of the relative behavior of the genotypes from a smaller number of parameters. According to 62 Eeuwijk et al. [12], there are other methodologies to assess the behavior of genotypes that are 63 of note, such as AMMI (Additive Main effects and Multiplicative Interaction) [13] and GGE 64 biplot (Genotype main effects and Genotype x Environment interaction effects) [14]. However, 65 the adaptability and stability analyses still have limitations, especially when used with trials 66 with genetic or statistical imbalances, heterogeneity of residual variances, and genetic 67 covariance. In this context, adaptability and stability analyses that use a mixed model approach 68are an effective alternative to the traditional analyses [15,16]. 69Another relevant factor is that traditional methodologies for the analysis of adaptability 70 and stability, consider a priori, that the behavior of a genotype across environments is linear, 71 which may not be true. As a consequence, recommendations based on these methodologies can 72 be biased. This can be outlined by means of reaction norm models via mixed modeling, as they 73 allow for improved modeling of the behavior of the different genotypes, based mostly on 74 orthogonal polynomials. Among this class of polynomials, the Legendre's polynomials stand 75 out, as they have the ability to describe the structures of variance and covariance between the 76 genetic and environmental components [17]. 77In this way, the use of the reaction norms obtained from the Legendre polynomials can 78 better quantify the adaptability and stability of a set of genotypes evaluated in different 79 environments, aiming for greater accuracy in cultivar recommendations. Thus, the objectives 80 of this investigation were to propose a new methodology for the analysis of adaptability and 81 genotypic stability, based on Legendre polynomials and genotype-ideotype distances.
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