Breeding for drought tolerance is a challenging task that requires costly, extensive, and precise phenotyping. Genomic selection (GS) can be used to maximize selection efficiency and the genetic gains in maize (Zea mays L.) breeding programs for drought tolerance. Here, we evaluated the accuracy of genomic selection (GS) using additive (A) and additive + dominance (AD) models to predict the performance of untested maize single-cross hybrids for drought tolerance in multi-environment trials. Phenotypic data of five drought tolerance traits were measured in 308 hybrids along eight trials under water-stressed (WS) and well-watered (WW) conditions over two years and two locations in Brazil. Hybrids' genotypes were inferred based on their parents' genotypes (inbred lines) using single-nucleotide polymorphism markers obtained via genotyping-by-sequencing. GS analyses were performed using genomic best linear unbiased prediction by fitting a factor analytic (FA) multiplicative mixed model. Two cross-validation (CV) schemes were tested: CV1 and CV2. The FA framework allowed for investigating the stability of additive and dominance effects across environments, as well as the additive-by-environment and the dominance-by-environment interactions, with interesting applications for parental and hybrid selection. Results showed differences in the predictive accuracy between A and AD models, using both CV1 and CV2, for the five traits in both water conditions. For grain yield (GY) under WS and using CV1, the AD model doubled the predictive accuracy in comparison to the A model. Through CV2, GS models benefit from borrowing information of correlated trials, resulting in an increase of 40% and 9% in the predictive accuracy of GY under WS for A and AD models, respectively. These results highlight the importance of multi-environment trial analyses using GS models that incorporate additive and dominance effects for genomic predictions of GY under drought in maize single-cross hybrids.

Resumo -O objetivo deste trabalho foi avaliar o potencial de melhoramento e a divergência genética de nove cultivares tropicais de milho-pipoca. A divergência genética foi estimada por meio da técnica de análise multivariada e as cultivares foram agrupadas com base na distância generalizada de Mahalanobis (DGM), utilizando o método de otimização de Tocher e a dispersão gráfica. Com produtividade de grãos acima de 3 t/ha, destacaram-se as cultivares CMS 43, IAC 112, Viçosa, CMS 42 e Branco, e com índices de capacidade de expansão acima de 24 (v/v), as cultivares IAC 112, RS 20 e Zélia. As estimativas da DGM indicaram (RS 20 e Beija-flor) e (Rosa-claro e RS 20) os pares de cultivares mais distantes geneticamente, e (IAC 112 e Viçosa) e (Branco e CMS 42), os pares mais similares. Foram identificados três ou quatro grupos divergentes dependendo do método de agrupamento. Para o melhoramento de milho-pipoca, as cultivares com maiores potenciais são RS 20, Zélia, IAC 112 e Beija-flor. As cultivares apresentam divergência genética.Termos para indexação: Zea mays, seleção, análise multivariada, método de melhoramento. Potential to breeding and genetic divergence in popcorn cultivarsAbstract -The objective of this paper was to evaluate the potential of breeding and genetic divergence in nine tropical popcorn cultivars. The genetic divergence was estimated using multivariate analysis techniques and the cultivars were grouped based in Mahalanobis' generalized distance (MGD), using Tocher's optimization and graphic dispersion. The best cultivars concerning the yield grain above 3 ton/ha were CMS 43, IAC 112, Viçosa, CMS 42 and Branco, and to popping expansion above 24 (v/v) were IAC 112, RS 20 and Zélia. The estimates of MGD indicated the pairs genetically more distant (RS 20, Beija-flor) and (Rosa-claro, RS 20) as well as pairs genetically more similar (IAC 112, Viçosa) and (Branco, CMS 42). Tree or four genetic divergences groups were formed depending on the method. To popcorn breeding, cultivars with best potential are RS 20, Zélia, IAC 112, and Beija-flor. The cultivars show genetic divergence.Index terms: Zea mays, selection, multivariate analysis, breeding methods.baixo acamamento e quebramento das plantas, a alta resistência às doenças e às pragas, a alta capacidade de expansão e boas características organolépticas como maciez, sabor, aroma e cor da flor da pipoca (Alexander & Creech, 1977).A capacidade de expansão (CE) dos grãos de milho é a característica mais importante para o consumidor e pode ser definida como a relação entre o volume de pipoca e o volume de grãos ou ainda a relação entre o volume de pipoca e o peso de grãos (Alexander & Creech, 1977). Quanto maior a capacidade de expansão, melhor é a qualidade da pipoca. A capacidade de expansão pode atingir o índice de 45 em cultivares americanas (Sawazaki, 1996). E-mail: glauco@ufv.br, coimbrarr@bol.com.br, becofc@bol.com.br, vagnosouza@bol.com.br, lauroguimaraes@bol.com.br, vazdemelo@bol.com.br IntroduçãoNo melhoramento de milho-pipoca, os interesses d...

-The objectives of this work were to evaluate the genotype x environment (GxE) interaction for popcorn and to compare two multivariate analyses methods. Nine popcorn cultivars were sown on four dates one month apart during each of the agricultural years 1998/1999 and 1999/2000. The experiments were carried out using randomized block designs, with four replicates. The cv. Zélia contributed the least to the GxE interaction. The cv. Viçosa performed similarly to cv. Rosa-claro. Optimization of GxE was obtained for cv. CMS 42 for a favorable mega-environment, and for cv. CMS 43 for an unfavorable environment. Multivariate analysis supported the results from the method of Eberhart & Russell. The graphic analysis of the Additive Main effects and Multiplicative Interaction (AMMI) model was simple, allowing conclusions to be made about stability, genotypic performance, genetic divergence between cultivars, and the environments that optimize cultivar performance. The graphic analysis of the Genotype main effects and Genotype x Environment interaction (GGE) method added to AMMI information on environmental stratification, defining mega-environments and the cultivars that optimized performance in those mega-environments. Both methods are adequate to explain the genotype x environment interactions.Index terms: Zea mays, adaptability, breeding, maize, popcorn, selection, stability. Análises multivariadas da interação genótipo x ambiente em milho-pipocaResumo -Os objetivos deste trabalho foram avaliar a interação genótipo x ambiente (GxA) em milho-pipoca e comparar dois métodos de análise multivariada (AMMI e GGE). Os tratamentos foram nove cultivares de milho-pipoca, plantadas em quatro épocas de semeadura em cada ano de cultivo em 1998/1999 e 1999/2000. O delineamento foi em blocos ao acaso, com quatro repetições. A cultivar Zélia foi a que menos contribuiu para a interação GxA. As cultivares Viçosa e Rosa-claro mostraram desempenhos similares. A otimização da interação GxA foi obtida com a cv. CMS 42 para mega-ambientes favoráveis e com a cv. CMS 43 para ambientes desfavoráveis. Os resultados das análises multivariadas corroboraram os resultados do método de Eberhart & Russell. A análise gráfica do método Additive Main effects and Multiplicative Interaction (AMMI) é simples e permite tirar conclusões sobre estabilidade, desempenho genotípico, divergência genética das cultivares, e sobre os ambientes que otimizam o desempenho das cultivares. A análise gráfica do método Genotype main effects and Genotype x Environment interaction (GGE) acrescentou informações de estratificação ambiental ao AMMI e definiu mega-ambientes e as cultivares que tiveram suas performances otimizadas nesses ambientes. Ambos os métodos são adequados para explicar a interação genótipo x ambiente.Termos para indexação: Zea mays, adaptabilidade, melhoramento genético, milho, milho-pipoca, seleção, estabilidade.

The development of successful advanced lines and cultivars in maize is dependent on parental selection and assignment to deWned heterotic groups. So, the objectives of this study were to evaluate genetic variability and identify heterotic groups among Brazilian popcorn varieties. Thus, diallel crosses of advanced generations of the popcorn hybrids, IAC 112 and Zélia, and of three open-pollinated popcorn varieties, RS 20, Branco, and SAM were performed. Ten hybrid combinations, the Wve parents, and Wve check treatments were arranged in a block design with four replicates in two tropical-zone locations (CWb climate). Both additive and non-additive eVects were important for grain yield, plant height, ear height, and husk cover. For popping expansion, only the additive eVects were important. Hybrid combinations between the local variety (Branco) and F 2 populations (IAC 112 and Zelia) resulted in the third and fourth highest values for popping expansion. The best grain yields were obtained with hybrid combinations involving SAM. Cultivars Zélia, IAC 112, and RS 20 increased popping expansion, whereas cultivar Branco increased grain yield of hybrid combinations. The following conclusions may be drawn: Brazilian popcorn populations have reduced heterosis and genetic variability to popping expansion in relation commercial cultivars; there is genetic variability among Brazilian popcorn populations that allows the exploitation of additive and nonadditive eVects for grain yield; it is possible to increase grain yield by using local varieties; but it would be diYcult to obtain commercial hybrids from local varieties because they have poor performance for popping expansion.

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