BackgroundThe selection of hybrids is an essential step in maize breeding. However, evaluating a large number of hybrids in field trials can be extremely costly. However, genomic models can be used to predict the expected performance of un-tested genotypes. Bayesian models offer a very flexible framework for hybrid prediction. The Bayesian methodology can be used with parametric and semi-parametric assumptions for additive and non-additive effects. Furthermore, samples from the posterior distribution of Bayesian models can be used to estimate the variance due to general and specific combining abilities even in cases where additive and non-additive effects are not mutually orthogonal. Also, the use of Bayesian models for analysis and prediction of hybrid performance has remained fairly limited.ResultsWe provided an overview of Bayesian parametric and semi-parametric genomic models for prediction of agronomic traits in maize hybrids and discussed how these models can be used to decompose the genotypic variance into components due to general and specific combining ability. We applied the methodology to data from 906 single cross tropical maize hybrids derived from a convergent population. Our results show that: (1) non-additive effects make a sizable contribution to the genetic variance of grain yield; however, the relative importance of non-additive effects was much smaller for ear and plant height; (2) genomic prediction can achieve relatively high accuracy in predicting phenotypes of un-tested hybrids and in pre-screening.ConclusionsGenomic prediction can be a useful tool in pre-screening of hybrids and could contribute to the improvement of the efficiency and efficacy of maize hybrids breeding programs. The Bayesian framework offers a great deal of flexibility in modeling hybrid performance. The methodology can be used to estimate important genetic parameters and render predictions of the expected hybrid performance as well measures of uncertainty about such predictions.Electronic supplementary materialThe online version of this article (10.1186/s13007-019-0388-x) contains supplementary material, which is available to authorized users.

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White mold, caused by Sclerotinea sclerotiorum (Lib.) de Bary is one of the most important diseases of the common bean (Phaseolus vulgaris L.) worldwide. Physiological resistance and traits related to disease avoidance such as architecture contribute to field resistance. The aim of this study was to verify the efficiency of recurrent selection in physiological resistance to white mold, "Carioca" grain type and upright habit in common bean. Thirteen common bean lines with partial resistance to white mold were intercrossed by means of a circulant diallel table, and seven recurrent selection cycles were obtained. Of these cycles, progenies of the S 0:1 , S 0:2 and S 0:3 generations of cycles III, IV, V and VI were evaluated. The best (8 to 10) progenies of the seven cycles were also evaluated, in two experiments, one in the greenhouse and one in the field. Lattice and/or randomized block experimental designs were used. The traits evaluated were: resistance to white mold by the straw test method, growth habit and grain type. The most resistant progenies were selected based on the average score of resistance to white mold. Subsequently, they were evaluated with regard to grain type and growth habit. Recurrent selection allowed for genetic progress of about 11 % per year for white mold resistance and about 15 % per year for the plant architecture.There was no gain among cycles for grain type. Progeny selection and recurrent selection were efficient for obtaining progenies with a high level of resistance to white mold with "Carioca" grain type and upright habit.

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Phenotypic datasets in plant breeding are commonly incomplete due to missing phenotypic information. The best approach for correcting these datasets for a stage‐wise genomic prediction (GP) is not unanimous in the scientific community. Therefore, this study evaluates a two‐step GP based on different methods of phenotypic correction considering complete and incomplete datasets of maize (Zea mays L.) single crosses. The dataset consists of 325 hybrids evaluated for grain yield and plant height in four sites. Sequential levels of data loss were simulated to the original dataset (from 0 to 30%) to assess the impact of missing information. The prediction was performed by an additive genomic best linear unbiased prediction model (GBLUP) using best linear unbiased estimations (BLUEs), best linear unbiased predictions (BLUPs), and deregressed BLUPs as the response variable. Mean reliability and predictive ability slightly decreased as missing phenotypic information increased, irrespective of the response variable. Regarding phenotypic correction, all methods yielded similar results for these parameters over most missing information percentages. The coincidence of selection between single‐ and two‐stage GP was not systematically affected by response variable across multiple selection intensities, and missing data only led to a minor decrease in coincidence. Therefore, from a breeding standpoint, regardless of phenotypic correction method and missing data level, a similar set of genotypes tend to be selected.

Genome-wide association studies (GWAS) is one of the most popular methods of studying the genetic control of traits. This methodology has been intensely performed on inbred genotypes to identify causal variants. Nonetheless, the lack of covariance between the phenotype of inbred lines and their offspring in cross-pollinated species (such as maize) raises questions on the applicability of these findings in a hybrid breeding context. To address this topic, we incorporated previously reported parental lines GWAS information into the prediction of a low heritability trait in hybrids. This was done by marker-assisted selection based on significant markers identified in the lines and by genomic prediction having these markers as fixed effects. Additive-dominance GWAS of hybrids, a non-conventional procedure, was also performed for comparison purposes. Our results suggest that incorporating information from parental inbred lines GWAS led to decreases in the predictive ability of hybrids. Correspondingly, inbred lines and hybrids-based GWAS yielded different results. These findings do not invalidate GWAS on inbred lines for selection purposes, but mean that it may not be directly useful for hybrid breeding. OPEN ACCESSCitation: Galli G, Alves FC, Morosini JS, Fritsche-Neto R (2020) On the usefulness of parental lines GWAS for predicting low heritability traits in tropical maize hybrids. PLoS ONE 15(2): e0228724. https://doi.org/10.1371/journal.

Maize plants can be N-use efficient or N-stress tolerant. The first have high yields in favorable environments but is drastically affected under stress conditions; whereas the second show satisfactory yields in stressful environments but only moderate ones under optimal conditions. In this context, our aim was to assess the possibility of selecting tropical maize lines

Several studies have shown differences in the abilities of maize genotypes to facilitate or impede Azospirillum brasilense colonization and to receive benefits from this association. Hence, our aim was to study the genetic control, heterosis effect and the prediction accuracy of the shoot and root traits of maize in response to A . brasilense . For that, we evaluated 118 hybrids under two contrasting scenarios: i) N stress (control) and ii) N stress plus A . brasilense inoculation. The diallel analyses were performed using mixed model equations, and the genomic prediction models accounted for the general and specific combining ability (GCA and SCA, respectively) and the presence or not of G×E effects. In addition, the genomic models were fitted considering parametric (G-BLUP) and semi-parametric (RKHS) kernels. The genotypes showed significant inoculation effect for five root traits, and the GCA and SCA were significant for both. The GCA in the inoculated treatment presented a greater magnitude than the control, whereas the opposite was observed for SCA. Heterosis was weakly influenced by the inoculation, and the heterozygosity and N status in the plant can have a role in the benefits that can be obtained from this Plant Growth-Promoting Bacteria (PGPB). Prediction accuracies for N stress plus A . brasilense ranged from 0.42 to 0.78, depending on the scenario and trait, and were higher, in most cases, than the non-inoculated treatment. Finally, our findings provide an understanding of the quantitative variation of maize responsiveness to A . brasilense and important insights to be applied in maize breeding aiming the development of superior hybrids for this association.