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Genome-environment Associations (GEA) or Environmental Genome-Wide Association scans (EnvGWAS) have been poorly applied for studying the genomics of adaptive traits in bread wheat landraces ( Triticum aestivum L.). We analyzed 990 landraces and seven climatic variables (mean temperature, maximum temperature, precipitation, precipitation seasonality, heat index of mean temperature, heat index of maximum temperature, and drought index) in GEA using the FarmCPU approach with GAPIT. Historical temperature and precipitation values were obtained as monthly averages from 1970 to 2000. Based on 26,064 high-quality SNP loci, landraces were classified into ten subpopulations exhibiting high genetic differentiation. The GEA identified 59 SNPs and nearly 89 protein-encoding genes involved in the response processes to abiotic stress. Genes related to biosynthesis and signaling are mainly mediated by auxins , abscisic acid ( ABA ), ethylene ( ET ) , salicylic acid ( SA ), and jasmonates ( JA ), which are known to operate together in modulation responses to heat stress and drought in plants. In addition, we identified some proteins associated with the response and tolerance to stress by high temperatures, water deficit, and cell wall functions. The results provide candidate regions for selection aimed to improve drought and heat tolerance in bread wheat and provide insights into the genetic mechanisms involved in adaptation to extreme environments.

When including genotype × environment interactions (G × E) in genomic prediction models, Hadamard or Kronecker products have been used to model the covariance structure of interactions. The relation between these two types of modeling has not been made clear in genomic prediction literature. Here, we demonstrate that a certain model based on a Hadamard formulation and another using the Kronecker product lead to exactly the same statistical model. Moreover, we illustrate how a multiplication of entries of covariance matrices is related to modeling locus × environmental-variable interactions explicitly. Finally, we use a wheat and a maize data set to illustrate that the environmental covariance E can be specified easily, also if no information on environmental variables - such as temperature or precipitation - is available. Given that lines have been tested in different environments, the corresponding environmental covariance can simply be estimated from the training set as phenotypic covariance between environments. To achieve a high level of increase in predictive ability, the environmental covariance has to be defined appropriately and records on the performance of the lines of the test set under different environmental conditions have to be included in the training set., (© 2020 The Authors. The Plant Genome published by Wiley Periodicals, Inc. on behalf of Crop Science Society of America.)

Breeding for grain yield (GY) in bread wheat at the International Maize and Wheat Improvement Center (CIMMYT) involves three-stage testing at Obregon, Mexico in different selection environments (SEs). To understand the efficiency of selection in the SEs, we performed a large retrospective quantitative genetics study using CIMMYT's yield trials evaluated in the SEs (2013-2014 to 2017-2018), the South Asia Bread Wheat Genomic Prediction Yield Trials (SABWGPYTs) evaluated in India, Pakistan, and Bangladesh (2014-2015 to 2017-2018), and the Elite Spring Wheat Yield Trials (ESWYTs) evaluated in several sites globally (2003-2004 to 2016-2017). First, we compared the narrow-sense heritabilities in the Obregon SEs and target sites and observed that the mean heritability in the SEs was 44.2 and 92.3% higher than the mean heritabilities in the SABWGPYT and ESWYT sites, respectively. Second, we observed significant genetic correlations between a SE in Obregon and all the five SABWGPYT sites and 65.1% of the ESWYT sites. Third, we observed high ratios of response to indirect selection in the SEs of Obregon with a mean of 0.80 ± 0.21 and 2.6 ± 5.4 in the SABWGPYT and ESWYT sites, respectively. Furthermore, our results also indicated that for all the SABWGPYT sites and 82% of the ESWYT sites, a response greater than 0.5 can be achieved by indirect selection for GY in Obregon. We also performed genomic prediction for GY in the target sites using the performance of the same lines in the SEs of Obregon and observed moderate mean prediction accuracies of 0.24 ± 0.08 and 0.28 ± 0.08 in the SABWGPYT and ESWYT sites, respectively using the genotype x environment (GxE) model. However, we observed similar accuracies using the baseline model with environment and line effects and no advantage of modeling GxE interactions. Overall, this study provides important insights into the suitability of the Obregon SEs in breeding for GY, while the variable genomic predictabilities of GY and the high year-to-year GY fluctuations reported, highlight the importance of multi-environment testing across time and space to stave off GxE induced uncertainties in varietal yields., (Copyright © 2020 Juliana, Singh, Braun, Huerta-Espino, Crespo-Herrera, Payne, Poland, Shrestha, Kumar, Joshi, Imtiaz, Rahman and Toledo.)

Whole genome epistasis models with interactions between different loci can be approximated by genomic relationship models based on Hadamard powers of the additive genomic relationship. We illustrate that the quality of this approximation reduces when the degree of interaction d increases. Moreover, considering relationship models defined as weighted sum of interactions of different degree, we investigate the impact of this decreasing quality of approximation of the summands on the approximation of the weighted sum. Our results indicate that these approximations remain on a reliable level, but their quality reduces when the weights of interactions of higher degrees do not decrease quickly., (Copyright © 2020 The Authors. Published by Elsevier Inc. All rights reserved.)

The application of biochar to soil combined with synthetic fertilizers has been proposed for enhancing N availability to plants and crop yields while reducing nitrous oxide (N 2 O) emissions. However, little is known about those interactions for tropical soils. Thus, this study evaluated the effects of sugarcane straw biochar on tropical soil attributes, crop productivity, N 2 O emissions and N use efficiency. It was conducted a greenhouse pot experiment with wheat cultivation using a 15 N-labelled source (NH 4 15 NO 3 ). The treatments evaluated were: Soil, with N, no biochar; Soil, with N and biochar at rates equivalent to 0.4%, 0.8% and 1.9% (w/w); and a control (soil only). Increasing biochar amendments decreased cumulative N 2 O emissions by 71% compared to the fertilized, no-biochar soil. Moreover, increasing biochar rates to soil increased available P up to 30% and led to 8-fold higher exchangeable K + concentrations. Grain yield and shoot biomass increased by 27 and 16%, respectively, with the rate of 1.9% biochar to soil, which also resulted in higher tillering and number of heads compared to fertilized, no-biochar soil. The amount of 15 N in grains was 28% higher with 0.8 and 1.9% of biochar compared to no-biochar soil, which correspond to 25% of the total 15 N-labelled fertilizer applied to soil. The 15 N loss by volatilization did not differ between treatments. Nevertheless, the biochar amended soils produced less N 2 O than the no-biochar treatment, indicating that biochar amendment to tropical soil led to gaseous N losses in forms other than N 2 O. The application of biochar to soil improved N utilization and the efficiency with which N is acquired by the plants and converted to grain yield, thereby enhancing crop performance, while simultaneously reducing N 2 O emissions from N fertilization, thus mitigating GHG emissions to the atmosphere under tropical conditions., (Copyright © 2019 Elsevier Ltd. All rights reserved.)

Some authors have evaluated the unconstrained optimum and decorrelated multistage linear phenotypic selection indices (OMLPSI and DMLPSI, respectively) theory. We extended this index theory to the constrained multistage linear phenotypic selection index context, where we denoted OMLPSI and DMLPSI as OCMLPSI and DCMLPSI, respectively. The OCMLPSI (DCMLPSI) is the most general multistage index and includes the OMLPSI (DMLPSI) as a particular case. The OCMLPSI (DCMLPSI) predicts the individual net genetic merit at different individual ages and allows imposing constraints on the genetic gains to make some traits change their mean values based on a predetermined level, while the rest of them remain without restrictions. The OCMLPSI takes into consideration the index correlation values among stages, whereas the DCMLPSI imposes the restriction that the index correlation values among stages be null. The criteria to evaluate OCMLPSI efficiency vs. DCMLPSI efficiency were that the total response of each index must be lower than or equal to the single-stage constrained linear phenotypic selection index response and that the expected genetic gain per trait values should be similar to the constraints imposed by the breeder. We used one real and one simulated dataset to validate the efficiency of the indices. The results indicated that OCMLPSI accuracy when predicting the selection response and expected genetic gain per trait was higher than DCMLPSI accuracy when predicting them. Thus, breeders should use the OCMLPSI when making a phenotypic selection., (© The Author(s) 2019.)

Bread wheat improvement using genomic tools is essential for accelerating trait genetic gains. Here we report the genomic predictabilities of 35 key traits and demonstrate the potential of genomic selection for wheat end-use quality. We also performed a large genome-wide association study that identified several significant marker-trait associations for 50 traits evaluated in South Asia, Africa and the Americas. Furthermore, we built a reference wheat genotype-phenotype map, explored allele frequency dynamics over time and fingerprinted 44,624 wheat lines for trait-associated markers, generating over 7.6 million data points, which together will provide a valuable resource to the wheat community for enhancing productivity and stress resilience.

The dna is the fundamental basis of genetic information, just as bits are for computers. Whenever computers are used to represent genetic data, the computational encoding must be efficient to allow the representation of processes driving the inheritance and variability. This is especially important across simulations in view of the increasing complexity and dimensions brought by genomics. This paper introduces a new binary representation of genetic information. Algorithms as bitwise operations that mimic the inheritance of a wide range of polymorphisms are also presented. Different kinds and mixtures of polymorphisms are discussed and exemplified. Proposed algorithms and data structures were implemented in C++ programming language and is available to end users in the R package "isqg" which is available at the R repository (cran). Supplementary data are available online., (Copyright © 2019 Toledo et al.)

Evidence that genomic selection (GS) is a technology that is revolutionizing plant breeding continues to grow. However, it is very well documented that its success strongly depends on statistical models, which are used by GS to perform predictions of candidate genotypes that were not phenotyped. Because there is no universally better model for prediction and models for each type of response variable are needed (continuous, binary, ordinal, count, etc.), an active area of research aims to develop statistical models for the prediction of univariate and multivariate traits in GS. However, most of the models developed so far are for univariate and continuous (Gaussian) traits. Therefore, to overcome the lack of multivariate statistical models for genome-based prediction by improving the original version of the BMTME, we propose an improved Bayesian multi-trait and multi-environment (BMTME) R package for analyzing breeding data with multiple traits and multiple environments. We also introduce Bayesian multi-output regressor stacking (BMORS) functions that are considerably efficient in terms of computational resources. The package allows parameter estimation and evaluates the prediction performance of multi-trait and multi-environment data in a reliable, efficient and user-friendly way. We illustrate the use of the BMTME with real toy datasets to show all the facilities that the software offers the user. However, for large datasets, the BME() and BMTME() functions of the BMTME R package are very intense in terms of computing time; on the other hand, less intensive computing is required with BMORS functions BMORS() and BMORS_Env() that are also included in the BMTME package., (Copyright © 2019 Montesinos-López et al.)

Plant and animal breeders are interested in selecting the best individuals from a candidate set for the next breeding cycle. In this paper, we propose a formal method under the Bayesian decision theory framework to tackle the selection problem based on genomic selection (GS) in single- and multi-trait settings. We proposed and tested three univariate loss functions (Kullback-Leibler, KL; Continuous Ranked Probability Score, CRPS; Linear-Linear loss, LinLin) and their corresponding multivariate generalizations (Kullback-Leibler, KL; Energy Score, EnergyS; and the Multivariate Asymmetric Loss Function, MALF). We derived and expressed all the loss functions in terms of heritability and tested them on a real wheat dataset for one cycle of selection and in a simulated selection program. The performance of each univariate loss function was compared with the standard method of selection (Std) that does not use loss functions. We compared the performance in terms of the selection response and the decrease in the population's genetic variance during recurrent breeding cycles. Results suggest that it is possible to obtain better performance in a long-term breeding program using the single-trait scheme by selecting 30% of the best individuals in each cycle but not by selecting 10% of the best individuals. For the multi-trait approach, results show that the population mean for all traits under consideration had positive gains, even though two of the traits were negatively correlated. The corresponding population variances were not statistically different from the different loss function during the 10 th selection cycle. Using the loss function should be a useful criterion when selecting the candidates for selection for the next breeding cycle., (Copyright © 2018 de Jesus et al.)

When a plant scientist wishes to make genomic-enabled predictions of multiple traits measured in multiple individuals in multiple environments, the most common strategy for performing the analysis is to use a single trait at a time taking into account genotype × environment interaction (G × E), because there is a lack of comprehensive models that simultaneously take into account the correlated counting traits and G × E. For this reason, in this study we propose a multiple-trait and multiple-environment model for count data. The proposed model was developed under the Bayesian paradigm for which we developed a Markov Chain Monte Carlo (MCMC) with noninformative priors. This allows obtaining all required full conditional distributions of the parameters leading to an exact Gibbs sampler for the posterior distribution. Our model was tested with simulated data and a real data set. Results show that the proposed multi-trait, multi-environment model is an attractive alternative for modeling multiple count traits measured in multiple environments., (Copyright © 2017 Montesinos-López et al.)

When information on multiple genotypes evaluated in multiple environments is recorded, a multi-environment single trait model for assessing genotype × environment interaction (G × E) is usually employed. Comprehensive models that simultaneously take into account the correlated traits and trait × genotype × environment interaction (T × G × E) are lacking. In this research, we propose a Bayesian model for analyzing multiple traits and multiple environments for whole-genome prediction (WGP) model. For this model, we used Half-[Formula: see text] priors on each standard deviation term and uniform priors on each correlation of the covariance matrix. These priors were not informative and led to posterior inferences that were insensitive to the choice of hyper-parameters. We also developed a computationally efficient Markov Chain Monte Carlo (MCMC) under the above priors, which allowed us to obtain all required full conditional distributions of the parameters leading to an exact Gibbs sampling for the posterior distribution. We used two real data sets to implement and evaluate the proposed Bayesian method and found that when the correlation between traits was high (>0.5), the proposed model (with unstructured variance-covariance) improved prediction accuracy compared to the model with diagonal and standard variance-covariance structures. The R-software package Bayesian Multi-Trait and Multi-Environment (BMTME) offers optimized C++ routines to efficiently perform the analyses., (Copyright © 2016 Montesinos-López et al.)

In this study, we aimed to establish strategies for value for cultivation and use (VCU) experiments for the tobacco crop in the southern region of Brazil with respect to the number of environments used to assess tobacco lines. Trials of the Virginia (18 sites) and Burley (17 sites) varietal groups were conducted in the three states of the southern region of Brazil in the 2009-2010 crop season. The experiment was conducted in a completely randomized block design with four replications of 10 tobacco lines in the final stage of evaluation; the plots had 6 rows of 7 plants each, or 42 plants per plot. The cured leaf weight per hectare (kg/ha) was obtained. To evaluate stability, the ecovalence and additive main effects and multiplicative interaction models were adopted. In addition, joint analyses of variance were carried out considering different site numbers by simulating resampling. The site number ranged from 2 to 17 or 2 to 16, depending on the varietal group, and sites were selected at random without replacement. The process was repeated 2000 times for each number of sites. All analyses were performed using the R software. The results are very similar for both varietal groups. There is no advantage of using a large number of sites for VCU experiments in the southern region of Brazil because many sites contributed little to the interaction or did not discriminate the tobacco lines. Furthermore, the classification of the best lines is very similar to that obtained in the total number of evaluated sites.

We aimed to establish standards for tobacco Valor de Cultivo e Uso (VCU) in Brazil. We obtained information regarding the size and design of plots of two varietal groups of tobacco (Virginia and Burley). Ten inbred lines of each varietal group were evaluated in a randomized complete block design with four replications. The plot contained 42 plants with six rows of seven columns each. For each experiment plant, considering the position of the respective plant in the plot (row and column) as a reference, cured leaf weight (g/plant), total sugar content (%), and total alkaloid content (%) were determined. The maximum curvature of the variations in coefficients was estimated. Trials with the number of plants per plot ranging from 2 to 41 were simulated. The use of a border was not justified because the interactions between inbred lines x position in the plots were never significant, showing that the behavior of the inbred lines coincided with the different positions. The plant performance varied according to the column position in the plot. To lessen the effect of this factor, the use of plots with more than one row is recommended. Experimental precision, evaluated by the CV%, increased with an increase in plot size; nevertheless, the maximum curvature of the variation coefficient method showed no expressive increase in precision if the number of plants was greater than seven. The result in identification of the best inbred line, in terms of the size of each plot, coincided with the maximum curvature method.

Information about the inheritance of threshold traits is scarce, especially in plants. We examined the genetic control of kernel row number in maize (Zea mays). Knowledge of this inheritance is especially important because it is a primary component of grain yield. This trait has a discontinuous distribution. Characters like these are conceptualized as threshold traits. Crosses were made between the inbred line Geneze 3 (G3) with many kernel rows and the inbreds Argentino IV (A4) and Dente de Cravo (DC), with fewer kernel rows. The F(1) and F(2) generations and the backcrosses BC(11) and BC(21) were obtained for the combinations G3 x A4 and G3 x DC. These populations were evaluated under field conditions, and the kernel row number was determined by direct counting of approximately 14, 140 and 75 ears for the F(1), F(2) and backcrosses, respectively. Genetic control was determined through estimates of generation means and variance analysis and was also performed by Wright's method for threshold traits. It was found that genetic control is predominantly due to additive alleles. The component a, was greater than zero, additive variance was positive and the variance of dominance did not differ from zero. In the F(2) generation, the range of the kernel row number was 10 to 28 in G3 x A4, while in G3 x DC it was 12 to 26. Inheritance of the number of kernel rows, estimated by the two methods, gave similar results. This correspondence is due to adjusting of the data to the normal distribution.