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Striga hermonthica (Del.) Benth., a parasitic weed, causes substantial yield losses in maize production in sub-Saharan Africa (SSA). Breeding for Striga resistance in maize is constrained by limited genetic diversity for Striga resistance within the elite germplasm and phenotyping capacity under artificial Striga infestation. Genomics-enabled approaches have the potential to accelerate identification of Striga resistant lines for hybrid development. The objectives of this study were to evaluate the accuracy of genomic selection for traits associated with Striga resistance and grain yield (GY) and to predict genetic values of tested and untested doubled haploid (DH) maize lines. We genotyped 606 DH lines with 8,439 rAmpSeq markers. A training set of 116 DH lines crossed to two testers was phenotyped under artificial Striga infestation at three locations in Kenya. Heritability for Striga resistance parameters ranged from 0.38‒0.65 while that for GY was 0.54. The prediction accuracies for Striga resistance-associated traits across locations, as determined by cross validation (CV) were 0.24 to 0.53 for CV0 and from 0.20 to 0.37 for CV2. For GY, the prediction accuracies were 0.59 and 0.56 for CV0 and CV2, respectively. The results revealed 300 DH lines with desirable genomic estimated breeding values (GEBVs) for reduced number of emerged Striga plants (STR) at 8, 10, and 12 weeks after planting. The GEBVs of DH lines for Striga resistance associated traits in the training and testing sets were similar in magnitude. These results highlight the potential application of genomic selection in breeding for Striga resistance in maize. The integration of genomic-assisted strategies and DH technology for line development coupled with forward breeding for major adaptive traits will enhance genetic gains in breeding for Striga resistance in maize., (© The Author(s) 2024. Published by Oxford University Press on behalf of The Genetics Society of America.)

"Sparse testing" refers to reduced multi-environment breeding trials in which not all genotypes of interest are grown in each environment. Using genomic-enabled prediction and a model embracing genotype × environment interaction (GE), the non-observed genotype-in-environment combinations can be predicted. Consequently, the overall costs can be reduced and the testing capacities can be increased. The accuracy of predicting the unobserved data depends on different factors including (1) how many genotypes overlap between environments, (2) in how many environments each genotype is grown, and (3) which prediction method is used. In this research, we studied the predictive ability obtained when using a fixed number of plots and different sparse testing designs. The considered designs included the extreme cases of (1) no overlap of genotypes between environments, and (2) complete overlap of the genotypes between environments. In the latter case, the prediction set fully consists of genotypes that have not been tested at all. Moreover, we gradually go from one extreme to the other considering (3) intermediates between the two previous cases with varying numbers of different or non-overlapping (NO)/overlapping (O) genotypes. The empirical study is built upon two different maize hybrid data sets consisting of different genotypes crossed to two different testers (T1 and T2) and each data set was analyzed separately. For each set, phenotypic records on yield from three different environments are available. Three different prediction models were implemented, two main effects models ( M1 and M2 ), and a model ( M3) including GE. The results showed that the genome-based model including GE ( M3 ) captured more phenotypic variation than the models that did not include this component. Also, M3 provided higher prediction accuracy than models M1 and M2 for the different allocation scenarios. Reducing the size of the calibration sets decreased the prediction accuracy under all allocation designs with M3 being the less affected model; however, using the genome-enabled models ( i.e. , M2 and M3 ) the predictive ability is recovered when more genotypes are tested across environments. Our results indicate that a substantial part of the testing resources can be saved when using genome-based models including GE for optimizing sparse testing designs., (Copyright © 2020 Jarquin et al.)

Kernel methods are flexible and easy to interpret and have been successfully used in genomic-enabled prediction of various plant species. Kernel methods used in genomic prediction comprise the linear genomic best linear unbiased predictor (GBLUP or GB) kernel, and the Gaussian kernel (GK). In general, these kernels have been used with two statistical models: single-environment and genomic × environment (GE) models. Recently near infrared spectroscopy (NIR) has been used as an inexpensive and non-destructive high-throughput phenotyping method for predicting unobserved line performance in plant breeding trials. In this study, we used a non-linear arc-cosine kernel (AK) that emulates deep learning artificial neural networks. We compared AK prediction accuracy with the prediction accuracy of GB and GK kernel methods in four genomic data sets, one of which also includes pedigree and NIR information. Results show that for all four data sets, AK and GK kernels achieved higher prediction accuracy than the linear GB kernel for the single-environment and GE multi-environment models. In addition, AK achieved similar or slightly higher prediction accuracy than the GK kernel. For all data sets, the GE model achieved higher prediction accuracy than the single-environment model. For the data set that includes pedigree, markers and NIR, results show that the NIR wavelength alone achieved lower prediction accuracy than the genomic information alone; however, the pedigree plus NIR information achieved only slightly lower prediction accuracy than the marker plus the NIR high-throughput data., (Copyright © 2019 Cuevas et al.)

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.)

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.)

One of the major issues in plant breeding is the occurrence of genotype × environment (GE) interaction. Several models have been created to understand this phenomenon and explore it. In the genomic era, several models were employed to improve selection by using markers and account for GE interaction simultaneously. Some of these models use special genetic covariance matrices. In addition, the scale of multi-environment trials is getting larger, and this increases the computational challenges. In this context, we propose an R package that, in general, allows building GE genomic covariance matrices and fitting linear mixed models, in particular, to a few genomic GE models. Here we propose two functions: one to prepare the genomic kernels accounting for the genomic GE and another to perform genomic prediction using a Bayesian linear mixed model. A specific treatment is given for sparse covariance matrices, in particular, to block diagonal matrices that are present in some GE models in order to decrease the computational demand. In empirical comparisons with Bayesian Genomic Linear Regression (BGLR), accuracies and the mean squared error were similar; however, the computational time was up to five times lower than when using the classic approach. Bayesian Genomic Genotype × Environment Interaction (BGGE) is a fast, efficient option for creating genomic GE kernels and making genomic predictions., (Copyright © 2018 Granato et al.)

In this study, we compared the prediction accuracy of the main genotypic effect model (MM) without G×E interactions, the multi-environment single variance G×E deviation model (MDs), and the multi-environment environment-specific variance G×E deviation model (MDe) where the random genetic effects of the lines are modeled with the markers (or pedigree). With the objective of further modeling the genetic residual of the lines, we incorporated the random intercepts of the lines ([Formula: see text]) and generated another three models. Each of these 6 models were fitted with a linear kernel method (Genomic Best Linear Unbiased Predictor, GB) and a Gaussian Kernel (GK) method. We compared these 12 model-method combinations with another two multi-environment G×E interactions models with unstructured variance-covariances (MUC) using GB and GK kernels (4 model-method). Thus, we compared the genomic-enabled prediction accuracy of a total of 16 model-method combinations on two maize data sets with positive phenotypic correlations among environments, and on two wheat data sets with complex G×E that includes some negative and close to zero phenotypic correlations among environments. The two models (MDs and MDE with the random intercept of the lines and the GK method) were computationally efficient and gave high prediction accuracy in the two maize data sets. Regarding the more complex G×E wheat data sets, the prediction accuracy of the model-method combination with G×E, MDs and MDe, including the random intercepts of the lines with GK method had important savings in computing time as compared with the G×E interaction multi-environment models with unstructured variance-covariances but with lower genomic prediction accuracy., (Copyright © 2018 Cuevas et al.)

Genomic selection (GS) increases genetic gain by reducing the length of the selection cycle, as has been exemplified in maize using rapid cycling recombination of biparental populations. However, no results of GS applied to maize multi-parental populations have been reported so far. This study is the first to show realized genetic gains of rapid cycling genomic selection (RCGS) for four recombination cycles in a multi-parental tropical maize population. Eighteen elite tropical maize lines were intercrossed twice, and self-pollinated once, to form the cycle 0 (C 0 ) training population. A total of 1000 ear-to-row C 0 families was genotyped with 955,690 genotyping-by-sequencing SNP markers; their testcrosses were phenotyped at four optimal locations in Mexico to form the training population. Individuals from families with the best plant types, maturity, and grain yield were selected and intermated to form RCGS cycle 1 (C 1 ). Predictions of the genotyped individuals forming cycle C 1 were made, and the best predicted grain yielders were selected as parents of C 2 ; this was repeated for more cycles (C 2 , C 3 , and C 4 ), thereby achieving two cycles per year. Multi-environment trials of individuals from populations C 0, C 1 , C 2 , C 3 , and C 4 , together with four benchmark checks were evaluated at two locations in Mexico. Results indicated that realized grain yield from C 1 to C 4 reached 0.225 ton ha -1 per cycle, which is equivalent to 0.100 ton ha -1  yr -1 over a 4.5-yr breeding period from the initial cross to the last cycle. Compared with the original 18 parents used to form cycle 0 (C 0 ), genetic diversity narrowed only slightly during the last GS cycles (C 3 and C 4 ). Results indicate that, in tropical maize multi-parental breeding populations, RCGS can be an effective breeding strategy for simultaneously conserving genetic diversity and achieving high genetic gains in a short period of time., (Copyright © 2017 Zhang et al.)

Multi-environment trials are routinely conducted in plant breeding to select candidates for the next selection cycle. In this study, we compare the prediction accuracy of four developed genomic-enabled prediction models: (1) single-environment, main genotypic effect model (SM); (2) multi-environment, main genotypic effects model (MM); (3) multi-environment, single variance G×E deviation model (MDs); and (4) multi-environment, environment-specific variance G×E deviation model (MDe). Each of these four models were fitted using two kernel methods: a linear kernel Genomic Best Linear Unbiased Predictor, GBLUP (GB), and a nonlinear kernel Gaussian kernel (GK). The eight model-method combinations were applied to two extensive Brazilian maize data sets (HEL and USP data sets), having different numbers of maize hybrids evaluated in different environments for grain yield (GY), plant height (PH), and ear height (EH). Results show that the MDe and the MDs models fitted with the Gaussian kernel (MDe-GK, and MDs-GK) had the highest prediction accuracy. For GY in the HEL data set, the increase in prediction accuracy of SM-GK over SM-GB ranged from 9 to 32%. For the MM, MDs, and MDe models, the increase in prediction accuracy of GK over GB ranged from 9 to 49%. For GY in the USP data set, the increase in prediction accuracy of SM-GK over SM-GB ranged from 0 to 7%. For the MM, MDs, and MDe models, the increase in prediction accuracy of GK over GB ranged from 34 to 70%. For traits PH and EH, gains in prediction accuracy of models with GK compared to models with GB were smaller than those achieved in GY. Also, these gains in prediction accuracy decreased when a more difficult prediction problem was studied., (Copyright © 2017 Bandeira e Sousa et al.)

The phenomenon of genotype × environment (G × E) interaction in plant breeding decreases selection accuracy, thereby negatively affecting genetic gains. Several genomic prediction models incorporating G × E have been recently developed and used in genomic selection of plant breeding programs. Genomic prediction models for assessing multi-environment G × E interaction are extensions of a single-environment model, and have advantages and limitations. In this study, we propose two multi-environment Bayesian genomic models: the first model considers genetic effects [Formula: see text] that can be assessed by the Kronecker product of variance-covariance matrices of genetic correlations between environments and genomic kernels through markers under two linear kernel methods, linear (genomic best linear unbiased predictors, GBLUP) and Gaussian (Gaussian kernel, GK). The other model has the same genetic component as the first model [Formula: see text] plus an extra component, F: , that captures random effects between environments that were not captured by the random effects [Formula: see text] We used five CIMMYT data sets (one maize and four wheat) that were previously used in different studies. Results show that models with G × E always have superior prediction ability than single-environment models, and the higher prediction ability of multi-environment models with [Formula: see text] over the multi-environment model with only u occurred 85% of the time with GBLUP and 45% of the time with GK across the five data sets. The latter result indicated that including the random effect f is still beneficial for increasing prediction ability after adjusting by the random effect [Formula: see text]., (Copyright © 2017 Cuevas et al.)

This study examines genomic prediction within 8416 Mexican landrace accessions and 2403 Iranian landrace accessions stored in gene banks. The Mexican and Iranian collections were evaluated in separate field trials, including an optimum environment for several traits, and in two separate environments (drought, D and heat, H) for the highly heritable traits, days to heading (DTH), and days to maturity (DTM). Analyses accounting and not accounting for population structure were performed. Genomic prediction models include genotype × environment interaction (G × E). Two alternative prediction strategies were studied: (1) random cross-validation of the data in 20% training (TRN) and 80% testing (TST) (TRN20-TST80) sets, and (2) two types of core sets, "diversity" and "prediction", including 10% and 20%, respectively, of the total collections. Accounting for population structure decreased prediction accuracy by 15-20% as compared to prediction accuracy obtained when not accounting for population structure. Accounting for population structure gave prediction accuracies for traits evaluated in one environment for TRN20-TST80 that ranged from 0.407 to 0.677 for Mexican landraces, and from 0.166 to 0.662 for Iranian landraces. Prediction accuracy of the 20% diversity core set was similar to accuracies obtained for TRN20-TST80, ranging from 0.412 to 0.654 for Mexican landraces, and from 0.182 to 0.647 for Iranian landraces. The predictive core set gave similar prediction accuracy as the diversity core set for Mexican collections, but slightly lower for Iranian collections. Prediction accuracy when incorporating G × E for DTH and DTM for Mexican landraces for TRN20-TST80 was around 0.60, which is greater than without the G × E term. For Iranian landraces, accuracies were 0.55 for the G × E model with TRN20-TST80. Results show promising prediction accuracies for potential use in germplasm enhancement and rapid introgression of exotic germplasm into elite materials., (Copyright © 2016 Crossa et al.)

Genomic tools allow the study of the whole genome, and facilitate the study of genotype-environment combinations and their relationship with phenotype. However, most genomic prediction models developed so far are appropriate for Gaussian phenotypes. For this reason, appropriate genomic prediction models are needed for count data, since the conventional regression models used on count data with a large sample size ([Formula: see text]) and a small number of parameters (p) cannot be used for genomic-enabled prediction where the number of parameters (p) is larger than the sample size ([Formula: see text]). Here, we propose a Bayesian mixed-negative binomial (BMNB) genomic regression model for counts that takes into account genotype by environment [Formula: see text] interaction. We also provide all the full conditional distributions to implement a Gibbs sampler. We evaluated the proposed model using a simulated data set, and a real wheat data set from the International Maize and Wheat Improvement Center (CIMMYT) and collaborators. Results indicate that our BMNB model provides a viable option for analyzing count data., (Copyright © 2016 Montesinos-López et al.)

Most genomic-enabled prediction models developed so far assume that the response variable is continuous and normally distributed. The exception is the probit model, developed for ordered categorical phenotypes. In statistical applications, because of the easy implementation of the Bayesian probit ordinal regression (BPOR) model, Bayesian logistic ordinal regression (BLOR) is implemented rarely in the context of genomic-enabled prediction [sample size (n) is much smaller than the number of parameters (p)]. For this reason, in this paper we propose a BLOR model using the Pólya-Gamma data augmentation approach that produces a Gibbs sampler with similar full conditional distributions of the BPOR model and with the advantage that the BPOR model is a particular case of the BLOR model. We evaluated the proposed model by using simulation and two real data sets. Results indicate that our BLOR model is a good alternative for analyzing ordinal data in the context of genomic-enabled prediction with the probit or logit link., (Copyright © 2015 Montesinos-López et al.)

Genotyping-by-sequencing (GBS) technologies have proven capacity for delivering large numbers of marker genotypes with potentially less ascertainment bias than standard single nucleotide polymorphism (SNP) arrays. Therefore, GBS has become an attractive alternative technology for genomic selection. However, the use of GBS data poses important challenges, and the accuracy of genomic prediction using GBS is currently undergoing investigation in several crops, including maize, wheat, and cassava. The main objective of this study was to evaluate various methods for incorporating GBS information and compare them with pedigree models for predicting genetic values of lines from two maize populations evaluated for different traits measured in different environments (experiments 1 and 2). Given that GBS data come with a large percentage of uncalled genotypes, we evaluated methods using nonimputed, imputed, and GBS-inferred haplotypes of different lengths (short or long). GBS and pedigree data were incorporated into statistical models using either the genomic best linear unbiased predictors (GBLUP) or the reproducing kernel Hilbert spaces (RKHS) regressions, and prediction accuracy was quantified using cross-validation methods. The following results were found: relative to pedigree or marker-only models, there were consistent gains in prediction accuracy by combining pedigree and GBS data; there was increased predictive ability when using imputed or nonimputed GBS data over inferred haplotype in experiment 1, or nonimputed GBS and information-based imputed short and long haplotypes, as compared to the other methods in experiment 2; the level of prediction accuracy achieved using GBS data in experiment 2 is comparable to those reported by previous authors who analyzed this data set using SNP arrays; and GBLUP and RKHS models with pedigree with nonimputed and imputed GBS data provided the best prediction correlations for the three traits in experiment 1, whereas for experiment 2 RKHS provided slightly better prediction than GBLUP for drought-stressed environments, and both models provided similar predictions in well-watered environments.