White lupin is a high-protein crop requiring drought tolerance improvement. This study focused on a genetically-broad population of 138 lines to investigate the phenotypic variation and genotype × environment interaction (GEI) for grain yield and other traits across drought-prone and moisture-favourable managed environments, the trait genetic architecture and relevant genomic regions by a GWAS using 9828 mapped SNP markers, and the predictive ability of genomic selection (GS) models. Water treatments across two late cropping months implied max. available soil water content of 60–80% for favourable conditions and from wilting point to 15% for severe drought. Line yield responses across environments featured a genetic correlation of 0.84. Relatively better line yield under drought was associated with an increased harvest index. Two significant QTLs emerged for yield in each condition that differed across conditions. Line yield under stress displayed an inverse linear relationship with the onset of flowering, confirmed genomically by a common major QTL. An adjusted grain yield computed as deviation from phenology-predicted yield acted as an indicator of intrinsic drought tolerance. On the whole, the yield in both conditions and the adjusted yield were polygenic, heritable, and exploitable by GS with a high predictive ability (0.62–0.78). Our results can support selection for climatically different drought-prone regions.  Lupinus albus L.) is a Mediterranean grain legume that used to be a major crop in various regions of the Roman Empire because of its ability to adapt to and improve infertile soils ,,42], 13 Our study revealed several genomic regions of potential interest for grain yield and onset of flowering selection by scanning a region as long as the mean chromosome distance at which LD dropped below 0.2 in both directions from each significant SNP . Inter aIn conclusion, this study generated information that could support the phenotypic and genomic selection of white lupin for drought-prone or climatically-diversified target regions. It confirmed the importance of an early phenology for drought stress escape on the ground of phenotypic and GWAS results. However, it revealed the presence of heritable, polygenic genetic variation for intrinsic drought tolerance that could be exploited through phenotypic selection or, less expensively, through moderately reliable genomic predictions. It also indicated the feasibility of phenotypic or genomic selection for wide adaptation to moisture-contrasting target environments. The high predictive ability of the current GS models for drought tolerance will be verified by future proof-of-concept work aiming to assess actual genetic gains obtained from GS application to independent germplasm sets.2 to F5 inbred lines for each of the 16 crosses from 2015 to 2017 were carried out in isolation under insect-proof nets to prevent any out-crossing. Within-cross selection for low alkaloid content was performed (a) on F3 and F4 individual seeds by the fluorescence method 2 to F5 i 3 to 10 . However2), keeping two edge plants as border plants. Sowing took place in the late winter (mid-February) in 2019 to avoid any confounding effect of susceptibility to low temperatures in addition to drought. Mineral fertilization was incorporated into the seedbed at the rates of 27 kg/ha of N, 46 kg/ha of P2O5, and 50 kg/ha of K2O. The seed was inoculated with NPPL HiStick inoculant  prior to sowing. Pre-emergence weed control was performed by applying 1.5 L/ha of Stomp Aqua . After an initial stage of favourable vegetative growth that implied 120 mm of irrigation, two conditions of water availability were imposed, starting from 16 April to 16 June . A Diviner 2000 capacitance sensor  monitored the soil moisture every two to three days. In the moisture-favourable environment, irrigation of about 20 mm was applied when the soil water content decreased beneath 60% of the maximum available soil water  in the upper 40 cm, bringing back the water content to a level exceeding 80% of the maximum available soil water. In the drought-stress environment, an irrigation of about 10 mm was applied at the soil water content corresponding to the wilting point, replenishing 15% of the maximum available soil water. The moisture-favourable environment received a total of 240 mm of irrigation in 12 applications, whereas the stress environment was irrigated five times with a total of 50 mm. Daily mean temperatures and daily maximum temperatures averaged 12.4 °C and 17.3 °C, respectively, in April, 14.3 °C and 19.3 °C in May, and 24.0 °C and 29.8 °C in June.The 138 inbred lines were grown in Lodi, northern Italy, in a phenotyping platform already used for other drought-tolerance studies . The plWe recorded on a plot basis the onset of flowering as the number of days from 1 April to when 50% of the plants displayed three open flowers. Dry grain yield, dry straw biomass, and harvest index  were assessed after harvesting and threshing the whole plot at crop maturity and oven drying the grain and the straw at 60 °C for four days to constant weight. m is the trait mean value, and gs is the square root of the genotypic component of variance (s2g) estimated along with the experimental error (s2e) component of variance by a restricted maximum likelihood (REML) method. Trait broad-sense heritability was computed from these components of variance by the equation: n is the number of experiment replicates, computing an approximate standard error as reported in [H2 values to compute the best linear unbiased prediction (BLUP) values according to [An ANOVA including the fixed factor genotype and the random factor block was performed for each trait in each environment to assess the significance of the variation among lines and its extent as the genetic coefficient of variation computed as: orted in . We usedrding to , which wt values.A second ANOVA including the fixed factor environment and the random factors genotype and block within environment was performed for each trait to test the variation relative to water treatments, genotypes, and GEI, assessing the extent of the last two effects by estimating the respective components of variance through a REML method. The consistency of the genotype responses across environments was assessed in terms of genetic correlation as described in  for one SY and FY stand for line grain yield under stress and favourable conditions, respectively, and SD is an index of drought severity estimated from irrigation water over the crop cycle for stress (SI) and favourable (FI) conditions:We verified whether genotype grain yields under severe drought were affected by the onset of flowering through a regression analysis, assessing the significance of linear and curvilinear responses. Line mean yields of flowering across environments were used in this analysis, given the lack of GEI observed for this trait. In the presence of a significant inverse linear response, we estimated for each line an ‘adjusted’ grain yield on a plot basis as the deviation of its actual yield from the yield value expected for the line as a function of its onset of flowering in the linear regression model, as described in an earlier study on pea . Such adNo ANOVA could be applied to DSI because its values were estimated from cultivar mean values within each condition. We assessed the line variation for DSI values in terms of phenotypic CV.® software [Simple correlation analyses were used to assess (a) interrelationships between traits within each environment and (b) patterns of covariation for GEI effects of different traits. The mean value of inbred line progenies issued from each parent provided an estimate of the parent value for yield under severe drought. All analyses were carried out using the SAS/STATsoftware .5 plants of each inbred line using the DNeasy Plant Mini Kit . Nucleic acid was quantified by a Quant-iT™ PicoGreen™ dsDNA Assay Kit , checking its quality by 1% agarose gel electrophoresis. A trial digestion was carried out on 10% of the DNA samples using the Optizyme EcoRI restriction enzyme , to compare bands of cut and uncut DNA. The reaction was performed at 37 °C for one hour and the enzyme was deactivated at 65 °C for 20 min. DNA samples were sent to The Elshire Group Ltd. laboratory  for outsourced library preparation and sequencing. GBS data were generated according to Elshire et al.’s [ApeKI enzyme ; then, the library was amplified with Kapa Taq polymerase Alpha  by 14 PCR cycles. Sequencing was performed on a single Illumina HiSeq X lane, at 2X150 bp paired-end. Adopting ApeKI as the restriction enzyme according to [Genomic DNA was extracted from young leaves of Frding to , which tLupinus albus genome version 1.0 [https://www.whitelupin.fr/ (accessed on 3 November 2022). The final genotype matrix, in the form of a vcf file, was further filtered for quality using the vcftools software [minQ 30 −max-non-ref-af 1 –non-ref-af 0.001. The resulting data set was filtered for monomorphic markers, minor allele frequency (MAF) > 5%, missing SNP marker rate < 10%, 20% or 30%, and a missing rate per individual < 50%. Following Nazzicari et al. [GBS raw reads were demultiplexed using Axe demultiplexer . Trimminsion 1.0 , which wsoftware  with pari et al. , we estii et al.  using thi et al.  with theBoth genotypes and SNPs were filtered for excess heterozygosis by using the mean plus three and two standard deviations as maximum thresholds, respectively.adegenet [find.clusters, dapc and optim.a.score.The presence and pattern of population structure were investigated by a discriminant principal components analysis (DPCA) . We usedadegenet  using fur2) between all pairwise combinations of SNPs within a 50 kb window from genotype data filtered by 0.3 missing data per marker, 0.5 missing data per sample, 0.05 MAF, and excess SNP and genotype heterozygosis, plotted against physical distance, and fitted by a polynomial curve, as described in [Linkage disequilibrium (LD) was estimated for each chromosome in R as the squared Pearson’s correlation  considering four possible statistical models described below, the presence or absence of population structure inputted as in the GWAS, and three thresholds of maximum missing rate per SNP marker . We first envisaged a single-environment  prediction scenario, assessing the predictive ability of GS models by standard 10-fold cross-validation. Each model was tested twice, repeating the analyses ten times and reporting the average results to ensure numerical stability. We also envisaged a cross-environment prediction scenario for grain yield assessed in the favourable and stress environments, using by turns one environment for training and the other for validation (by splitting the training data in a 90/10 fashion as done for single-environment predictions). The whole procedure was repeated ten times for numerical stability.We considered four possible whole-genome regression models: Ridge Regression BLUP (rrBLUP), Bayesian Lasso (BL), Bayesian Reproducing Kernel Hilbert Space (RKHS), and Weighted G-BLUP (WGBLUP). All models were implemented using R package GROAN .2q) is the vector of marker effects; and ε is the vector of residuals. The model is solved in a maximum likelihood context estimating the ridge parameter λ = σ2e/σ2q representing the ratio between residual and markers variance. When the population structure is included in the model the above formula is updated as follows:2b) is the vector of (fixed) effects corresponding to the population structure.The rrBLUP model  assumes BL  solves t2g where G is the genomic relationship matrix and σ2g is the genetic variance for this model. In the context of RKHS the G matrix is considered as the reproducing kernel function mapping from each pair of markers to covariance. The system is then solved with a standard Gibbs sampling as done in BL, with the same configuration to accommodate for population structure if required.RKHS model is used to solve the so-called genomic BLUP (G-BLUP) in the Bayesian context. First, a genomic kinship additive matrix G is computed following . The matp values resulting from an association study. The association scores were computed programmatically inside each cross-validation cycle on the training set using statgenGWAS R package [i is the observed MAF of all genotyped individuals.WGBLUP  is very  package . Once th


The proposed multi-trait reaction norm methodology is a comprehensive approach that allows capitalizing on the benefits of multi-trait models accounting for between-trait correlations and reaction norm models exploiting high-dimensional genomic and environmental information.Multi-trait and multi-environment analyses can improve genomic prediction by exploiting between-trait correlations and genotype-by-environment interactions. In the context of reaction norm models, genotype-by-environment interactions can be described as functions of high-dimensional sets of markers and environmental covariates. However, comprehensive multi-trait reaction norm models accounting for marker × environmental covariates interactions are lacking. In this article, we propose to extend a reaction norm model incorporating genotype-by-environment interactions through (co)variance structures of markers and environmental covariates to a multi-trait reaction norm case. To do that, we propose a novel methodology for characterizing the environment at different growth stages based on growth degree-days (GDD). The proposed models were evaluated by variance components estimation and predictive performance for winter wheat grain yield and protein content in a set of 2,015 F6-lines. Cross-validation analyses were performed using leave-one-year-location-out (CV1) and leave-one-breeding-cycle-out (CV2) strategies. The modeling of genomic [SNPs] × environmental covariates interactions significantly improved predictive ability and reduced the variance inflation of predicted genetic values for grain yield and protein content in both cross-validation schemes. Trait-assisted genomic prediction was carried out for multi-trait models, and it significantly enhanced predictive ability and reduced variance inflation in all scenarios. The genotype by environment interaction modeling  Genomic selection GS,  is an efThe advantages of MT models lie in that they can represent and exploit the correlation between traits, which can increase prediction accuracy and reduce bias in predictions compared to single-trait models . The useModeling G×E has been valuable for wheat genomic prediction (GP), as it has shown increases in prediction accuracy ranging from 10 to 40 % variance structures. Approaches for incorporating both MT and ME information in GS have been developed using different methodologies . HoweverI.It simplifies the implementation of RN models since phenological records or crop simulations are no longer needed to infer the phenology of the lines. This may be convenient for wheat breeding because, in most cases, the full phenological stages are not recorded, or alternatively, it avoids the use of crop simulations that can represent a challenge for breeders since crop simulations are not commonly used in breeding programs.II.GDD periods represent a convenient approach to deal with the differences in growth stages of breeding lines. Accurately capturing differences in the growth stages of breeding lines can be difficult using crop simulation because the critical periods for different breeding lines can occur at different moments within the same environment (year-location combinations). Nevertheless, this is no longer a problem when GDD periods are used.III.Using GDD periods can be helpful when ECs is determined for traits where the relationships between the environmental conditions and resulting phenotype are not well established; while this may not represent a problem for wheat grain yield since these relationships have been extensively defined , it can In addition, the proposed MTRN model using (co)variance structures to incorporate G×E represent a convenient choice to reduce the high demand on computational resources, which have often been a relevant restriction for developing MTME models. This study uses a large set of winter wheat breeding lines phenotyped for grain yield and protein content in multiple environments. The proposed models were evaluated for both traits using cross-validation (CV) and trait-assisted genomic prediction (TA-GP) in two prediction scenarios relevant to plant breeders: (i) predicting the performance of breeding lines that have been tested in some environments but not in others , and (ii) predicting the performance of new lines across breeding cycles . The TA-GP was performed considering the phenotypes of the additional trait to exploit between-trait correlations, which is intended to improve predictions of breeding values for the trait of interest.6) winter wheat lines (T. aestivum L.) from the breeding company Nordic Seed A/S were used; a subset of these data has been used in earlier studies  at three locations in Denmark (DK): Odder , Holeby (South DK), and Skive (North-west DK). For breeding cycles from 2014 to 2016  lines were tested in 2 years instead of one in order to have a quick construction of a reliable training population for genomic prediction. Each year the field trials were designed in 15 blocks of 46 line plots of 8.25 m2, having two replicates of 21 F6 lines and two checks randomly assigned per year-location combination. The traits analyzed were grain yield measured as kg per plot (8.25 m2) and protein content (%) determined by near-infrared spectroscopy (NIRS), and both traits were chosen according to their high relevance for breeding. Similar agronomic management was applied for all trials .In this study, 2,015 sixth-generation . Soil information was available in each locality for depths 0–30, 30–60, 60–100, 100–200 cm and described texture , carbon content, hydraulic conductivity and plant available water .The climatic variables were used to compute ECs summarizing environmental descriptors linked to water availability, radiation, and temperature at different crop stages see , which tIn this study, five models were proposed to evaluate the effect of including G×E interaction and MT modeling for grain yield and protein content. The full data set was used for VCs estimation to obtain estimates as accurate as possible. First, a baseline mixed model without genomic information (M1) was used as a starting point for constructing the other models; a similar baseline model has been used in earlier works with Nordic Seed A/S data . Second,The M1 (Equation 1) is a mixed model considering the main sources of variability affecting the data and the experimental design. It was defined as:ny is the vector of phenotypes for grain yield (n = 1) or protein content (n = 2); X and nZ are design matrices for fixed and random effects, respectively; b is the vector of fixed trial effects nested within year-location-breeding cycle, which is intended to capture the variation due to overall effects of year, location, the interaction between year and location as well as effects of the spatial location of the trial within the field.; l is a vector of line effect with I is an identity matrix and f is a vector of line × environment interaction (L×E) with s is a vector of spatial effect, which follows a multivariate normal density (MVN) with S is a spatial relationship matrix and S was computed as n× q is a n × q matrix, with n = number of observations , and q = number of real plus virtual plots. The Xn× q is an indicator matrix relating observations to spatial effects in S. A heatmap of the S matrix for a subset of the data  is shown in S, and they used the regression of the 9-spatial covariates for each plot observation directly as random effects. However, although these two implementations are mathematically equivalent, our implementation is computationally faster. The e is a vector of random residuals with where get plot . VirtualThe M2 (Equation 2) extend M1 by adding a genomic [SNP] additive effect using the ny, X, nZ, b, l, f, s, and e were defined as in M1; g is a vector of the genomic additive breeding values (GEBVs), with G is the genomic relationship matrix (GRM) based on the first method proposed by ip is the minor allele frequency (MAF) of the thSNPi;Z is M−P; M is a SNP matrix coded −1, 0, 1, and P is a matrix with the MAF of SNP i calculated as 1(2(pi−0.5)) for column i.where l) was kept in all genomic models since it is intended to capture non-additive variance and additive variance not captured by SNPs in the genomic effect; therefore, this model definition helps to improve the characterization for the specific additive genomic variance captured by the SNPs.The line effect (h2) and broad-sense (H2) plot heritabilities were estimated for M2 as d(G) is the mean diagonal value of G with d(G) = 1.869, the d(G) value can be interpreted as 1 plus the average genomic inbreeding coefficient for the population (d(G), h2 and H2 were reported at the plot level and not for family means as sometimes are used in plant breeding.The narrow , and therefore, it can be viewed as a linear RN model where the genetic and environmental gradients are specified as regressions on markers and ECs. As pointed in The M3 (Equation 3) is the most developed model in terms of definition of effects as it extends M2 by including a genomic [SNPs] × ECs interaction effect variance matrix computed as in nxq is a matrix of centered and scaled ECs with n rows (number of phenotypic observations) and q columns (number of ECs). The operator “°” represents the cell-by-cell (or Hadamard) product between matrices, and where f) and the genomic [SNPs] × ECs interaction effects together in M3 is justified since ECs do not capture all the environmental variability, and therefore, this definition of interactions with the environment contribute to specifying what is not captured by ECs. A similar concept is also extended to the main line effect (L) effect, which are present in all the defied models and are intended to cover the misspecification of the SNPs on genetic effects. The inclusion of an additional model term defining the main effect of ECs have also been used in previous works  approach for grain yield and protein content. In the following section we summarize the extension of ST models to the MT case.The M2 and M3 were extended to the MT case by M4 and M5 (Equation 4), respectively. The MT models considered grain yield and protein content in a bivariate analysis. The MT methodology allows exploiting between traits (co)variances for the different model effects, which modified the definition of the random effects from ST models. Following, we present the definition of the effects for the M5 (the most developed model in terms of effects and traits included):ny, X, nZ, b, l, f, s, g, gw are the same as defined in the previous models for grain yield and protein content, except for the random effect variances which under the MT framework becomes: NIID, where ⊗ denotes the Kronecker product, and L the line (co)variance matrix NIID with F the line × environment (co)variance matrix MVN with H the spatial (co)variance matrix MVN with K the genomic (co)variance matrix P the genomic [SNPs] × ECs (co)variance matrix NIID with R the residual (co)variance matrix COVg12 is the between-trait covariance for the genomic effect, and where 2 = 0.90 to approximate the R2 expected of our models  was carried out by masking the phenotypes of one year-location in the validation set and using the remaining phenotyped lines to predict the masked lines . This prt-test . The maximum PA was calculated for g and g + wg predictions in the different models; for M2, M4 it was calculated as n was the average number of lines repetitions within year-location, The predictive ability  on the estimated with partial information : A test for variance inflation in the predicted genetic effects was performed as the slope of the regression of predicted values obtained with whole information (subscript r(up^) .2 with a coefficient of variation of 11.63%. Protein content had an average value of 9.84%, with a coefficient of variation of 8.11%. The between traits correlation based on the observed phenotypes was in general negative for the different breeding cycles and had an average of −0.18 (The descriptive statistics for grain yield and protein content are shown in of −0.18 . The varFive proposed models differing in the incorporation (M2–M5) or not (M1) of genomic information, the incorporation of genomic [SNPs] × ECs interaction (M3 and M5), and the single-trait  or multi-trait case (M4 and M5) were used to estimate VCs for grain yield  and proth2 = 0.282 (PSD = 0.025) and H2 = 0.414 (PSD = 0.017) than for grain yield: h2 = 0.168 (PSD = 0.020), H2 = 0.307 (PSD = 0.153). The G×E variability was accounted for the line × environment (f) and genomic [SNPs] × ECs interaction (wg) effects, and a higher amount of G×E variance was observed for grain yield (~40% of The phenotypic variances (l), additive (g)], and the interaction effects (line × environment (f), and genomic [SNPs] × ECs interaction (gw).The VCs estimates for single-trait models M2 and M4 were similar to MT models M3 and M5, respectively. The between-trait correlations were analyzed for all terms in M3 and M5 , and neg–4 or lower, the high ESS, and the appropriate trace and posterior density plots.The MCMC errors, effective sample (ESS), and graphical analysis of trace and posterior density plots were performed as control of convergence for VCs estimates . The parThe PAs (g + wg) compared to using only predictions from the main additive effect (g). The inclusion of the wg effect represented a significant increase of 16.4% for grain yield and 7.1% for protein content (M3 compared to M2). The MT models performing TA-GP (M4 and M5) showed a significant improvement in PA compared to the ST models and MT models without TA-PA. The TA-GP showed a significant PA increase of 37.9% for grain yield and 17.2% for protein content (M5 compared to M3). The highest PAs were obtained for both traits when combined TA-GP and G×E modeling through the genomic [SNPs] × ECs interaction effect in M5 .The PA in CV1 varied from 0.296 to 0.528 for grain yield and 0.463 to 0.601 for protein content. A significant improvement in PA was observed for using predictions of the main additive effect plus the genomic [SNPs] × ECs interaction effect (g + wg predictions compared to models using only predictions from the g effect. Using g + wg predictions represented a significant increase of 40.2% for grain yield and 14.1% for protein content (M3 compared to M2). The TA-GP for MT models provided a significant increase compared to the ST models and MT models without TA-PA, revealing a PA increase of 94.8% for grain yield and 59.7% for protein content (M5 compared to M3). The highest PA was obtained for both traits when TA-GP and G×E modeling through the genomic [SNPs] × ECs interaction effect in M5 . In comparison, the CV2 had lower PA than CV1 for both traits, and higher benefits were observed in CV2 for modeling G×E and using TA-GP.In CV2, the PA showed similar trends as CV1. A significant PA improvement was observed for models using the The maximum potential PA followed a similar trend for both traits, and the highest values were observed for the models accounting for genomic [SNPs] × ECs predictions (M3 and M5). The M1 (baseline) was not included in this section because such a model has no PA in CVs due to independence between lines is assumed.bw,p) of the predicted genetic effects (The estimates for variance inflation ( effects  for CV1 g) did not present variance inflation in CV1 since bw,p values were close to one for both analyzed traits. The bw,p for predictions of the genomic [SNPs] × ECs interaction effect (wg) indicated a moderate over-dispersion for M3  and M5  for grain yield. The use of TA-GP resulted in a reduction of over-dispersion in predictions of the wg effect for grain yield . For protein content the bw,p values for predictions of the wg effect varied from 0.92 to 1.0, revealing lower over-dispersion than grain yield.Predictions for the main additive effect (g) presented the highest variance inflation for M2  and the MT model M4 without TA-GP . A systematic improvement in the variance inflation for predictions of the main additive effect (g) was observed for both traits when the genomic [SNPs] × ECs interaction was included in the models . The bw,p for predictions of the genomic [SNPs] × ECs interaction effect (wg) varied from 0.79 to 0.98 for grain yield and 0.86 to 0.98 for protein content, where in general, the lowest values were associated in both traits to M3 and the MT model M4 without TA-GP, and the highest bw,p to the M5 using TA-GP.CV2 had higher variance inflation of predicted values than CV1, and trends were similar for both analyzed traits. The predictions of the main additive effect (via (co)variance structures in single-trait (ST) and multi-trait (MT) frameworks. The developed models were used for VCs estimation and genomic prediction of grain yield and protein content in a large set of advanced wheat breeding lines from the commercial company Nordic Seed A/S. The proposed models were evaluated using cross-validation (CV) analysis and trait-assisted genomic prediction (TA-GP) in two prediction problems relevant for plant breeding: (i) predicting breeding values for lines that have been tested in some environments but not in others , and (ii) predicting breeding values for new lines across breeding cycles . In CV1, the RN developed models have the potential to predict in environments where no lines have been tested, and thus, it could be used either to retrieve information from lines whose phenotyping has failed in a target environment or to predict for a completely new environment where no phenotyping has been performed before. Combining the proposed RN methodology and TA-GP proved to be an efficient approach to improve the predictive ability (PA) and reduce variance inflation of grain yield and protein content predictions in both CVs.In this study, we proposed a growth degree-day (GDD) based reaction norm (RN) methodology to introduce genomic [SNPs] × environmental covariates (ECs) interactions h2) and broad-sense (H2) heritabilities for M2. In agreement with previous studies using Nordic Seed A/S data, higher heritability for protein content than grain yield was observed (wg) was included in M3. The wg effect captured a significant proportion of variance for grain yield, and models including the G×E interaction terms f (line × environment) and wg (M3 and M5) captured higher proportion of G×E variance than models only including the f effect . The higher G×E variance captured by M3 and M5 can be likely attributed to better accounting for genetic and environmental covariances between lines. The trends were similar for protein content, but the variance for G×E interaction was considerably lower than for grain yield. As reported in previous studies (wg explain a limited proportion of G×E variance. It can happen due to SNPs and ECs not fully capturing the additive genetic effects (due to incomplete LD of QTLs and SNPs) and the environmental variation , respectively. To deal with this issue, the line × environment interaction effect is defined in the models to account for the mentioned misspecifications. In addition, another model term specifying genomic [SNPs] × environment interactions have been considered in the models; however, no significant contribution was observed and data has not been displayed since such an effect does not have the capacity of performing predictions in CV1. The inclusion of an additional term defining the main effect of ECs has been used in previous studies . The predictions for the main additive effect (g) had the lowest values of PAs, and they were significantly outperformed by the models accounting for the genomic [SNPs] × ECs interaction when the sum of g + gw effects was used. In CV1, using the sum of g + gw effects results in an increase of 16.4% for grain yield and 7.1% for protein content (comparing M3 to M2). Predictions for g + gw in CV1 are year-location specific and cannot be generalized to future years. In CV2, similar trends to CV1 were observed, but the increments for including the gw predictions were considerably higher than in CV1, representing a 40.2% and 14.1% increase for grain yield and protein content, respectively (comparing M3 to M2). As shown in h2, where for the lower h2 values as in grain yield, lower PA is expected  by 14.0% (M2 compared to M4-TA) and 37.9% (M3 compared to M5-TA) for CV1, and by 57.9% (M2 compared to M4-TA) and 94.8% (M3 compared to M5-TA) for CV2. For protein content, the benefits provided by TA-GP were lower but still significant , increasing PA by 5.4% (M2 compared to M4-TA) and 14.3% (M3 compared to M5-TA) for CV1, and by 28.2% (M2 compared to M4-TA) and 59.7% (M3 compared to M5-TA) for CV2. As reported by The MT models were evaluated for GP with and without TA-GP. The PAs of MT models without TA-GP were similar to ST models for the two CVs and traits , 5. Simibw,p) for prediction of the main additive (g) and the genomic [SNPs] × ECs (wg) interaction effects in CV1 and CV2 are shown in g predictions as expected due to the high information in the training population for the g effect. However, wg predictions revealed over-dispersion in CV1. A possible explanation for this can be associated with the design of CV1, where no phenotypes for the environment predicted are kept in the training population, and therefore, differences in the QTL effect/expression in the specific environment may not be captured by SNPs, resulting in inflation of the predicted effects. In CV2, over-dispersion was observed in g and gw predictions for both traits. This was expected as the genetic relationships between training and validation population are low, and over-dispersion due to genomic erosion by recombination can occur . The developed models work under the Bayesian Ridge Regression (BRR) framework and assume Gaussian distribution for random effects, implying no specific QTLs or ECs with large effects. Further studies exploring alternative methodologies capable of performing differential shrinkage or variable selection for genetic and environmental effects is warranted.via genomic [SNPs] × environmental covariates interactions, combined with trait-assisted genomic prediction, boosted the benefits in predictive performance.In this study, we proposed a growth degree-day (GDD) based reaction norm methodology to introduce genomic [SNPs] × environmental covariates interactions through (co)variance structures in a single-trait or multi-trait framework. The growth degree-day based methodology provides a simplified approach to introduce environmental information in prediction models and assists in the implementation of multi-trait reaction norm models. The modeling of genomic [SNPs] × environmental covariates interactions, and the use of trait-assisted genomic prediction in multi-trait models, significantly enhanced the predictive ability and reduced variance inflation in the predicted genetic values for grain yield and protein content in leave-one-year-location-out (CV1) and leave-one-breeding-cycle-out (CV2) cross-validations. The genotype by environment interaction modeling https://doi.org/10.7910/DVN/WEXJWW.The original contributions presented in this study are publicly available. This data can be found here: JJ, MR, PS, and JA: conceptualization. MR, JA, PS, and JO: data curation. MR: formal analysis. JJ, MR, JA, JO, and AJ: funding acquisition. MR and JJ: investigation, methodology, and project administration. JJ and PS: resources and supervision. MR: software, validation, visualization, and writing—original draft. JJ, PS, JA, JO, and AJ: writing—review and editing. All authors contributed to the article and approved the submitted version.


Artificial and natural selection for important economic traits and genetic adaptation of the populations to specific environments have led to the changes on the sheep genome. Recent advances in genome sequencing methods have made it possible to use comparative genomics tools to identify genes under selection for traits of economic interest in domestic animals.In this study, we compared the genomes of Assaf and Awassi sheep breeds with those of the Cambridge, Romanov and British du cher sheep breeds to explore positive selection signatures for milk traits using nucleotide diversity (Pi) and FST statistical methods.Genome sequences from fourteen sheep with a mean sequence depth of 9.32X per sample were analysed, and a total of 23 million single nucleotide polymorphisms (SNPs) were called and applied for this study. Genomic clustering of breeds was identified using ADMIXTURE software. The FST and Pi values for each SNP were computed between population A (Assaf and Awassi) and population B .ST3GAL1 (the synthesis of oligosacáridos), CSN1S1 (milk protein), CSN2 (milk protein), OSBPL8 (fatty acid traits), SLC35A3 (milk fat and protein percentage), VPS13B , DPY19L1 (peak yield), CCDC152 (lactation persistency and somatic cell count), NT5DC1 (lactation persistency), P4HTM (test day protein), CYTH4 (FAT Production) and METRNL (somatic cell), U1 (milk traits), U6 (milk traits) and 5S_RRNA (milk traits).The results of the PCA grouped two classes for these five dairy sheep breeds. The selection signatures analysis displayed 735 and 515 genes from FST and nucleotide diversity (Pi) statistical methods, respectively. Among all these, 12 genes were shared between the two approaches. The most conspicuous genes were related to milk traits, including The findings provide new insight into the genetic basis of sheep milk properties and can play a role in designing sheep breeding programs incorporating genomic information. The purpose of the present study was to identify important genomic regions and genes associated with milk production traits in dairy sheep breeds. Using whole genome sequences analysis important candidate genes related to sheep milk production were identified. After artificial selection, different breeds were formed with different morphology, coat colour or main production (milk or wool and meat). For the last few decades, reproductive breeding methods using calculated breeding values of reproductive traits from pedigree and phenotype information have significantly increased sheep performance  arrays, have allowed identifying causal genes and variants related to different traits. Compared to the other two methods, the next‐generation sequencing method has been proven to be a valuable strategy for detecting functional genes and genetic variants related to important economic traits in sheep  simplified efforts to realise the genetic basis of phenotypic differences of several sheep breeds with re‐sequencing methods.Various methods have been expanded and applied to distinguish the positive selection signatures in the genomes of different livestock species or breeds. Some are based on significantly reduced nucleotide diversity levels, long‐range haplotype homozygosity . Burrows‐Wheeler Aligner (BWA) (Li & Durbin ftp://ftp.ensembl.org/pub/release‐91/fasta/ovis_aries/dna/). By using SAMtools .We utilised 14 whole genomes, including an Assaf breed , seven Cambridge breeds , four Romanov breeds  and a British du Cher breed . The data were downloaded from the Sequence Read Archive at the NCBI site  segments are introduced as contiguous homozygous regions of the genome, which can provide an insight into a population's history, genomic inbreeding, and signatures of selection  were created in PLINK software to draw possible population/genetic structure between and within different populations under study. Then these files were handled in an R‐programming environment (http://www.R‐project.org) for eigenvector formation and PCA plotting along two axes. The first two principal components (PCs)  were concurrently calculated for each dataset. In the end, these PCs were graphically plotted against each other in two axes. Also, Nei's genetic distances  with a maximum likelihood approach. The admixture runs were done for ces Nei,  among dices Nei,  packages2.6https://github.com/vcftools/vcftools) was applied. The values were estimated in a sliding window size of 50 kb and a step size of 25 kb. Pairwise FST values for each SNP were calculated based on Weir and Cockerham method  and population B . To characterise genetic differentiation (FST) and also nucleotide diversities ((Δπ or ΔPi) = πpopA – πpopB) between two populations, VCFtools v0.1.14 software .Functional enrichment analysis was performed using the ‘g:Profiler’ enrichment analysis tool to identify their biological functions  were more frequent than longer ROHs (200 and 300 kb) Figure . The mea3.3K in five sheep breeds is presented in Figure Principal components analysis (PCA) was performed to study the genetic separation of five sheep breeds Figure . PCA gro3.4p < 0.01). Potential candidate genes for milk traits are listed in the table  and FST statistical methods, we compared the genomes of Assaf and Awassi breeds with Cambridge, Romanov and British du cher breeds to explore positive selection signatures. The first percentile rank was applied as a threshold to detect candidates all over the analysis. Several protein‐coding genes with significant higher FST , similar to a previous study  that play a role in RNA splicing. The 5S ribosomal RNA gene encodes 5SrRNA, a structural and functional component of the large subunit of the ribosome. It has been previously reported to be positively selected for milk traits  were involved. P4HTM and METRNL genes were formerly presented associated with the test day protein  revealed GO terms related to different biological processes. For example, the term ‘regulation of homeostatic process’ was enriched to which genes for milk traits  statistical method and output of g: profiler related to themClick here for additional data file.TABLE S3 Gene functional enrichment categories found in positively selected genes detected by the methods Pi and FST methodsClick here for additional data file.TABLE S4 Candidate gene putatively selected by two statistical methods affecting milk productionClick here for additional data file.


Success in any genomic prediction platform is directly dependent on establishing a representative training set. This is a complex task, even in single-trait single-environment conditions and tends to be even more intricated wherein additional information from envirotyping and correlated traits are considered. Here, we aimed to design optimized training sets focused on genomic prediction, considering multi-trait multi-environment trials, and how those methods may increase accuracy reducing phenotyping costs. For that, we considered single-trait multi-environment trials and multi-trait multi-environment trials for three traits: grain yield, plant height, and ear height, two datasets, and two cross-validation schemes. Next, two strategies for designing optimized training sets were conceived, first considering only the genomic by environment by trait interaction (GET), while a second including large-scale environmental data  as genomic by enviromic by trait interaction (GWT). The effective number of individuals (genotypes × environments × traits) was assumed as those that represent at least 98% of each kernel (GET or GWT) variation, in which those individuals were then selected by a genetic algorithm based on prediction error variance criteria to compose an optimized training set for genomic prediction purposes.The combined use of genomic and enviromic data efficiently designs optimized training sets for genomic prediction, improving the response to selection per dollar invested by up to 145% when compared to the model without enviromic data, and even more when compared to cross validation scheme with 70% of training set or pure phenotypic selection. Prediction models that include G × E or enviromic data + G × E yielded better prediction ability.Our findings indicate that a genomic by enviromic by trait interaction kernel associated with genetic algorithms is efficient and can be proposed as a promising approach to designing optimized training sets for genomic prediction when the variance-covariance matrix of traits is available. Additionally, great improvements in the genetic gains per dollar invested were observed, suggesting that a good allocation of resources can be deployed by using the proposed approach. Zea mays L.) has become one of the essential crops for the economic and food security of many countries [As one of the main cross-pollinated species cultivated worldwide, maize  is key , 43. In As phenotyping is a high-cost activity, the adoption of strategies for optimizing the TRS could represent important gains in breeding efficiency, such as reduction of phenotyping costs, efficient resource allocation, and the possibility to increase the prediction ability (PA) of unobserved genotypes , 45, 51 Hence, the ideal strategy in GS is to design optimized training sets for GP, which maintains the accuracy of prediction at satisfactory levels using a training set that is representative , 18. In Using multi-trait (MT) models, Lado et al.  tested oCosta-Neto et al.  investigLopez-Cruz, and de los Campos, G . proposeOther studies proposed different methods of optimizing training sets for GS. Rincent et al.  used preBased on the above considerations, the main objective of this study was to test the performance of optimized training sets (OTS) for MTMET, along with the use of environmental covariates matrices (W matrix) in genomic prediction models. Thus, we aimed to diminish the phenotypic labor due to lower but optimally selected population sizes while keeping the prediction ability at satisfactory levels. Finally, we were interested in comparing the response to selection of OTS with MTMET and phenotypic selection, to estimate the genetic gain per unit of dollar invested. For that, we (i) fitted and compared the performance of five different prediction models, the baseline GBLUP with additive + dominance effects (M1), then added G × E M2), including enviromic data (W) (M3), then fitted W + G × E (M4), and finally achieving W + G × W (M5); (ii) estimated the genomic prediction ability of the five prediction models for single-trait multi-environment trials (STMET) and MTMET for three traits in two tropical maize datasets; and (iii) estimated the genomic prediction ability using OTS with controlled unbalancing of G, E and trait (T) information, selected by a combination of two genetic algorithms, the APY , 39 and , includiHEL dataset, GY had a moderately negative correlation with PH and EH, of − 0.55 and − 0.58, respectively, while PH and EH had a high positive correlation of 0.82. For the USP dataset, GY had weak negative correlations with PH and EH, of − 0.44 and − 0.33, respectively, while PH and EH had a high positive correlation of 0.70.Pearson’s correlation between traits was calculated for each dataset using the BLUEs obtained in the first step. As a result of the variable transformation, EH and PH assumed a negative correlation with GY, which agrees with the selection targets. Therefore, we attempted to increase GY while fixing or reducing EH and PH. For the HEL dataset, trait heritability was 0.62, 0.78, and 0.80 for GY, PH, and EH, respectively; for the USP dataset, heritability was 0.56 for GY, 0.84 for PH, and 0.89 for EH.Estimated heritability was intermediate to high: for the As expected, a lower correlation was found between the complex trait GY and the other traits than for PH and EH. Moreover, GY had a lower heritability than EH and PH , suggesting so far that the latter has greater optimization capability.The sample size differs depending on the kernel and germplasm. Notice that regardless of the germplasm, sample sizes are larger for GET than for GWT  by combining information of genotype × environment × trait. For that reason, samples were trait and environment specific. The difference in selected information among the three samples from the different OTS scenarios can be seen in the heatmaps for HEL Fig. a-f and UAs mentioned in the material and methods section, we assessed PA in two ways, however, general results will be presented referring to the average of environments across traits, while specific cases from the PA per trait per environment results will be highlighted.M1 and M3) were used. In contrast, models including G × E (M2 and M4) increased PA by 100 to 104%, and G × W (M5) increased PA by 92% for this particular trait × environment combination. CV2 (Table M5) and G × E interactions (M2 and M4) were used, respectively.CV1 resulted in PAs varying from 0.53 to 0.73 , and M2 and M4 (with G × E interaction), where M4 and M2 outperformed M3 and M1 by a range of 25 and 30%; however, M5 also outperformed M3 and M1 by 29%.Comparing CV1 and CV2, PAs increased on average by 3 to 8%. In general, M4 performed better.As for the STMET analysis, the results of the multi-trait (MTMET) analysis showed a similar pattern of responses, both for CV1 and CV2, varying from 0.54 to 0.73 and 0.53 to 0.79, respectively  presented an inferior performance for EH when models without G × E interaction (M1 and M3) were used. In contrast, models with G × E (M2 and M4) increased the accuracy up to 440% for EH at PI.17, and models with G × W (M5) increased PA by 420%. When considering the average between environments, PA for EH only varied from 0 to 7% between models. CV2 produced similar patterns as those for CV1. For EH in the PI.17 environment, PA increased by 340% when models with G × E interactions were used and by 320% when using G × W. In general, M2 and M4 showed the best performances.CV1 showed PAs varying from 0.46 to 0.65  for the optimized training sets (OTS), the five models M1 to M5 were also tested. However, the model with the best performance was the HEL dataset: On average, with OTS 1, we achieved PAs across traits of 0.55 and 0.41 for GET and GWT kernels, respectively  and 0.30 (+ 25%) for OTS 2, to 0.52 (+ 10.6%) and 0.44 (+ 46.7%) for OTS 3, while the maximum PA obtained by the benchmark was 0.61 . Then, the estimated genetic gain was compared between scenarios as follows: OTS vs. MTMET CV2 (benchmark) and OTS vs. phenotypic selection (PS).HEL dataset, results showed an inversion of the response to selection per amount invested between kernels across scenarios. Even though GET had a higher cost per gain for OTS1 than GWT, it decreased its response throughout the scenarios while GWT remained constant. The genetic gain per 10,000 USD invested ranged from 0.80 × 10-3 vs 0.70 × 10-3 (OTS 1), for GET and GWT respectively, and to 0.58 × 10-3 vs 0.67 × 10-3 in OTS 3. For PS, the gain was 0.14 × 10-3 , and the gains per investment were 0.16 × 10− 3 for HEL and 0.02 × 10− 3 for the USP dataset.As a matter of comparison, we did the same procedure for the benchmark scenario MTMET CV2 . Here we present the genetic gains in each TRS scenario under a fixed budget of 10,000 dollars, enabling a direct comparison. For small training population sizes, as in OTS, predictive abilities are lower, but the investments in TRS are also lower, which results in a satisfactory gain per dollar invested.The major goal of GS can be defined as increasing the genetic gain with no increase in costs compared to only phenotypic selection , 57, thuThe traits evaluated here are moderate to strongly positively correlated by Pearson’s correlation coefficient. However, the selection targets in breeding programs are in opposite directions. While we want to increase grain yield, we want to decrease plant height and stabilize ear height. Dwarf plants with high yields are already a reality in other crops like wheat and rice. In maize, dwarfing mutant genes have been studied, and unlike wheat and rice, PH in maize is a quantitative trait that affects other plant characteristics like yield losses, making it difficult to apply . Since wGET and GWT), can be partially attributed to differences in Pearson’s correlation coefficient between traits, since the prediction ability is directly related to the correlation between traits [As reported by Ibba et al. , as welln traits .W) and interaction terms (G × E and G × W), which can better capture the portion of variance explained by the model [We saw that some models outperformed others, which was also expected since they include additional terms such as the environmental covariates matrix (he model . The reshe model  suggesteM4 - G × E + W) was chosen for the prediction using the optimized training set populations, and those validations were also used as a comparison parameter for prediction accuracies while increasing the sample sizes of TRS  [Studies involving SNP data, such as GP, require the inverse of the genomic relationship matrix (GRM). However, as the number of individuals to be evaluated increases, the computational cost of this matrix’s inversion is relatively high, with limitations in memory and time. To minimize this problem, Misztal  proposedet (OTS) . In thiset (OTS)  used theet (OTS)  to selecNevertheless, in the present work, we extended these algorithms to more complex relationship matrices, such as the Kronecker product (⊗) of the genomic relationship matrix (GRM), with the environmental variance and covariance matrix (W) and the traits of interest (T) (G ⊗ E ⊗ T or G ⊗ W ⊗ T). Even though these scenarios lead to a high level of imbalance in the data, they determine exactly what needs to be phenotyped to compose an optimized training set, which is called selective phenotyping . In summVoss-Fels et al.  said thaIt is interesting to notice that with similar increases in the sample size, of approximately 90-100% from OTS 1 to OTS 2, and from OTS 2 to OTS 3, the increases in PA were different for each kernel-dataset combination, as given in Figs. Considering that the cost of genotyping is decreasing, whereas the costs of field testing in maize are either stagnating or rising and knowing that genotypic information is stable and not influenced by seasonal variation, less effort is expended, saving resources, and making genotypic selection more efficient . In addi− 3 against 0.16 × 10− 3, with optimized (GWT) against standard scenario (MTMET CV2) TRS, respectively, for the HEL dataset and 1.42 × 10− 3 against 0.16 × 10− 3 for the USP dataset.Looking to reduce costs with phenotyping, Lado et al.  found thThe genetic gain per dollar invested was estimated as a basis for comparing responses across different sizes of TRS datasets, and mainly to justify optimization to form training sets for GS. From the results, we can infer that the optimized populations have advantages over the standard scenario (70% TRS-30% TS). The difference in gains between the datasets is due to their specific characteristics, such as the number of inbred lines used as parents and the PA obtained. For the HEL dataset, although the PA was higher, the costs of genotyping were also higher, given the great number of inbred lines, resulting in lower gains. There was also an inversion of gains between GET and GWT, where the efficiency of the GWT kernel remains practically constant while that of GET drops. For the USP dataset, it was the opposite; the PA was lower, but there were fewer individuals for both genotype and phenotype. Thus, the costs were lower, and the gains were higher; also, GWT outperformed GET in all the scenarios. Altogether, GWT reduced the TRS by up to 58% compared with GET. From this point of view, although the PA using GWT is the lowest, regardless of the scenario, its advantage can be offset by the gain in response to selection per dollar invested  and genetic algorithms (APY and LA-GA-T) to optimize resource allocation. To our knowledge, this is the first study to test the optimization of training set populations using genetic algorithms, which determine the size of the population and select the individuals based on complex kernels, causing a high level of imbalance. We observed that using a smaller optimized training set reduced the need for phenotypic evaluation in the field, saving money that can be reallocated for genotyping. Moreover, we estimated the genetic gains per 10,000USD invested, which indicated that, by applying optimization and maintaining a constant selection intensity, under a fixed budget, a greater number of breeding candidates could be tested per cycle and at early stages, increasing the gains.The initial investments in GS are considerably high; however, they are offset by gains per unit of time. Nevertheless, it is known that the genetic variance of a given population decreases over the breeding cycles, especially in small population sizes, which limits the selection gains . Hence, Genomic prediction models that include G × E and G × W interaction effects always increase PA, performing better than main effects models; G × E interaction is the best scenario, with a small increase in multi-trait multi-environment analysis when compared with single-trait multi-environment analysis. Furthermore, our results indicate GWT kernel associated with genetic algorithms is efficient and can be proposed as a promising approach to designing optimized training sets for genomic prediction when the variance-covariance matrix of traits is available. Additionally, great improvements in the genetic gains per dollar invested were observed, suggesting that a good allocation of resources can be deployed. However, it is worth remembering that a specific interaction between combinations of germplasm, environments, experimental network, and evaluated traits must be considered when using the proposed approach.− 1), plant height , and ear height . For GY assessment, ears were harvested at physiological maturity. Grains were weighed and adjusted to 13% moisture, and then the yield was corrected by area and plant population. PH and EH were measured from the ground to the flag leaf collar and from the ground to the base of the ear, respectively, on five representative plants within each plot. Below, we have a description of each one of the datasets.The phenotypic data consisted of two datasets of tropical maize single-cross hybrids. These datasets were chosen as a proof of concept and were extensively used and detailed by previous studies , 6. HereThe first dataset was composed of the phenotypic and genotypic data of 452 maize hybrids, obtained from single crosses in a partial diallel mating design among 106 tropical maize inbred lines, provided by Helix Seeds/Biomatrix (HEL), a seed company from the Agroceres group. A randomized complete block design (RCBD) with two blocks, two replications per genotype per location was used. Hybrids were evaluated over the 2014/15 growing season at three locations in Brazil: Ipiaçu (IP) , and Pato de Minas (PM)  in the state of Minas Gerais; and Sertanópolis (SE)  in the state of Paraná.The second dataset belongs to the University of Sao Paulo (USP). The data consisted of 903 maize single crosses, obtained from a diallel mating design between 49 inbred lines. Hybrids were evaluated at two locations in Brazil: Piracicaba (PI) and Anhumas (AN), in the state of São Paulo. They were evaluated for 2 years, during the second growing season of 2016 and 2017. The experimental design was an augmented randomized complete block design, with two commercial hybrids as checks per block. Although the locations are relatively close geographically, the soil and climate conditions are so contrasting that they characterize different environments, whereby each location × year combination was considered as an environment as follows: Anhumas ×2016 (AN.16), Piracicaba ×2016 (PI.16), Anhumas ×2017 (AN.17), and Piracicaba ×2017 (PI.17).Given the sparse field trial design of both datasets, not all hybrids were evaluated at all locations. To balance the data, only hybrids evaluated at all locations for all traits were considered so that 247 and 623 genotypes remained for analysis, for HEL and USP, respectively. Balancing the data will later lead to the creation of controlled imbalances. Further details about both datasets can be found in , 6, 33.Parental inbred lines from HEL and USP datasets were genotyped with an Affymetrix® Axiom® Maize Genotyping SNP array of 616 K . The genThe genotypic data of the hybrids were obtained by combining the homozygous markers of their parental lines. At first, allele frequencies and linkage disequilibrium were computed using the genotypes of the hybrids. Then, markers with minor allele frequency (MAF) ≤ 0.05 were removed. After QC, 30,467 and 62,409 high-quality SNPs were available to analyze the HEL and USP datasets, respectively. All the analyses were performed in the R software .ECs were obtained with the EnvRtype R package  and wereFor the HEL dataset, each environment was characterized by 217 ECs. For the USP dataset, each environment was characterized by 238 ECs. The resulting matrices have dimensions of 3 × 217 and 4 × 238 for HEL and USP, respectively. They were then used to estimate the W matrix. In the enviromic kernel, the rows represent the environments, and the columns are the ECs.KE is defined as the “enviromic-based kernel” accounting for the similarity between environments, W is the matrix of ECs, tr is the trace of the matrix and q is the number of environments [KE is q x q dimension.Afterward, we can calculate an enviromic kernel, that is equivalent to a genomic relationship matrix but for environments, using the linear kernel approach proposed by Jarquín et al. :\documenronments . KE is qEHtr is the transformed EH, and EHij is the EH for genotype i at environment j, in centimeters. According to this transformation, the closer to zero, the closer to our ideal height. The direction of selection for GY and EH is opposite, i.e., we want to select high-yielding varieties but with an ear at 80 cm, however, those traits are positively correlated. Therefore, the absolute value of the difference between the actual EH and the ideotype was multiplied by −1 to force a negative correlation between EHtr and GY.We established a transformation for EH that represents the distance from the actual EH to an ideal ideotype, defined here as 80 cm, according to the following formula:x~N in which x is the trait .For PH, values were normalized to obtain a normal distribution interval. To fit the models, the phenotypic records were mean-centered and scaled to a normal distribution with We used a linear mixed model for the two-step analysis to calculate the best linear unbiased estimates (BLUEs) of each trait’s hybrids. BLUEs were obtained across environments for the USP and HEL datasets by the following respective models:yij is the estimated phenotypic value of the ith genotype at the jth environment, μ is the general mean or intercept, gi is the fixed effect of the hybrid genotype i, g* is the fixed effect of check genotypes, bl is the random effect of blocks for the USP dataset .where The blocking effect was considered as random for USP dataset given the nature of the augmented blocks experimental design, while it was considered as fixed for HEL dataset because the RCBD contained only two blocks, which is not a representative sample size to be considered as random.Phenotypic analyses were performed using the ASReml-R package  of R sof2).The variance components estimated for each model’s effect were used to estimate the average broad-sense heritability  and multi-trait multi-environment trials (MTMET), with 70% of data used as TRS; and optimized training sets (OTS), with varying percentages of data used as TRS. One of our objectives was to obtain PA for OTS. However, to make inferences about economics and the advantages of using the proposed approach, we needed reference values for comparison, hereafter referred to as benchmarks.To obtain the benchmark values of PA for the models, we tested them (described in section 2.5.3) in full STMET and MTMET genomic prediction analyses through cross-validation schemes with replication (described in section 2.6). From those results, we obtained the highest possible PA for the specific datasets used in this study, using all the phenotypic information available .G ⨂ ΣE ⨂ ΣT and ΣG ⨂ ΣW ⨂ ΣT, hereafter called GET and GWT, respectively. These kernels, used as inputs for the algorithms, assemble combinations between our variables.For the OTS, two different kernels were built from the Kronecker product (⨂) between the variance-covariance matrices (Σ) of genotypes (G), environments (E), environmental covariates matrix (W), and traits (T) as follows: ΣFor comparison matters, random samples with the same size of the OTS for the different kernels were also used as training sets in the prediction model. After sampling, a hybrid was added as a check. According to sample sizes, Random1 corresponds to OTS1, Random2 to OTS2, and Random3 to OTS3, described subsequently.The algorithms APY , 39 and These three samples were taken for each kernel (GET and GWT) × dataset (HEL and USP), and constitute our optimized training set 1, hereafter referred to as OTS 1. At each model iteration, one of the three samples was used as TRS, and the remaining information was used as TS. In addition, two other scenarios were created from the original samples. The first one was created by combining two samples at a time, resulting the scenario OTS 2. In the second one, the three samples of OTS 1 were combined, creating OTS 3, resulting in just one bigger TRS, when compared to OTS 1 and OTS 2. see Fig. .Fig. 6ScIt is important to clarify that, for training set optimization, we used the two kernels, GET and GWT, to obtain specific combinations of genotype × environment × trait that compose our OTS. For that reason, sampled individuals were trait and environment-specific, and dependent on the kernel. Moreover, a hybrid was added as a check, and therefore its full phenotypic information  was included to create connectivity between environments.The genomic prediction was first performed by five GBLUP additive + dominance models for STMET and MTMET scenarios. The following models were previously described and tested. For further details, see Costa-Neto et al. .yt is the adjusted observed values (BLUEs) correspondent to the t trait, obtained from the first step for the hybrids. The fixed effects of the environment were modeled by ZE  β, with the incidence matrix ZE, and ZG is the incidence matrix for the genotypic effects. uA is the vector of additive genetic effects, where uA ~MN  for additive and dominant effects, respectively, given as follows:WA are equal to 0, 1 and 2, for genotypes markers of A1A1, A1A2 and A2A2, respectively, and pi is the frequency of one allele from the ith locus [WD contains values equal to 0 − 2q2, 2pq, and 0 − 2p2 for A1A1, A1A2 and A2A2, respectively [.M1 is the most basic model tested, and is described as follows:th locus .\documenectively .uAE and uDE are the vectors of random effects of the interactions. uAE and uDE have a multivariate normal distribution, uAE ~ MN , adding the additive × environment and dominance × environment interactions effects (AE and DE). product , 29.uW is the matrix of environmental covariates. According to Costa-Neto et al. [This third model includes environmental covariable information (W) from envirotyping data.o et al. , it is aThis model extends the previous model (M3), adding the environment’s additive and dominance interactions.uAW and uDW are the vectors of random effects of interactions. uAW and uDW have a multivariate normal distribution, uAW ~ MN  reaction-norm variation; it replaces the genomic × environment interactions with the genomic × enviromic effects interactions.All models were fitted with the Bayesian Generalized Linear Regression BGLR R package , using aIt is important to point out that the “Multitrait” function of the BGLR package has some basic premises that must be met for the model to work, one of them is the availability of complete information from at least one genotype. Here, as we used multiple traits with the multiple environments approach, we selected a genotype as a check, with complete phenotypic data available, common to all environments. Additionally, the covariance matrix between traits was assumed as known, and therefore the covariance matrices between traits of the full datasets were predefined and used for the multi-trait multi-environment under OTS and Random prediction scenarios.The PA of GP models for STMET and MTMET was assessed using two cross-validations schemes (CV), proposed by Burgueño et al. . The firWe assessed PA in two ways: 1) per trait only, where the PA is the average between environments for each trait, and 2) per trait per environment. In this context, PA is the average Pearson’s correlation coefficient of all TRS-TS partitions, calculated between the genomic estimated breeding values (GEBVs) and the estimated genetic values (BLUEs) of TS individuals within trait or within trait and environment. Finally, PAs were used to compare the performance of each model.For OTS and Random scenarios, we did not use cross-validation schemes. The samples used as TRS already gave us a high imbalance of information, sometimes mimicking CV1, where the genotype was not observed in any environment, and sometimes CV2, where the genotype was evaluated in some environments but not in others. PA was calculated as the Pearson’s correlation coefficient between the predicted value and the BLUE of the TS individuals within each environment for each trait; then the average across traits was calculated, like in the previous scenarios.H2 trait specific) was then calculated separately for each trait. The genetic gain was then estimated by dividing the average accuracy obtained for each scenario (under M4) by the corresponding total cost, genotyping + phenotyping for GP scenarios, and only phenotyping cost for PS; given that all other components of the breeder’s equation [We finally estimated the response to selection per unit of dollar invested by comparing the efficiency of the different scenarios tested in this study with pure phenotypic selection (PS). The methodology was based on Krchov & Bernardo  and Muleequation  were con


To gain more insight into the biological factors that mediate vulnerability to display externalizing behaviors, we leveraged genome-wide association study summary statistics on 13 externalizing phenotypes.After data classification based on genetic resemblance, we performed multivariate genome-wide association meta-analyses and conducted extensive bioinformatic analyses, including genetic correlation assessment with other traits, Mendelian randomization, and gene set and gene expression analyses.Neff = 523,150 and 1,506,537, respectively), yielding 50 and 257 independent genetic signals. The statistics of DB, much more than RTB, signaled genetic predisposition to adverse cognitive, mental health, and personality outcomes. We found evidence for bidirectional causal influences between DB and substance use behaviors. Gene set analyses implicated contributions of neuronal cell development (DB/RTB) and synapse formation and transcription (RTB) mechanisms. Gene-brain mapping confirmed involvement of the amygdala and hypothalamus and highlighted other candidate regions . At the cell-type level, we noted enrichment of glutamatergic neurons for DB and RTB.The genetic data could be categorized into disruptive behavior (DB) and risk-taking behavior (RTB) factors, and subsequent genome-wide association meta-analyses provided association statistics for DB and RTB (This bottom-up, data-driven study provides new insights into the genetic signals of externalizing behaviors and indicates that commonalities in genetic architecture contribute to the frequent co-occurrence of different DBs and different RTBs, respectively. Bioinformatic analyses supported the DB versus RTB categorization and indicated relevant biological mechanisms. Generally similar gene-brain mappings indicate that neuroanatomical differences, if any, escaped the resolution of our methods. Externalizing psychopathologies are highly common in the general population , 2, 3, 4Externalizing symptoms generally co-occur substantially , which sTo broaden our understanding of common genetic and neurobiological backgrounds that underlie the co-occurrence of different externalizing behaviors, we leveraged publicly available genome-wide association study (GWAS) summary statistics on lifetime cannabis use , antisocUsing these data, we first identified clusters of traits with high genetic resemblance that together comprise the higher-order externalizing behavior dimension. Subsequently, the GWAS data of the clusters were meta-analyzed using N-weighted meta-analysis . To charet al.   ,25 to corg) see .rg) as genetic distance measures between phenotypes and with linkage based on Ward’s method  , which iWe computed pairwise genetic correlations using LDSC ,25 for oFor one of the identified clusters characterized by DBs, we applied MR to test for causal relationship with substance use behaviors see .http://ctg.cncr.nl/software/magma) .We performed gene-based analyses in MAGMA version 1.08 (e/magma)  with theWe used the gene associations of the two factors as input for a tissue-type analysis using MAGMA version 1.08 . We inveWe continued with competitive gene set analyses using MAGMA version 1.08  to test For the significantly associated tissue types and gene sets, we performed conditional analyses using MAGMA version 1.08  to evaluWe applied stratified LDSC to investigate which tissues and cell types are enriched for the identified factors see .To identify brain regions where genes relevant for externalizing behavior factors are differently expressed, we computed stratified LD scores based on differential gene expression, using data from 3707 gene expression measurements across 211 different brain regions  see Sup.n = 14,963) from the prefrontal cortex and hippocampus of multiple human donors studied by Habib et al.  and phenotypes characterized by risk-taking behaviors (RTBs) , with less genetic overlap between pairs of phenotypes characterized by the different behavior types . Hierarchical clustering on genetic resemblance    . For RTB506,537) . The LD rg = −0.34, SE = 0.02) and income , whereas genetic correlations for RTB with these phenotypes were close to zero. In addition, DB was more positively correlated with depressive symptoms  and neuroticism  and more negatively correlated with agreeableness  compared with RTB .p = 2.0 × 10−7) and decreases the odds of being able to successfully quit smoking    and measures of smoking  and alco = .002) . Effect  = .002) . Some ev× 10−33)  but not × 10−33) . Steiger× 10−33) . No cons× 10−33) .Table 2Rp = .004), which was consistent (but weaker) in direction of effect across multiple MR methods (p = .457)  . Steiger = .457) .p = 9.9 × 10−31), which was consistent across weighted median, weighted mode, and generalized summary data–based MR (MR-Egger not available). Steiger filtered analyses and MR-PRESSO did not change the results (p = 7.3 × 10−46)  . There wCADM2 showed an exceptionally strong association (2.10 × 10−29) with RTB.Genome-wide gene-based association analysis identified 81 genes significantly associated with DB  and 318 We used the gene-based test statistics as input for gene set analysis in MAGMA. Starting with a tissue-type analysis, we found significant associations at the Bonferroni level for nine brain regions for DB and 13 brain regions for RTB . ConditiSubsequent gene set analyses identified three gene sets for DB involved in cell development and 13 gene sets for RTB involved in cell development, synapse formation, and transcription . ConditiCNS = 6.84) (CNS = 7.97)  for both DB (Z = 6.84)  and RTB  = 7.97) . It has  = 7.97) . Zooming = 7.97) . A simil = 7.97) .Z = 3.35, p = .0004)  and additional enrichment in the cuneiform nucleus       . For RTB × 10−6) , claustr × 10−5) , paracen= .0004) , lateral= .0009) , and pre= .0004) .Figure 4Z = 2.88, p = .002) and the hippocampal CA3 region    . For RTB= .0008) .In a bottom-up approach to evaluate overlap in genetic and neurobiological backgrounds underlying externalizing symptoms, we collected 13 publicly available GWAS summary statistics for a range of externalizing phenotypes. Assessment of genetic resemblance indicated a categorization into two externalizing-related factors, one characterized by DB and another by RTB, that together explained 53% of the total genetic variance. Meta-analyzing the factor-specific phenotypes yielded 50 loci for DB and 257 loci for RTB.Clustering of aggression, angriness, and irritability items in the DB factor fits very well with the general finding that these are highly comorbid behaviors and also cluster together in diagnoses of conduct and oppositional defiant disorder . AdditioAssessment of genetic relationships with other traits indicated associations for DB with higher neuroticism and lower conscientiousness and agreeableness, corroborating previous findings . For RTBIn addition, we applied MR to explore causal relationships between the DB factor and smoking and alcohol use. In full agreement with previous findings ,48, we oBiological annotation by gene set analysis and stratified LDSC converged on genetic enrichment in the brain for both DB and RTB traits. An atlas of differential brain region gene expression pointed specifically to the dentate nucleus of the cerebellum, for both DB and RTB, and the cuneiform nucleus of the brainstem, preoptic region of the hypothalamus, lateral nucleus of the amygdala, and the claustrum and paracentral cortical lobule, which were significant for RTB.Involvement of these brain regions confirms current hypotheses on the neurobiological background of externalizing symptoms but also points to the importance of relatively underrepresented regions. Especially for the medial part of the preoptic hypothalamic region, animal studies indicate an important role in stimulating aggression to facilitate reproduction , as wellThe other brain regions have been implicated less frequently, despite previous evidence for associations. For the cerebellar dentate, a relevant role in the development of reinforcement learning relevant to addiction has been indicated , and theFinally, testing for specific biological mechanisms using gene set analysis indicated associations for gene sets primarily related to neuronal development for both DB and RTB. In addition, synaptic functions and transcription regulation were identified for RTB. These three biological mechanisms have been related to a wide range of psychiatric disorders  and may rg < 1), and therefore, we note that including GWAS statistics of all three phenotypes does provide additional genetic information in GWAMAs. Third, in the MR analyses, the tested effects from smoking and alcohol use to DB did not fully comply with the expected temporal order. The aggression and ADHD variables of DB included children . This means that smoking and alcohol use were, for those variables, not valid exposures. In addition, we limited assessment of causal directions to the relationship between the DB factor and smoking and alcohol use. We also demonstrated interesting relationships of DB and RTB with several other traits, such as personality and health characteristics. Given the complexity of the included study cohorts forming the different summary statistics, it was beyond the scope of this study to also test for causal relationships with these traits. Fourth, except for ADHD, the GWAS data in our study related to behavioral extremes that did not exceed the diagnostic threshold. Given previous evidence of genetic heterogeneity between nondiagnosed and diagnosed individuals (rg = 0.33) and therefore not completely independent. In addition, the effective sample size of RTB is ∼3 times larger than that of DB , so there is likely more power to detect significant associations for RTB. For example, differential gene expression indicated more brain regions with statistically significant enrichment for RTB, but we note that the same regions also showed relatively increased enrichment among the 211 brain regions tested for DB.This study comes with a number of limitations. First, the two identified factors DB and RTB combine several distinct phenotypic measures, which inevitably leads to etiologic heterogeneity (reflected by the imperfect genetic correlations). In addition, phenotyping could be as poor as a single question . Poor and heterogenous phenotyping, with the trade-off of having large sample sizes available, are a common phenomenon in GWAS meta-analyses of single traits  or multiividuals ,69, we eIn summary, we extend previous findings involving externalizing behavior and provide further evidence for common genetic architectures, particularly for different DBs and RTBs. Follow-up evaluations of the data in this study indicated genetic relationships with personality traits and mental and physical health behaviors in agreement with the DB versus RTB categorization and highlighted possible bidirectional causal relationships between DB and substance use traits. Biological annotation revealed generally similar gene-brain mappings that mediate the predisposition to comorbid externalizing phenotypes. Possible subtle differences in neurobiological backgrounds between DB and RTB traits may be resolved in future studies based on higher-resolution genetic association and gene expression data that are becoming increasingly available.


Sparse testing using genomic prediction can be efficiently used to increase the number of testing environments while maintaining selection intensity in the early yield testing stage without increasing the breeding budget.Sparse testing using genomic prediction enables expanded use of selection environments in early-stage yield testing without increasing phenotyping cost. We evaluated different sparse testing strategies in the yield testing stage of a CIMMYT spring wheat breeding pipeline characterized by multiple populations each with small family sizes of 1–9 individuals. Our results indicated that a substantial overlap between lines across environments should be used to achieve optimal prediction accuracy. As sparse testing leverages information generated within and across environments, the genetic correlations between environments and genomic relationships of lines across environments were the main drivers of prediction accuracy in multi-environment yield trials. Including information from previous evaluation years did not consistently improve the prediction performance. Genomic best linear unbiased prediction was found to be the best predictor of true breeding value, and therefore, we propose that it should be used as a selection decision metric in the early yield testing stages. We also propose it as a proxy for assessing prediction performance to mirror breeder’s advancement decisions in a breeding program so that it can be readily applied for advancement decisions by breeding programs.The online version contains supplementary material available at 10.1007/s00122-022-04085-0. Genomic prediction (GP) is a statistical method to predict the genetic potential of unobserved lines based on genomic information. It has been identified as a viable tool to accelerate genetic gain and to reduce phenotyping costs in plant breeding programs, particularly as genotyping costs become cheaper than phenotyping costs  . These candidates are then tested internationally through collaborative trials with partners selecting elite lines for use as parents in national breeding programs and/or for variety release. The SEs are defined by varying sowing time and management conditions in a single location . Although the SEs were defined within a single location, they are constructed to predict the performance in global target populations of environments  increased number of lines tested across multiple, diverse environments and (2) increased number of testing environments while maintaining the same selection intensity , and thIn most plant breeding programs, the genetic value of genotypes is estimated through adjusted best linear unbiased estimates (BLUEs)  highlighting selection accuracy using GBLUP as a selection metric for line advancement decisions in direct stage 2 skipping stage 1 testing; (2) determining the optimal sparse testing aided GP strategy in direct stage 2 trials; (3) determining the contribution of historical data to increasing the calibration set size and improving prediction accuracy of untested lines across SEs without increasing cost; and (4) determining the appropriate method for evaluating prediction accuracy to closely mirror breeder advancement decisions.The genetic material used in this study consisted of F4:8 (stage 1) and F4:9 (stage 2) CIMMYT spring wheat breeding lines. The genetic material was classified into three datasets . DS1 consisted of 1260 stage 1 lines grouped into 45 trials, each with 28 entries and two checks, evaluated for grain yield (GY) and other agronomic traits in an optimal five irrigation bed planting SE (B5IR). Each trial was planted in an alpha-lattice incomplete block design with two replicates in the 2019–2020 crop season at Norman E. Borlaug research station, Ciudad Obregon, Sonora, Mexico . DS2 consisted of the 280 stage 2 lines advanced from the DS1 1260 lines based on GY performance, agronomic, disease, grain zinc and processing quality traits. They were evaluated in six SEs at the same location in the 2020–2021 season. In each SE, the lines were grouped into five trials, each with 56 entries and 4 checks, and the trials were planted in an alpha-lattice incomplete block design with two replicates.Optimal planting date and five irrigations bed planting (B5IR). Approximately 500 mm of water was applied through flood irrigation. Optimal planting date implies planting during the third week of November to first week of December.Optimal planting date and five irrigations flat planting (F5IR), with the same total amount of water applied as B5IR, through drip irrigation.Optimal planting date and two irrigations bed planting (B2IR). Approximately 250 mm of water was applied through flood irrigation.Optimal planting date and drought stress flat planting (FDRIP). Approximately 180 mm of water applied through drip irrigation.st week of November) than the optimal planting date with the aim of evaluating the lines for heat tolerance during the early growth stage. Approximately 500 mm of water was applied through flood irrigation.Early heat stress bed planting (BEHT). Lines were planted about 3 weeks earlier (1Late heat stress bed planting (BLHT). Contrary to BEHT, lines were sown 90 days after optimal planting date to evaluate the lines for heat tolerance during the flowering and grain filling stages of the plant. Approximately 500 mm of water was applied through flood irrigation.The SEs were defined by a combination of factors including planting date, irrigation, and planting condition (flat or bed) as follows:DS3 consisted of the stage 2 lines advanced from 2018–2019 stage 1 (data not used) and consisted of 253 lines evaluated in six SEs at the same location in the 2019–2020 season.To account for spatial variation in the field, the trials were sown as a grid of  rows and  columns for DS1, DS2 and DS3 data, respectively.DS2 advanced lines from DS1, and DS3 lines were genotyped using genotyping-by-sequencing (GBS) and 93,349 SNP markers were generated. After removing SNPs with more than 20% missing values and with a minor allele frequency less than 5%, 20,985 SNPs remained and were used for the analysis. Missing SNPs imputed with Beagle 5.1   calculated using all observed records of tested and untested lines in each SE. Secondly, we used a Smith–Hazel (SH) selection index Smith  to definTo assess the accuracy of GBLUP as a selection decision metric in the early yield testing stages, we estimate the BLUE and GBLUP of the 1260 DS1 lines and the 280 DS2 advanced lines using the full data set. Given that the 1260 DS1 lines were only evaluated in a single SE (B5IR), only information from this SE was used for this analysis. We calculated the Pearson correlation of the GBLUP obtained for the complete 280 DS2 lines as well as BLUEs in the two stages of yield testing. We also measured accuracy as percentage of lines that intersect between select top  lines in the two testing stages to account for possible selection intensity in the early yield testing stage.We fitted a multi-environment linear mixed model in ASREML Gilmour  for the y (n × 1) is the vector of phenotypes of the lines measured in the environments (1…k), μ is the overall mean and n × 1) is a of vector ones, g-th line, g-th line and k-th SE, p-th random effect expect I is either genomic (G) or pedigree (A) relationship matrix. In Eqs. G or A relationship matrix with dimension g × g and the k × k variance–covariance matrix of the genomic effect of lines in and between SEs  model which is a parsimonious approach for fitting GEI and complex covariance structure among environments Piepho  was usede Piepho .FA model for Cov for the lines were computed using Eqs. As expected, GBLUP was found to be a more effective metric for line advancement from stage 1 (DS1) to stage 2 (DS2). The GBLUP correlation between the two yield testing stages was 0.45 compared to 0.35 when BLUEs were used as the advancement decision metric  ranged from moderate to high except BEHT which had a low plot-level heritability value of 0.18 Fig. . SimilarPredictive ability increased with higher heritability and genetic correlation between SEs. The BEHT SE had the lowest plot-level heritability (0.18) and had consistently low predictive ability irrespective of the sparse testing strategy and prediction model used Fig. . Higher The augmentation of the calibration set with DS1 or DS3 improved predictive ability of untested lines for some SEs, especially with DS1 using only the 280 lines evaluated in the B5IR SE. For example, when lines were not repeated across SEs, the predictive ability of the 234 lines in F5IR SE increased by 21 and 1% using DS1 and DS3, respectively, to augment the calibration set. While it increased by 5 and 8% in FDRIP SE using DS1 and DS2, respectively, to increase the size of the calibration set. In general, the use of DS1 to augment the calibration set improved predictive ability in each SE compared to DS3. However, the result of the population structure of the datasets assessed by spectral decomposition of the genomic relationship matrix of the lines in DS2 and DS3 shows significant overlap across the datasets . This possibly indicates that genetic correlation between environments influences predictive ability in multi-environment genomic prediction.The prediction performance of the PBLUP model was similar to the GBLUP model which is not surprising as DS2 consisted of multiple populations with family sizes that ranged from 1 to 9 . However, the predictive ability was lowest when DS3 was combined with the calibration set in each SE. For example, with no overlapping lines across SEs, using the DS3 to increase the calibration set size resulted in a predictive ability obtained from the PBLUP model across the SEs ranging from 4 to 31%, while the prediction ability obtained from the GBLUP model ranged from 9 to 46% across the SEs.The prediction performance improved with increasing size of the calibration set, further corroborating the importance of genetic connectivity across SEs/environments in sparse testing Fig. . ContrarGenomic prediction is a powerful tool to reduce selection cycle time and increase selection intensity Below is the link to the electronic supplementary material.