Improving stability of crop yield in a target production environment is an important breeding objective. It is well known that selection for better stability generally results in lower mean yields and, conversely, that selection for higher mean yields may lead to poorer stability. This paper explores the equivalence between the singular value decomposition used in AMMI analysis and the spectral decomposition used in principal components analysis. This equivalence enables scores of a "supplementary genotype" made up of the highest yield value within each environment to be obtained, and these may serve as the ideal check treatment for selection purposes. These scores are used to (1) display this check in a biplot graph, thereby providing a qualitative comparison with the real genotypes related to their interaction with environments; (2) obtain estimates of the squared distances from the projection of each real genotype to the projection of the "supplementary treatment", thereby allowing conclusions to be made on the yield stability of each real genotype. This procedure was effective in identifying the most stable soybean cultivars in an example shown for illustration.

Resumo -O objetivo deste trabalho foi estabelecer uma estratificação ambiental consistente, para a recomendação e a avaliação de linhagens experimentais e cultivares de soja na região do Cerrado, a partir de análises da interação entre genótipos e ambientes (GxA) quanto à produtividade de grãos, além de avaliar a atual rede de ensaios de valor de cultivo e uso (VCU) para sua otimização. Os dados provieram de 559 ensaios de competição de linhagens de soja, realizados em 57 localidades, durante sete safras agrícolas (2002/2003 a 2008/2009). Realizaram-se análises conjuntas de variância, pelo modelo AMMI ("additive main effects and multiplicative interaction"), e de estratificação ambiental, pela abordagem correlata de "genótipos vencedores". A interação GxA foi sempre significativa, como resultado da resposta diferencial dos genótipos à variação ambiental. Os locais de teste se agruparam de modo diferente de acordo com os grupos de maturação. Observou-se redundância em 20% dos locais, o que indica a possibilidade de otimização da rede de ensaios, via eliminação ou substituição dessas localidades. A região-alvo deve receber estratificações distintas, congêneres a cada grupo de maturação, e pode ser dividida em 22 (ciclo precoce), 23 (ciclo médio) e 21 (ciclo tardio) estratos ambientais.Termos para indexação: Glycine max, análise AMMI, genótipo vencedor, interação genótipo x ambiente, locais-chave, mega-ambiente. Environmental stratification and optimization of a multi-environment trial net for soybean genotypes in CerradoAbstract -The objective of this work was to establish a consistent environmental stratification for recommendation and evaluation of experimental soybean lines and cultivars in the Cerrado region, from the analyses of genotype by environment interaction (GxE) for grain yield, besides evaluating the current trial network on the value for cultivation and use (VCU), for its optimization. Data were obtained from 559 competition trials of soybean lines, performed in 57 locations, during seven harvest periods (2002/2003 to 2008/2009). Joint analyses of variance were carried out by the AMMI (additive main effects and multiplicative interaction) model, and the environmental stratification by the related statistical approach of "winning genotypes". The GxE interaction was always significant as a result of the genotype differential response to environmental change. Test locations clustered differently according to maturity groups. Redundancy was observed in 20% of the locations, which indicates the possibility of optimizing the trial network by the elimination or replacement of these locations. The target region should receive different stratifications, congenerous to each maturity group, and may be divided into 22 (early cycle), 23 (medium cycle), and 21 (long cycle) environmental strata.Index terms: Glycine max, AMMI analysis, winner genotype, genotype x environment interaction, key locations, mega-environment. IntroduçãoNo Brasil, a soja é amplamente cultivada, com grande variação nas condições de cultivo...

-The objective of this work was to identify key locations for the establishment of soybean (Glycine max) genetic breeding programs, in the Central Region of Brazil. Grain yield data of three maturity groups of soybean genotypes, from regional trials conducted over three years, at 18 locations in Brazilian Cerrado were used. A key location for the early phases of the breeding program was defined as the site that best classifies the winning genotypes in the region. Key locations for the final phases were defined as those sites that best represent each environmental stratum, in relation to the adaptability of the respective winning genotype. This adaptability was estimated by additive main effects and multiplicative interaction (AMMI) model analysis, using the distance between the score of each location in a stratum and the score of the winning genotype, which characterizes such stratum in an AMMI biplot. The locations that best classified the winning genotypes over space and time were Mineiros, Placas and Rio Verde. For the final phases of genotype selection, with data from the three maturity group, the recommended locations were: Buritis, Chapadão do Céu, Iraí, Pamplona, Placas, Planaltina, Rio Verde, Sacramento, Senador Canedo, Uberaba, and Uberlândia.Index terms: Glycine max, adaptability, AMMI analysis, environmental stratification, G×E interaction. Locais-chave para avaliação de genótipos de soja na Região Central do BrasilResumo -O objetivo deste trabalho foi identificar locais-chave para o estabelecimento de programas de melhoramento genético de soja (Glycine max), na Região Central do Brasil. Foram utilizados dados de produtividade de grãos de genótipos de soja, de três ciclos de maturação, obtidos de ensaios regionais conduzidos por três anos em 18 localidades da região. O local-chave para a condução das fases preliminares do programa foi definido como a localidade que melhor classifica os genótipos vencedores na região. Os locais-chave para as fases finais foram definidos como os que melhor representam cada estrato ambiental identificado, em termos da adaptabilidade do respectivo genótipo vencedor. Essa adaptabilidade foi estimada por meio do modelo de efeitos principais aditivos e interação multiplicativa (AMMI), tendo-se utilizado a distância entre os pontos (escores) correspondentes a cada local em um estrato e o escore do genótipo vencedor que caracteriza aquele estrato, em um "biplot" AMMI. Os locais que melhor classificaram os genótipos vencedores ao longo do espaço e do tempo foram: Mineiros, Placas e Rio Verde. Para as fases finais de seleção de genótipos, com os dados dos três ciclos de maturação, os locais recomendados foram: Buritis, Chapadão do Céu, Iraí, Pamplona, Placas, Planaltina, Rio Verde, Sacramento, Senador Canedo, Uberaba e Uberlândia.Termos para indexação: Glycine max, adaptabilidade, análise AMMI, estratificação ambiental, interação G×E.

ABSTRACT. Stratification of environments is a strategy to capitalize genotype x environment (GxE) interaction, which can optimize the process of assessment and cultivar recommendation, increasing productivity in a target environmental population. The objective of this study was to assess environmental stratification methods based on the analysis of GxE interaction, to identify consistent agronomic zones across time for soybean. Grain yield data of inbred lines from three maturity groups (early, medium, and late) were used. Lines and cultivars were tested in regional variety trials during three growing seasons at eighteen locations in the tropics of Central Brazil. Three methods were applied to stratify the environments. The first was based on joint analyses of variance for all the pairs of locations within each growing year. The second was based on a distance measure between each pair of locations, which was related to the GxE interaction estimated via additive main effects and multiplicative interaction analysis. The third was based on the approach of winning genotypes. The stratification results from the first two methods were not consistent across the growing seasons. However, the winning genotype approach provided consistent environmental stratification across years. From locations used in the genotypic assessment, three environmental clusters were identified for the early and medium maturity groups of soybean, and four clusters for the late maturity group. The use of different genotypic sets across years reinforces the predictive value of the environmental stratification established.