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Grain yield plateau is a serious concern in many countries, including Italy. A specific‐adaptative strategy might apply to contrast this unfavourable condition. This study aimed to investigate the gain in grain yield and yield‐related traits of bread wheat in Italy over a 16‐year period. A historical dataset concerning 105 sites across Italy and observations on grain yield, heading date, plant height and thousand kernel weight was used. The target population of environments (TPEs) were defined using several environmental parameters. The results showed that while there was a general increase in thousand kernel weight over the 16 years, there was no significant improvement in grain yield and heading date. By contrast, plant height showed a slight decrease over the years. The study also identified five TPEs presenting different climate scenarios in Italy. The TPEs showed varying levels of performance for the traits of interest, with the Po valley (TPE4) showing the highest values for grain yield and thousand kernel weight. The study also identified the best‐performing genotypes for each TPE, providing valuable insights for future wheat breeding programmes in Italy. [ABSTRACT FROM AUTHOR]

Genomic prediction relates a set of markers to variability in observed phenotypes of cultivars and allows for the prediction of phenotypes or breeding values of genotypes on unobserved individuals. Most genomic prediction approaches predict breeding values based solely on additive effects. However, the economic value of wheat lines is not only influenced by their additive component but also encompasses a non-additive part (e.g., additive × additive epistasis interaction). In this study, genomic prediction models were implemented in three target populations of environments (TPE) in South Asia. Four models that incorporate genotype × environment interaction (G × E) and genotype × genotype (GG) were tested: Factor Analytic (FA), FA with genomic relationship matrix (FA + G), FA with epistatic relationship matrix (FA + GG), and FA with both genomic and epistatic relationship matrices (FA + G + GG). Results show that the FA + G and FA + G + GG models displayed the best and a similar performance across all tests, leading us to infer that the FA + G model effectively captures certain epistatic effects. The wheat lines tested in sites in different TPE were predicted with different precisions depending on the cross-validation employed. In general, the best prediction accuracy was obtained when some lines were observed in some sites of particular TPEs and the worse genomic prediction was observed when wheat lines were never observed in any site of one TPE. [ABSTRACT FROM AUTHOR]

Introduction: Genomic selection (GS) has gained global importance due to its potential to accelerate genetic progress and improve the efficiency of breeding programs. Objectives of the research: In this research we proposed a method to improve the prediction accuracy of tested lines in new (untested) environments. Method-1: The new method trained the model with a modified response variable (a difference of response variables) that decreases the lack of a nonstationary distribution between the training and testing and improved the prediction accuracy. Comparing new and conventional method: We compared the prediction accuracy of the conventional genomic best linear unbiased prediction (GBLUP) model (M1) including (or not) genotype × environment interaction (GE) (M1_GE; M1_NO_GE) versus the proposed method (M2) on several data sets. Results and discussion: The gain in prediction accuracy of M2, versus M1_GE, M1_NO_GE in terms of Pearson's correlation was of at least 4.3%, while in terms of percentage of top-yielding lines captured when was selected the 10% (Best10) and 20% (Best20) of lines was at least of 19.5%, while in terms of Normalized Root Mean Squared Error (NRMSE) was of at least of 42.29%. [ABSTRACT FROM AUTHOR]

Genomic selection (GS) is transforming plant and animal breeding, but its practical implementation for complex traits and multi-environmental trials remains challenging. To address this issue, this study investigates the integration of environmental information with genotypic information in GS. The study proposes the use of two feature selection methods (Pearson’s correlation and Boruta) for the integration of environmental information. Results indicate that the simple incorporation of environmental covariates may increase or decrease prediction accuracy depending on the case. However, optimal incorporation of environmental covariates using feature selection significantly improves prediction accuracy in four out of six datasets between 14.25% and 218.71% under a leave one environment out cross validation scenario in terms of Normalized Root Mean Squared Error, but not relevant gain was observed in terms of Pearson´s correlation. In two datasets where environmental covariates are unrelated to the response variable, feature selection is unable to enhance prediction accuracy. Therefore, the study provides empirical evidence supporting the use of feature selection to improve the prediction power of GS. [ABSTRACT FROM AUTHOR]

Multi-environment trials (METs) of potato breeding clones and cultivars allow to precisely determine their performance across testing sites over years. However, these METs may be affected by the genotype × environment interaction (GEI) as noted in tuber yield. Furthermore, trials are replicated several times to optimize the predictive value of the data collected because knowledge on spatial and temporal variability of testing environments is often lacking. Hence, the objectives of this research were to use components of variance from METs to estimate broad sense heritability (H2) based on best linear unbiased predictors and use these estimates to determine the optimum number of sites, years, and replications for testing potato breeding clones along with cultivars. The data were taken from METs in southern and northern Sweden comprising up to 256 breeding clones and cultivars that underwent testing using a simple lattice design of 10-plant plots across three sites over 2 years. Percentage starch in the tuber flesh had the largest H2 in each testing environment (0.850–0.976) or across testing environments (0.905–0.921). Total tuber weight per plot also exhibited high H2 (0.720–0.919) in each testing environment or across them (0.726–0.852), despite a significant GEI. Reducing sugar content in the tuber flesh had the lowest, but still medium H2 (0.426–0.883 in each testing environment; 0.718–0.818 across testing environments). The H2 estimates were smaller when their variance components were disaggregated by year and site, instead of lumping them as environments. Simulating H2 with genetic, site, year, site × year, genetic × site, genetic × year, genetic × site × year, and residual variance components led to establish that two replicates at each of two sites in 2-year trials will suffice for testing tuber yield, starch and reducing sugars. This article provides a methodology to optimize the number of testing size and years for METs of potato breeding materials, as well as tabulated information for choosing the appropriate number of trials in same target population of environments. [ABSTRACT FROM AUTHOR]

The genomic selection (GS) methodology proposed over 20 years ago by Meuwissen et al. (Genetics, 2001) has revolutionized plant breeding. A predictive methodology that trains statistical machine learning algorithms with phenotypic and genotypic data of a reference population and makes predictions for genotyped candidate lines, GS saves significant resources in the selection of candidate individuals. However, its practical implementation is still challenging when the plant breeder is interested in the prediction of future seasons or new locations and/or environments, which is called the "leave one environment out" issue. Furthermore, because the distributions of the training and testing set do not match, most statistical machine learning methods struggle to produce moderate or reasonable prediction accuracies. For this reason, the main objective of this study was to explore the use of the multi-trait partial least square (MT-PLS) regression methodology for this specific task, benchmarking its performancewith the Bayesian Multi-trait Genomic Best Linear Unbiased Predictor (MT-GBLUP) method. The benchmarking process was performed with five actual data sets. We found that in all data sets the MT-PLS method outperformed the popular MT-GBLUP method by 349.8% (under predictor E + G), 484.4% (under predictor E + G + GE; where E denotes environments, G genotypes and GE the genotype by environment interaction) and 15.9% (under predictor G + GE) across traits. Our results provide empirical evidence of the power of the MT-PLS methodology for the prediction of future seasons or new environments. Furthermore, the comparison between single univariate-trait (UT) versus MT for GBLUP and PLS gave an increase in prediction accuracy of MT-GBLUP versus UTGBLUP, but not for MT-PLS versus UT-PLS. [ABSTRACT FROM AUTHOR]

Potato breeding must improve its efficiency by increasing the reliability of selection as well as identifying a promising germplasm for crossing. This study shows the prediction accuracy of genomic-estimated breeding values for several potato (Solanum tuberosum L.) breeding clones and the released cultivars that were evaluated at three locations in northern and southern Sweden for various traits. Three dosages of marker alleles [pseudo-diploid (A), additive tetrasomic polyploidy (B), and additive-non-additive tetrasomic polyploidy (C)] were considered in the genome-based prediction models, for single environments and multiple environments (accounting for the genotype-by-environment interaction or G × E), and for comparing two kernels, the conventional linear, Genomic Best Linear Unbiased Prediction (GBLUP) (GB), and the non-linear Gaussian kernel (GK), when used with the single-kernel genetic matrices of A, B, C, or when employing two-kernel genetic matrices in the model using the kernels from B and C for a single environment (models 1 and 2, respectively), and for multi-environments (models 3 and 4, respectively). Concerning the single site analyses, the trait with the highest prediction accuracy for all sites under A, B, C for model 1, model 2, and for GB and GK methods was tuber starch percentage. Another trait with relatively high prediction accuracy was the total tuber weight. Results show an increase in prediction accuracy of model 2 over model 1. Non-linear Gaussian kernel (GK) did not show any clear advantage over the linear kernel GBLUP (GB). Results from the multi-environments had prediction accuracy estimates (models 3 and 4) higher than those obtained from the single-environment analyses. Model 4 with GB was the best method in combination with the marker structure B for predicting most of the tuber traits. Most of the traits gave relatively high prediction accuracy under this combination of marker structure (A, B, C, and B-C), and methods GB and GK combined with the multi-environment with G × E model. [ABSTRACT FROM AUTHOR]

Key message: Using phenotype data of three spring wheat populations evaluated at 6–15 environments under two management systems, we found moderate to very high prediction accuracies across seven traits. The phenotype data collected under an organic management system effectively predicted the performance of lines in the conventional management and vice versa. There is growing interest in developing wheat cultivars specifically for organic agriculture, but we are not aware of the effect of organic management on the predictive ability of genomic selection (GS). Here, we evaluated within populations prediction accuracies of four GS models, four combinations of training and testing sets, three reaction norm models, and three random cross-validations (CV) schemes in three populations phenotyped under organic and conventional management systems. Our study was based on a total of 578 recombinant inbred lines and varieties from three spring wheat populations, which were evaluated for seven traits at 3–9 conventionally and 3–6 organically managed field environments and genotyped either with the wheat 90 K SNP array or DArTseq. We predicted the management systems (CV0M) or environments (CV0), a subset of lines that have been evaluated in either management (CV2M) or some environments (CV2), and the performance of newly developed lines in either management (CV1M) or environments (CV1). The average prediction accuracies of the model that incorporated genotype × environment interactions with CV0 and CV2 schemes varied from 0.69 to 0.97. In the CV1 and CV1M schemes, prediction accuracies ranged from − 0.12 to 0.77 depending on the reaction norm models, the traits, and populations. In most cases, grain protein showed the highest prediction accuracies. The phenotype data collected under the organic management effectively predicted the performance of lines under conventional management and vice versa. This is the first comprehensive GS study that investigated the effect of the organic management system in wheat. [ABSTRACT FROM AUTHOR]

Although durum wheat (Triticum turgidum var. durum Desf.) is a minor cereal crop representing just 5–7% of the world's total wheat crop, it is a staple food in Mediterranean countries, where it is used to produce pasta, couscous, bulgur and bread. In this paper, we cover multi-trait prediction of grain yield (GY), days to heading (DH) and plant height (PH) of 270 durum wheat lines that were evaluated in 43 environments (country–location–year combinations) across a broad range of water regimes in the Mediterranean Basin and other locations. Multi-trait prediction analyses were performed by implementing a multi-trait deep learning model (MTDL) with a feed-forward network topology and a rectified linear unit activation function with a grid search approach for the selection of hyper-parameters. The results of the multi-trait deep learning method were also compared with univariate predictions of the genomic best linear unbiased predictor (GBLUP) method and the univariate counterpart of the multi-trait deep learning method (UDL). All models were implemented with and without the genotype × environment interaction term. We found that the best predictions were observed without the genotype × environment interaction term in the UDL and MTDL methods. However, under the GBLUP method, the best predictions were observed when the genotype × environment interaction term was taken into account. We also found that in general the best predictions were observed under the GBLUP model; however, the predictions of the MTDL were very similar to those of the GBLUP model. This result provides more evidence that the GBLUP model is a powerful approach for genomic prediction, but also that the deep learning method is a practical approach for predicting univariate and multivariate traits in the context of genomic selection. [ABSTRACT FROM AUTHOR]

On-farm trials of bread and durum wheat in the Yaqui Valley region of southern Sonora, Mexico, were established for three cropping seasons (2012, 2013, and 2015) using the management practices implemented by farmers. The trials comprised bread and durum wheats that were sown together under two regimes: full irrigation and reduced irrigation. The experiments were replicated and unbalanced, as several bread wheat and durum wheat lines were not repeated during the 3 yr. We studied the interaction between bread and durum wheats and environments (farmer-irrigation-year combinations). To model the crossover interaction (COI) and the non-COI components of the genotype x environment interaction (GxE) between the wheat lines and the environments, we used a linear mixed model with the Factor Analytic (FA) model, a parsimonious model that is similar to the multiple regression of lines on environments based on latent variables. In this case, we modeled the combined effects of the wheat lines and their interactions with the farmer-irrigation-year combinations. Results show the separation of the dynamic (unpredictable) component of the interaction (year) from the more static component of the interaction due to farmer and irrigation level. The FA model offers a useful alternative for modeling interactions in agronomy-breeding experiments to dissect and account for complex interactions that are common in agriculture experiments. Furthermore, stable wheat lines across all environments were also detected, as well the environments that caused most of the interaction. [ABSTRACT FROM AUTHOR]

Key message: A new genomic model that incorporates genotype × environment interaction gave increased prediction accuracy of untested hybrid response for traits such as percent starch content, percent dry matter content and silage yield of maize hybrids. Abstract: The prediction of hybrid performance (HP) is very important in agricultural breeding programs. In plant breeding, multi-environment trials play an important role in the selection of important traits, such as stability across environments, grain yield and pest resistance. Environmental conditions modulate gene expression causing genotype × environment interaction (G × E), such that the estimated genetic correlations of the performance of individual lines across environments summarize the joint action of genes and environmental conditions. This article proposes a genomic statistical model that incorporates G × E for general and specific combining ability for predicting the performance of hybrids in environments. The proposed model can also be applied to any other hybrid species with distinct parental pools. In this study, we evaluated the predictive ability of two HP prediction models using a cross-validation approach applied in extensive maize hybrid data, comprising 2724 hybrids derived from 507 dent lines and 24 flint lines, which were evaluated for three traits in 58 environments over 12 years; analyses were performed for each year. On average, genomic models that include the interaction of general and specific combining ability with environments have greater predictive ability than genomic models without interaction with environments (ranging from 12 to 22%, depending on the trait). We concluded that including G × E in the prediction of untested maize hybrids increases the accuracy of genomic models. [ABSTRACT FROM AUTHOR]

In agriculture and plant breeding, multienvironment trials over multiple years are conducted to evaluate and predict genotypic performance under different environmental conditions and to analyze, study, and interpret genotype x environment interaction (G x E). In this study, we propose a hierarchical Bayesian formulation of a linear-bilinear model, where the conditional conjugate prior for the bilinear (multiplicative) G x E term is the matrix von Mises-Fisher (mVMF) distribution (with environments and sites defined as synonymous). A hierarchical normal structure is assumed for linear effects of sites, and priors for precision parameters are assumed to follow gamma distributions. Bivariate highest posterior density (HPD) regions for the posterior multiplicative components of the interaction are shown within the usual biplots. Simulated and real maize (Zea mays L.) breeding multisite data sets were analyzed. Results showed that the proposed model facilitates identifying groups of genotypes and sites that cause G x E across years and within years, since the hierarchical Bayesian structure allows using plant breeding data from different years by borrowing information among them. This model offers the researcher valuable information about G x E patterns not only for each 1-yr period of the breeding trials but also for the general process that originates the response across these periods. [ABSTRACT FROM AUTHOR]

A study was performed to evaluate the effects of environment (E) and genotype (G) × E interactions (GGE) for quality traits and grain yield in bread wheat (Triticum aestivum L.). ANOVA and GGE biplots were used to assess quality performance and stability in 36 genotypes of bread wheat through a three-location trial over two cropping seasons in the Thrace Region of Turkey. The 36 wheat genotypes used were classified into eight different groups, including landraces, 1960s, 1970s, 1980s, 1990s, 2000s, and advanced lines. The data showed a wide range of variation for milling quality parameters with regard to gluten quantity and quality, as well as for grain yield. Genotypes, location, and year, in this order, contributed to this diversity. Remarkably, all the traits except grain protein content showed a larger genotype effect than location (L) effect; the interaction G × L was usually more important than the G × Y. Genotypic and location components markedly exceeded G × L and Y × L for all variables, with the exception of grain yield, in which the G × Y effect was greater than locations according to ANOVA analysis. Noticeable continuous progress (53%) was observed in genetic grain yield during the last 60 yr without limiting wheat quality. GGE biplot analysis found that, on average, the biplots accounted for 80 to 85% of G and G × E variation present. Krasunia and Sagittario were the best genotypes (best performance and higher stability) of the study based on the traits evaluated. [ABSTRACT FROM AUTHOR]

Genotype × environment interaction (G × E) plays a fundamental role in important agricultural traits such as grain yield or disease resistance. Therefore, modeling G × E is essential for the selection of high yielding and well-adapted varieties. The availability of new sources of genetic and environmental information (e.g., dense panels for molecular markers coupled with large numbers of environmental covariates [EC]) provides important opportunities for studying and exploiting G × E. However, incorporating highdimensional genetic and environmental data and accounting for potential interactions is not an easy task. Recently we developed a genomic model that incorporates molecular markers, EC, and the interactions between them using covariance functions. In this paper we demonstrate how the same approach can be applied in cases where genetic information is based on pedigrees instead of molecular markers. We evaluated the models using a collection of 7809 grain yield records obtained from 582 cotton lines evaluated in 2 yr (2011 and 2012) over nine locations. A total of 76 EC were available and used to model main and interaction effects. Estimates of variance components indicated that G × E explained a sizable proportion of the phenotypic variance, and two cross-validation analyses indicated that modeling G × E increases prediction accuracy by a considerable margin. To the best of our knowledge, this is the first study considering both pedigree and EC for the analysis of cotton yield. The models described here can be used for prediction of genetic merit and for selection for target environments. [ABSTRACT FROM AUTHOR]

Crop breeding programs using conventional approaches, as well as new biotechnological tools, rely heavily on data resulting from the evaluation of genotypes in different environ mental conditions (agronomic practices, locations, and years). Statistical methods used for designing field and laboratory trials and for analyzing the data originating from those trials need to be accurate and efficient. The statistical analysis of multi-environment trails (MET) is useful for assessing genotypex environment interaction (GEI), mapping quantitative trait loci (QTLs), and studying QTLx environment interaction (QEI). Large populations are required for scientific study of QEI, and for determining the association between molecular markers and quantitative trait variability. Therefore, appropriate control of local variability through efficient experimental design is of key importance. In this chapter we present and explain several classes of augmented designs useful for achieving control of variability and assessing genotype effects in a practical and efficient manner. A popular procedure for unreplicated designs is the one known as "systematically spaced checks." Augmented designs contain "c" check or standard treatments replicated "r" times, and "n" new treatments or genotypes included once (usually) in the experiment. [ABSTRACT FROM AUTHOR]

Much research has been conducted using least squares estimates of the linear-bilinear model additive main effects and multiplicative interaction (AMMI). The main difficulty with the standard linear-bilinear models is that statistical inference on the bilinear effects of genotype x environment interaction cannot be incorporated easily into the biplot of the first two components. This research proposes a Bayesian approach for the inference on the parameters of the AMMI model using a Gibbs sampler that saves computing time and makes the algorithm stable. Data from one maize (Zea mays L.) multi-environment trial (MET) was used for illustration. Vague but proper prior distributions were introduced Results show that the various Markov chain Monte Carlo convergence criteria were met for all parameters. Bivariate highest posterior density (HPD) regions for the Bayesian-AMMI interactions are shown in the biplot of the first two bilinear components; these regions offer a statistical inference on the bilinear parameters and allow visualizing homogeneous groups of environments and genotypes. [ABSTRACT FROM AUTHOR]

Fixed linear models have been used for describing genotype x environment interaction (GE). Previous attempts have been made to assess the predictive ability of some linear mixed models when GE components are treated as random effects and modeled by the factor analytic (FA) model. This study compares the predictive ability of linear mixed models when the GE is modeled by the FA model with that of simple linear mixed models when the GE is not modeled. A cross-validation scheme is used that randomly deletes some genotypes from sites; the values for these genotypes are then predicted by the different models and correlated with their observed values to assess model accuracy. A total of six multienvironment trials (one potato [Solanum tuberosum L.] trial, three maize [Zea mays L.J trials, and two wheat [Triticum aestivum L.] trials) with GE of varying complexity were used in the evaluation. Results show that for data sets with complex GE, modeling GE using the FA model improved the predictability of the model up to 6%. When GE is not complex, most models (with and without FA) gave high predictability, and models with FA did not seem to lose much predictive ability. Therefore, we concluded that modeling GE with the FA model is a good thing. [ABSTRACT FROM AUTHOR]

A numerical classification problem encountered by breeders and gene-bank curators is how to partition the original heterogeneous population of genotypes into non-overlapping homogeneous subpopulations. The measure of distance that may be defined depends on the type of variables measured (i.e., continuous and/or discrete). The key points are whether and how a distance may be defined using all types of variables to achieve effective classification. The objective of this research was to propose an approach that combines the use of hierarchical multiple-factor analysis (HMFA) and the two-stage Ward Modified Location Model (Ward-MLM) classification strategy that allows (i) combining different types of phenotypic and genetic data simultaneously; (ii) balancing out the effects of the different phenotypic, genetic, continuous, and discrete variables; and (iii) measuring the contribution of each original variable to the new principal axes (PAs). Of the two strategies applied for developing PA scores to be used for clustering genotypes, the strategy that used the first few PA scores to which phenotypic and genetic variables each contributed 50% (i.e., a balanced contribution) formed better groups than those formed by the strategy that used a large number of PA scores explaining 95% of total variability. Phenotypic variables account for much variability in the initial PA; then their contributions decrease. The importance of genetic variables increases in later PAs. Results showed that various phenotypic and genetic variables made important contributions to the new PA. The HMFA uses all phenotypic and genetic variables simultaneously and, in conjunction with the Ward-MLM method, it offers an effective unifying approach for the classification of breeding genotypes into homogeneous groups and for the formation of core subsets for genetic resource conservation. [ABSTRACT FROM AUTHOR]

Linkage disequilibrium can be used for identifying associations between traits of interest anti genetic markers. This study used mapped diversity array technology (DArT) markers to find associations with resistance to stern rust, leaf rust, yellow rust, and powdery mildew, plus grain yield in five historical wheat international multienvironment trials from the International Maize and Wheat Improvement Center (CIMMYT). Two linear mixed models were used to assess marker-trait associations incorporating information on population structure and covariance between relatives. An integrated map containing 813 DArT markers and 831 other markers was constructed. Several linkage disequilibrium clusters bearing multiple host plant resistance genes were found. Most of the associated markers were found in genomic regions where previous reports had found genes or quantitative trait loci (QTL) influencing the same traits, providing an independent validation of this approach. In addition, many new chromosome regions for disease resistance and grain yield were identified in the wheat genome. Phenotyping across up to 60 environments anti years allowed modeling of genotype X environment interaction, thereby making possible the identification of markers contributing to both additive and additive X additive interaction effects of traits. [ABSTRACT FROM AUTHOR]

In self-pollinated species, the variance-covariance matrix of breeding values of the genetic strains evaluated in multienvironment trials (MET) can be partitioned into additive effects, additive x additive effects, and their interaction with environments. The additive relationship matrix A can be used to derive the additive x additive genetic variance-covariance relationships among strains, A. This study shows how to separate total genetic effects into additive and additive x additive and how to model the additive x environment interaction and additive x additive x environment interaction by incorporating variance-covariance structures constructed as the Kronecker product of a factor-analytic model across sites and the additive (A) and additive x additive relationships (A), between strains. Two CIMMYT international trials were used for illustration. Results show that partitioning the total genotypic effects into additive and additive x additive and their interactions with environments is useful for identifying wheat (Trificum aestivum L.) lines with high additive effects (to be used in crossing programs) as well as high overall production. Some lines and environments had high positive additive x environment interaction patterns, whereas other lines and environments showed a different additive x additive x environment interaction pattern. [ABSTRACT FROM AUTHOR]

Genotype × environment interaction (GEI) affects marketable fruit yield and average fruit weight of both hybrid and open-pollinated (OP) tomato genotypes. Cultivars vary significantly for marketable fruit yield, with hybrid cultivars having, on average, higher yield than OP cultivars. However, information is scanty on environmental factors affecting the differential response of tomato genotypes across environments. Hence, the aim of this research was to use factorial regression (FR) and partial least squares (PLS) regression, which incorporate external environmental and genotypic covariables directly into the model for interpreting GEI. In this research, data from an FAO multi-environment trial comprising 15 tomato genotypes (7 hybrid and 8 OP) evaluated in 18 locations of Latin America and the Caribbean were analyzed using FR and PLS. Environmental factors such as days to harvest, soil pH, mean temperature (MET), potassium available in the soil, and phosphorus fertilizer accounted for a sizeable portion of GEI for marketable fruit yield, whereas trimming, irrigation, soil organic matter, and nitrogen and phosphorus fertilizers were important environmental covariables for explaining GEI of average fruit weight. Locations with relatively high minimum and mean temperatures favored the marketable fruit yield of OP heat-tolerant lines CL 5915-223 and CL 5915-93. An OP cultivar (Catalina) and a hybrid (Apla) showed average marketable fruit yield across environments, while two hybrids (Sunny and Luxor) exhibited outstanding marketable fruit yield in high yielding locations (due to lower temperatures and higher pH) but a sharp yield loss in poor environments. Two stable hybrid genotypes in high yielding environments, Narita and BHN-39, also showed high and stable yield in average and low yielding environments. [ABSTRACT FROM AUTHOR]

Several statistical models can be used for assessing genotype x environment interaction (GEI) and studying genotypic stability. The objectives of this research were to show how (i) to use Bayesian methodology for computing Shukla's phenotypic stability variance and (it) to incorporate prior information on the parameters for better estimation. Potato [Solanum tuberosum subsp, andigenum (Juz. & Bukasov) Hawkes], wheat (Triticum aestivum L.), and maize (Zea mays L.) multi environment trials (MET) were used for illustrating the application of the Bayes paradigm. The potato trial included 15 genotypes, but prior information for just three genotypes was used. The wheat trial used prior information on all 10 genotypes included in the trial, whereas for the maize trial, noninformative priors for the nine genotypes was used. Concerning the posterior distribution of the genotypic means, the maize MET with 20 sites gave less disperse posterior distributions of the genotypic means than did the posterior distribution of the genotypic means of the other METs, which included fewer environments. The Bayesian approach allows use of other statistical strategies such as the normal truncated distribution (used in this study). When analyzing grain yield, a lower bound of zero and an upper bound set by the researcher's experience can be used. The Bayesian paradigm offers plant breeders the possibility of computing the probability of a genotype being the best performer. The results of this study show that although some genotypes may have a very low probability of being the best in all sites, they have a relatively good chance of being among the five highest yielding genotypes. [ABSTRACT FROM AUTHOR]

In genetic resource conservation and plant breeding, multivariate data on continuous and categorical traits are collected with the objective of selecting genotypes and accessions that best represent the entire population or gene collection with the minimum loss of genetic diversity. Therefore, the best numerical classification strategy is the one that produces the most compact and well-separated groups, that is, minimum variability within each group and maximum variability among groups. In this study, we review geometric classification techniques as well as statistical models based on mixed distribution models. The two-stage sequential clustering strategy uses all variables, continuous and categorical, and it tends to form more homogeneous groups of individuals than other clustering strategies. The sequential clustering strategy can be applied to three-way data comprising genotypes × environments × attributes. This approach groups genotypes with consistent responses for most of the continuous and categorical traits across environments. [ABSTRACT FROM AUTHOR]

Multi-trait and multi-environment data are common in animal and plant breeding programs. However, what is lacking are more powerful statistical models that can exploit the correlation between traits to improve prediction accuracy in the context of genomic selection (GS). Multi-trait models are more complex than univariate models and usually require more computational resources, but they are preferred because they can exploit the correlation between traits, which many times helps improve prediction accuracy. For this reason, in this paper we explore the power of multi-trait deep learning (MTDL) models in terms of prediction accuracy. The prediction performance ofMTDL models was compared to the performance of the Bayesian multi-trait and multienvironment (BMTME) model proposed by Montesinos-López et al. (2016), which is a multi-trait version of the genomic best linear unbiased prediction (GBLUP) univariate model. Both models were evaluated with predictors with and without the genotype×environment interaction term. The prediction performance of both models was evaluated in terms of Pearson's correlation using cross-validation. We found that the best predictions in two of the three data sets were found under the BMTME model, but in general the predictions of both models, BTMTE and MTDL, were similar. Among models without the genotype×environment interaction, the MTDL model was the best, while among models with genotype×environment interaction, the BMTME model was superior. These results indicate that the MTDL model is very competitive for performing predictions in the context of GS, with the important practical advantage that it requires less computational resources than the BMTME model. [ABSTRACT FROM AUTHOR]

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 x environment interaction (G x E), because there is a lack of comprehensive models that simultaneously take into account the correlated counting traits and G x 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. [ABSTRACT FROM AUTHOR]

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 (nT) 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 (n[sub T]). Here, we propose a Bayesian mixed-negative binomial (BMNB) genomic regression model for counts that takes into account genotype by environment (G x E) 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. [ABSTRACT FROM AUTHOR]

Envirotyping is an essential technique used to unfold the nongenetic drivers associated with the phenotypic adaptation of living organisms. Here, we introduce the EnvRtype R package, a novel toolkit developed to interplay large-scale envirotyping data (enviromics) into quantitative genomics. To start a user-friendly envirotyping pipeline, this package offers: (1) remote sensing tools for collecting (get_weather and extract_GIS functions) and processing ecophysiological variables (processWTH function) from raw environmental data at single locations or worldwide; (2) environmental characterization by typing environments and profiling descriptors of environmental quality (env_typing function), in addition to gathering environmental covariables as quantitative descriptors for predictive purposes (W_matrix function); and (3) identification of environmental similarity that can be used as an enviromic-based kernel (env_typing function) in whole-genome prediction (GP), aimed at increasing ecophysiological knowledge in genomic best-unbiased predictions (GBLUP) and emulating reaction norm effects (get_kernel and kernel_model functions). We highlight literature mining concepts in fine-tuning envirotyping parameters for each plant species and target growing environments. We show that envirotyping for predictive breeding collects raw data and processes it in an eco-physiologically smart way. Examples of its use for creating global-scale envirotyping networks and integrating reaction-norm modeling in GP are also outlined. We conclude that EnvRtype provides a cost-effective envirotyping pipeline capable of providing high quality enviromic data for a diverse set of genomic-based studies, especially for increasing accuracy in GP across untested growing environments. [ABSTRACT FROM AUTHOR]

Genome-enabled prediction plays an essential role in wheat breeding because it has the potential to increase the rate of genetic gain relative to traditional phenotypic and pedigree-based selection. Since the performance of wheat lines is highly influenced by environmental stimuli, it is important to accurately model the environment and its interaction with genetic factors in prediction models. Arguably, multi-environmental best linear unbiased prediction (BLUP) may deliver better prediction performance than single-environment genomic BLUP. We evaluated pedigree and genome-based prediction using 35,403 wheat lines from the Global Wheat Breeding Program of the International Maize and Wheat Improvement Center (CIMMYT). We implemented eight statistical models that included genome-wide molecular marker and pedigree information as prediction inputs in two different validation schemes. All models included main effects, but some considered interactions between the different types of pedigree and genomic covariates via Hadamard products of similarity kernels. Pedigree models always gave better prediction of new lines in observed environments than genome-based models when only main effects were fitted. However, for all traits, the highest predictive abilities were obtained when interactions between pedigree, genomes, and environments were included. When new lines were predicted in unobserved environments, in almost all trait/year combinations, the marker main-effects model was the best. These results provide strong evidence that the different sources of genetic information (molecular markers and pedigree) are not equally useful at different stages of the breeding pipelines, and can be employed differentially to improve the design and prediction of the outcome of future breeding programs. [ABSTRACT FROM AUTHOR]

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 multienvironment 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 (l) 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. [ABSTRACT FROM AUTHOR]

The traditional molecular selection index (MSI) employed in marker-assisted selection maximizes the selection response by combining information on molecular markers linked to quantitative trait loci (QTL) and phenotypic values of the traits of the individuals of interest. This study proposes an MSI based on an eigenanalysis method (molecular eigen selection index method, MESIM),where the first eigenvector is used as a selection index criterion, and its elements determine the proportion of the trait's contribution to the selection index. This article develops the theoretical framework of MESIM. Simulation results show that the genotypic means and the expected selection response from MESIM for each trait are equal to or greater than those from the traditional MSI. When several traits are simultaneously selected, MESIM performs well for traits with relatively low heritability. The main advantages of MESIM over the traditional molecular selection index are that its statistical sampling properties are known and that it does not require economic weights and thus can be used in practical applications when all or some of the traits need to be improved simultaneously. [ABSTRACT FROM AUTHOR]