The 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. We 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. Genomic 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.

Breeding forest species can be a costly and slow process because of the extensive areas needed for field trials and the long periods (e.g., five years) that are required to measure economically and environmentally relevant phenotypes (e.g., adult plant biomass or plant height). Genomic selection (GS) and indirect selection using early phenotypes (e.g., phenotypes collected in greenhouse conditions) are two ways by which tree breeding can be accelerated. These approaches can both reduce the costs of field‐testing and the time required to make selection decisions. Moreover, these approaches can be highly synergistic. Therefore, in this study, we used a data set comprising DNA genotypes and longitudinal measurements of growth collected from a population of Populus deltoides W. Bartram ex Marshall (eastern cottonwood) in the greenhouse and the field, to evaluate the potential impact of integrating large‐scale greenhouse phenotyping with conventional GS. We found that the integration of greenhouse phenotyping and GS can deliver very early selection decisions that are moderately accurate. Therefore, we conclude that the adoption of these approaches, in conjunction with reproductive techniques that shorten the generation interval, can lead to an unprecedented acceleration of selection gains in P. deltoides and, potentially, other commercially planted tree species.

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 that are simultaneously N-stress tolerant and N-use efficient and check for differences between simultaneous selection statistical methods. Sixty-four tropical maize lines were evaluated for Nitrogen Agronomic Efficiency (NAE) and Low Nitrogen Tolerance (LNTI) response indices and two per se selection indices, Low Nitrogen Agronomic Efficiency (LNAE) and Harmonic Mean of Relative Performance (HMRP). We performed eight selection scenarios: LNAE; HMRP; Additive index; Mulamba-Mock index; and Independent culling levels. The last three was predicted by REML/BLUP single-trait and multi-trait using genotypic values of NAE and LNTI. The REML/BLUP multi-trait analysis was superior to the single-trait analysis due to high unfavorable correlation between NAE and LNTI. However, the accuracy and genotypic determination coefficient of NAE and LNTI were too low. Thus, neither single- nor multi-trait analysis achieved a good result for simultaneous selection nor N-use efficiency nor N-stress tolerance. LNAE obtained satisfactorily accurate values and genotypic determination coefficient, but its performance in selection gain was worse than HMRP, particularly in terms of N-use efficiency. Therefore, because of the superior performance in accuracy, genotypic determination coefficient and selection, HMRP was considered the best simultaneous selection methodology of the scenarios tested for N-use efficiency and N-stress tolerance.

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.