Genomic Prediction with Pedigree and Genotype × Environment Interaction in Spring Wheat Grown in South and West Asia, North Africa, and Mexico

Developing genomic selection (GS) models is an important step in applying GS to accelerate the rate of genetic gain in grain yield in plant breeding. In this study, seven genomic prediction models under two cross-validation (CV) scenarios were tested on 287 advanced elite spring wheat lines phenotyped for grain yield (GY), thousand-grain weight (GW), grain number (GN), and thermal time for flowering (TTF) in 18 international environments (year-location combinations) in major wheat-producing countries in 2010 and 2011. Prediction models with genomic and pedigree information included main effects and interaction with environments. Two random CV schemes were applied to predict a subset of lines that were not observed in any of the 18 environments (CV1), and a subset of lines that were not observed in a set of the environments, but were observed in other environments (CV2). Genomic prediction models, including genotype × environment (G×E) interaction, had the highest average prediction ability under the CV1 scenario for GY (0.31), GN (0.32), GW (0.45), and TTF (0.27). For CV2, the average prediction ability of the model including the interaction terms was generally high for GY (0.38), GN (0.43), GW (0.63), and TTF (0.53). Wheat lines in site-year combinations in Mexico and India had relatively high prediction ability for GY and GW. Results indicated that prediction ability of lines not observed in certain environments could be relatively high for genomic selection when predicting G×E interaction in multi-environment trials.

Wheat is the most widely cultivated cereal crop in the world, and provides 20% of the protein and calories consumed by the world population (FAOSTAT). Several studies have reported that the present rate of genetic gain in spring wheat is ,1% yr 21 (Aisawi et al. 2015;Sayre et al. 1997;Manes et al. 2012;Lopes et al. 2012); that rate needs to improve to meet future wheat demand . This can be done through improvements in plant structure and reproduction, and in crop physiology (radiation use efficiency), as well as improved genotyping or phenotyping methods, increased genetic diversity of breeding germplasm, or through the use of complementary genomic selection approaches in plant breeding Tester and Langridge 2010).
Traditional breeders use the pedigree selection method for breeding most crops, which requires several generations of testing and advancing the lines. An alternative method is marker-assisted selection (MAS), where markers associated with genes of major effect are used (Spindel et al. 2015). The first to propose predicting breeding values of complex traits for unobserved phenotypes using all available high density markers were Meuwissen et al. (2001). This initial study was followed, in plants, by Bernardo and Yu (2007), who demonstrated, by simulation, that whole genome regression predicts complex traits more accurately than using only a few markers. These seminal investigations led to the application of different statistical parametric and nonparametric genomic models with pedigree information in different crops (Crossa et al. 2010Jarquin et al. 2014;Pérez-Rodríguez et al. 2015;Velu et al. 2016;de los Campos and Pérez-Rodríguez 2013;Arruda et al. 2015).
wheat breeding, especially when multi-environment testing of lines is routine in their development and release (Braun et al. 2010). Multienvironment testing is prone to high levels of genotype · environment (G·E) interaction due to varying climatic zones, dynamic weather parameters, and different management factors. Burgueño et al. (2012) were the first to use marker-and pedigree-based Best Linear Unbiased Predictor (BLUP) models for assessing G·E under genomic prediction; these models account for correlated environmental  structures of markers and environmental covariables in a reaction norm model. The reaction norm model of Jarquín et al. (2014) has been widely used in multi-environment data of different crops, including wheat data with pedigree and genomic information and their interaction with environments (Pérez-Rodríguez and de los Campos 2014; Crossa et al. 2016;Velu et al. 2016). This model is flexible and allows the incorporation of highly dimensional environmental covariable data. Furthermore, a similar genomic G·E model was recently developed and used on wheat breeding data, with the novelty that it decomposes the total marker · environment effect into a marker main effect across all the environments, and a markerspecific effect for each environment (López-Cruz et al. 2015). A recent study by Crossa et al. (2015) showed how the marker · environment model can be used both as a prediction model, by means of shrinkage regression, and/or as a variable selection to estimate marker effects.
Previous genomic and pedigree studies on assessing the prediction ability of G·E have considered a very limited number of environments; they usually included combinations of sites under a few agronomic management systems (i.e., levels of managed drought and heat stress). In the present study, we assess the genomic prediction ability of several models within the framework of the reaction norm model of Jarquín et al. (2014) using the Wheat Association Mapping Initiative (WAMI) panel-designed to evaluate G·E for grain yield (GY), while avoiding the confounding effects of extreme phenology (Lopes et al. 2015). The main objective of this study was to detect prediction ability of different international sites established in different years, with the objective of examining and identifying possible key testing sites to be further used in a genomic-assisted breeding program. A total of 287 spring wheat lines included in the WAMI data were grown in international multienvironment trials in 18 site-year combinations in South and West Asia, North Africa, and Mexico. Traits included in this study are grain yield (GY), grain number (GN), thousand-grain weight (GW) and thermal time for flowering (TTF).
The WAMI panel used in this study is very appropriate for studying genomic and pedigree prediction because its lines were phenotyped under a very diverse set of environments around the world. Also, the WAMI panel has already been studied for several complex traits: adaptation to plant density (Sukumaran et al. 2015b), grain yield and yield components (Sukumaran et al. 2015a), drought stress (Edae et al. 2014), and earliness per se (Sukumaran et al. 2016).

MATERIALS AND METHODS
The genetic material The WAMI population was assembled from the elite advanced wheat nurseries distributed through the International Wheat Improvement Network (IWIN). It consists of 287 diverse elite lines selected from nurseries bred for high yield potential environments (Lopes et al. 2015;Sukumaran et al. 2015a,b).

Phenotyping and genotyping
The WAMI population was phenotyped in major wheat-growing areas of India, Pakistan, Nepal, Bangladesh, Iran, Egypt, Sudan, and Mexico. These growing environments are diverse in terms of rainfall, heat stress, drought stress, and solar radiation patterns. Phenotyping was conducted at the following locations: Bangladesh Agricultural Research Institute (BARI), Joydebpur, Bangladesh (BGLD J); Indian Agricultural Research Institute (IARI), Delhi (India D); University of Agricultural Sciences, n  (Figure 1). Table 1 shows the countries, locations, and abbreviations used in this study, as well as the four traits that were recorded and analyzed: GY per square meter, GN per square meter, GW estimated using standard protocols (Sayre et al. 1997), and TTF estimated based on a base temperature of zero and the sowing date. Minimum and maximum temperatures, and the coordinates of the environments, were described in an earlier publication (Sukumaran et al. 2016). The WAMI panel was genotyped using 90K Illumina SNPs array (Sukumaran et al. 2015a). From the polymorphic SNPs after using a minor allele frequency cut-off of 5%, 15K SNPs were used for genomic prediction. The population structure associated with the 1B.1R translocation was described in earlier publications (Lopes et al. 2015;Sukumaran et al. 2015a). b Names of the environments are given in Table 1.

Statistical models
The Best Linear Unbiased Estimators (BLUEs) were computed for mixed model analysis for each of the traits in each environment. The model used to calculate BLUEs for each environment is where y jkm is the phenotypic response value for the specific trait measured on the jth line of the mth incomplete block within the kth replicate, L j is a fixed effect of the jth wheat line, r k is the random effect of the kth replicate assumed independent and identically multivariate normally distributed (iid) N(0, Is 2 r ) (where I is the identity matrix, and s 2 r is the variance of replicate), b mðkÞ denotes the random effect of the mth incomplete block within the kth replicate assumed independent and identically distributed (iid) with N(0, Is 2 b ), where s 2 b is the variance of the incomplete block, e jkm is the random error associated to the trait measured on the jth line of the mth incomplete block within the kth replicate, and assumed iid with N(0, Is 2 e ), where s 2 e denotes the error variance. Broad-sense heritability (H 2 ) for each environment was computed on an entry mean basis as H 2 ¼ s 2 s 2 g is the wheat line variance, r is the number of replicates, and s 2 e is n Table 4 Correlations (mean 6 SD) between the observed and predicted values for GW under CV1 and CV2 schemes for seven prediction models (M1-M7) b Names of the environments are given in Table 1.
the error variance. Heritability estimates across environments were also estimated using the following formula, where s is the number of environments, and s 2 ge is the variance of the wheat line · environment obtained from the combined analyses across environments.
For GS, we used the reaction norm model that is an extension of the random effect Genomic Best Linear Unbiased Predictor (GBLUP) model, where the main effect of lines, the main effect of environments, the main effect of markers, the main effect of pedigree, and their interactions with environments, are modeled using random covariance structures that are functions of marker or pedigree genotypes and environmental covariates (Jarquín et al. 2014). Brief descriptions of the baseline model, as well as the reaction norm models with G·E, are given below.

Baseline model
The response of the phenotypes (y ij ) defined by random baseline model is b Names of the environments are given in Table 1. where m is the overall mean, E i is the random effect of the ith environment, L j is the random effect of the jth line, EL ij is the interaction between the ith environment and the jth line, and e ij is the random error term. All random effects follow a iid multivariate normal distribution such that E i $ Nð0; Is 2 E Þ; L j $ Nð0; Is 2 L Þ; EL ij $ Nð0; Is 2 EL Þ; and e ij $ Nð0; Is 2 e Þ where s 2 E ; s 2 L ; and s 2 EL are the environment, line, and line · environment variances, respectively. In the model above, the random effect of the line (L j ) can be replaced by g j ; which is an approximation of the genetic value of the jth line from the genomic relationship matrix. Also, the effects of the line (L j ) can be replaced by a j ; which is the additive effect obtained from the pedigree information. In the models described below, we used either g j or a j ; both g j and a j , as well as their interactions with environment E i ðgE ij ; or aE ij Þ: Full descriptions of the different reaction norm models can be found in Jarquín et al. (2014) and Zhang et al. (2014), among others. Below, we give a brief description of the different reaction norm models that were fitted using pedigree and genomic information.

Reaction norm models
We fitted seven different models (M1-M7) with different components including E = environments, L = line, A = pedigree, G = genomic, AE = pedigree · environment interaction, GE = genomic · environment interaction, and e = residual error.

M1: Environment and line main effects (Y = E + L + e)
The response of the phenotypes (y ij ) from the baseline model, but excluding the interaction term, EL ij ; is described as M2: Environment, line, and pedigree main effects (Y = E + L + A + e) By adding the random effect that incorporates pedigree information by means of the numerical relationship matrix (A) to M1, we get model M2, defined as where a j is a random additive effect of the line, which, in this case accounts for pedigree-relationships, where a ¼ ða; . . . ; a J Þ9 contains the pedigree values of all the lines, and is assumed to follow a multivariate normal density with zero mean and covariance matrix CovðaÞ ¼ As 2 a ; where A is the numerical relationship matrix, and s 2 a is the additive genetic variance. The random effects a ¼ ða; . . . ; a J Þ9 are correlated such that model M2 allows borrowing of information across lines based on the numerical relationship matrix (A) computed from the pedigree information.
M3: Environment, line, and genomic main effects (Y = E + L + G + e) Model M3 is fitted by adding the genomic random effect of the line g j to M1, which is an approximation of the genetic value of the jth line, and is defined by the regression on marker covariates g j ¼ P p l¼1 x jl c l ; where x jl is the genotype of the jth line at the lth marker, and c l is the effect of the lth marker assuming iid c l $ Nð0; s 2 c Þ (l=1,. . .,p), and s 2 c is the variance of the marker effects. The vector g ¼ ðg 1 ; . . . ; g J Þ9 contains the genomic values of all the lines, and is assumed to follow a multivariate normal density with zero mean and covariance matrix CovðgÞ ¼ Gs 2 g ; where G is the genomic relationship matrix computed as suggested by VanRaden (2008) (i.e., G}ðXX9=2 P p l¼1 p l ð1 2 p l ÞÞ; with X as the centered and standardized matrix of molecular markers and p l the frequency of the lth marker); and s 2 g }s 2 c is the genomic variance. Thus, model M3 is with g $ Nð0; Gs 2 g Þ: The random effects g ¼ ðg 1 ; . . . ; g J Þ9 are correlated such that model M3 allows borrowing information across lines.
M4: Environment, line, pedigree, and pedigree 3 environment interaction effects (Y = E + L + A + AE + e) By adding the interaction between the additive relationship matrix and environments (Ea ij ) to model M2, model M4 becomes where the term Ea ij is the interaction between the additive value of the ith genotype in the jth environment and Ea $ N½0; ðZ a GZ 9 a Þ°ðZ E Z 9 E Þs 2 Ea Matrices Z a and Z E are the incidence matrices for the effects of the additive genetic values of genotypes and environments, respectively, s 2 Ea is the variance component of the interaction term Ea ij , and "∘" stands for Hadamart product between two matrices. M5: Environments, lines, genomic, genomic 3 environment interaction effect (genomic 3 environment) (Y = E + L + G + GE + e) By adding the interaction between markers and environments (Eg ij ) to model M3, model M5 becomes where the term Eg ij is the interaction between the genetic value of the ith genotype in the jth environment; then Eg $ N½0; ðZ g GZ9 g Þ°ðZ E Z9 E Þ½s 2 Eg : Matrices Z g and Z E are the incidence matrices for the effects of the genetic values of the genotypes and the environments, respectively, s 2 Eg is the variance component of the interaction term Eg ij : M6: Environment, line, pedigree, and genomic main effects (Y = E + L + A + G + e) We added both the pedigree and genomic effects of the lines (g j ; and a j ) to model M1, so that it contains the genomic random vector g ¼ ðg 1 ; :::; g J Þ9; and the pedigree random vector a ¼ ða; :::; aÞ9: Therefore, model M6 is M7: Environment, line, pedigree, genomic, pedigree 3 environment interaction and genomic 3 environment interaction effects (M7 = E + L + A + G + AE + GE + e) By adding both the interaction between pedigree and environment (Ea ij ), and the interaction between markers (genomic) and environments (Eg ij ) to model M6, model M7 becomes All the terms in this model have already been defined above.

Prediction assessment by cross-validation
Two distinct cross-validation (CV) schemes were used. The first, CV1, evaluates the prediction ability of models when a set of lines has not been evaluated in any of the environments (Burgueño et al. 2012). Predictions derived using CV1 are based entirely on phenotypic records of other lines. The second scheme, CV2, evaluates the prediction ability of models when some lines have been evaluated in some environments, but not in others. In CV2 prediction, information from related lines and the correlated environments is used, and prediction assessment benefits from borrowing information between lines within an environment, between lines across environments, and among correlated environments (Burgueño et al. 2012). Prediction ability is the Pearson correlation coefficient between the observed and predicted values for each genotype.
In both CV1 and CV2, a fivefold cross-validation scheme was used to generate the training (TRN) and testing (TST) sets, and to assess the prediction ability of each testing set. The data were divided randomly into five subsets, with 80% of the lines assigned to the training set and 20% assigned to the testing set. Four subsets were combined to form the training set, and the remaining subset was used as the validation set. Permutation of five subsets led to five possible training and validation data sets. This procedure was repeated 20 times, and a total of 100 runs was performed on each population for each trait-environment combination. The same partitions were analyzed with all models. The average value of the correlations between the phenotype and the genomic estimated breeding values from 100 runs was calculated in each population for each trait-environment combination, and was defined as the prediction ability.

Software
The genomic prediction analyses were computed using R, and the models were fitted using the BGLR package de los Campos and Pérez-Rodríguez 2013). The ANOVA was performed in the SAS 9.2 (SAS Institute Inc 2010) program, and the boxplots created in R. Tukey's test for significant differences between the models' predictions (correlations) were generated in the SAS 9.2 (SAS Institute Inc 2010) program.

Data availability
All the phenotypic data for each environment and trait, as well as the genomic data, can be downloaded from the link http://hdl.handle.net/ 11529/10714.

Variation in the studied traits
The WAMI panel was grown in seven countries, comprising a total of 18 environments (site-year combinations). India had the largest number of environments (6) followed by Mexico (4), and Bangladesh, Nepal, Pakistan, Iran, and Sudan with one site each. The ANOVA showed significant differences between the wheat lines and environments (Table  A1, Appendix A). Environment Mex 110 was the highest yielding environment (7.02 ton/ha), followed by Pak I11 (6.9 ton/ha). The lowest yield was obtained in BGLD J10 (2.2 ton/ha) with a GW value of 30.9. The highest GW value was recorded in Mex I10 (43.4), followed by India L11 (38.3), and the lowest was India H10 (27.6). TTF ranged from 976°D in Mex H10 to 1474°D in Sudan W. The highest GN was recorded in Pak I11 (21920), followed by Iran D10 (Table 1). Heritability estimates of individual and combined environments for each trait were also calculated. Trait GW (0.74) had the highest H 2 values, followed by GN (0.51), TTF (0.48), and GY (0.41) (Table A1, Appendix A). A box plot of the data at the individual locations indicated TTF had the highest variation and the lowest G · E was observed for GW ( Figure  2 and Figure 3).
For CV1, 28 environment-model combinations had prediction ability values above 0.30 for GY. Among the sites, when using M7, Mexican environments (Mex I10, Mex D10, and Mex H10) had high prediction ability values (.0.41) for CV1 using M6 and M7. CV2 values were above 0.40 for 52 site-model combinations. For India V10 and India D10, prediction ability was above 0.5 for all models. In the CV1 scenario, 14 sites had the highest values when M6 and M7 were used (Table 2). Trait GN mostly followed a similar pattern as that shown for GY but the CV1 values ranged from 20.05 (BGLD J10) to 0.56 (Mex I10). Forty-three environment-model combinations had CV1 values .0.30. Models 6 and 7 had five sites with CV1 values .0.4. Two sites (Sudan W10 and Mex I10) had CV1 values . 0.4 for six models. Models 6 and 7 had CV1 values . 0.50 for four environments (Mex H10, Mex HD10, Sudan W10, and Mex I10). On average, the highest CV1 values were recorded for M5 (0.32) and M7 (0.32) (Table 3). Tukey's test also grouped M5 and M7 with the highest prediction ability models for CV1 and CV2 scenarios ( Figure 5) Table 4). Tukey's test group showed models M3 and M7 as the most significant models with the highest prediction ability in the CV1 scenario ( Figure 6). In the CV2 scenario, all models had the same prediction ability (0.63) ( Figure 6 and Table 4).
For TTF, the prediction ability in the CV1 scenario ranged from 20.11 (India L11, M1) to 0.44 (India K11, M5). A total of 29 model-site combinations had CV1 values .0.3, with M7 predicting eight sites with correlations .0.3. Mex I10 had five models predicting the sites with .0.3 for CV1, followed by Nepal. On average, M5 had the highest CV1 values (0.28) when compared with other models (Table 5) (Table 5). On average, correlations for M5-M7 for CV1 were 0.28, 0.24, and 0.27, respectively, and prediction ability values for M5-M7 for CV2 were 0.54, 0.52, and 0.53, respectively. Tukey's test groups indicated that M5-M7 were the best predictive models for CV1, while for CV2 all models had the same prediction ability (Figure 7).
In summary, for the complex trait GY, M6 and M7 with interactions had the highest average prediction ability across environments for CV1 (0.29 and 0.31, respectively), and for CV2 (0.37 and 0.38, respectively). For the less complex trait GW, M3 and M7 showed the highest mean prediction ability for CV1 (0.45), and it was around 0.63 for all models in CV2. For grain number (GN) (which is a GY component and a complex trait), M5 and M7 gave the highest prediction ability for CV1 (0.32) and CV2 (0.43). For trait TTF, M5-M7 (0.28, 0.24, and 0.27, respectively) were the best for CV1; all models performed similarly for CV2 (0.52-0.53).
Trends in prediction ability vs. heritability The best model for GY was M7 and, for CV1, it showed increasing values of environment heritability with their corresponding prediction accuracies, whereas M1 prediction ability was not related to heritability values ( Figure B1-A, Appendix B). For GY in the CV2 scenario, the best and worst models had similar prediction ability, and showed an increasing trend of up to H 2 = 0.50; values decreased thereafter ( Figure B1-B, Appendix B). For trait GW in the CV1 scenario, a positive trend of increased prediction ability with increased H 2 values was observed for the best model (M3), which had no interaction terms. The worst model (M1) did not show a response with increased H 2 values ( Figure B2-A, Appendix  B). For the CV2 scenario, the best and worst models showed increased correlation values, and an increase in H 2 values ( Figure B2-B, Appendix B).
For GN, the correlations and H 2 values of the best model (M7) showed a positive trend in the CV1 scenario, whereas the basic model (M1) showed no association with H 2 values ( Figure B3-A, Appendix B). Similar to GY, the best and basic models showed very close prediction ability and H 2 values for environments in the CV2 scenario for GN ( Figure B3-B, Appendix B). For TTF, the best model (M5) did not show greater prediction ability, the positive trend was lower (R 2 = 0.12), and the basic model M1 showed no association with H 2 values (R 2 = 0.08) ( Figure B4-A, Appendix B). In the CV2 scenario, the best and basic model for TTF did not show high association between prediction values and H 2 estimates, with some sites with high heritability estimates showing lower prediction values (Fig. B4-B, Appendix B).

DISCUSSION
The WAMI panel has been extensively studied for several complex traits: adaptation to density (Sukumaran et al. 2015b), GY and yield components (Sukumaran et al. 2015a), drought stress (Edae et al. 2013(Edae et al. , 2014, and earliness per se (Sukumaran et al. 2016). Since it was also phenotyped under diverse environments around the world, it is a perfect panel for testing some of the genomic and pedigree selection models. Data from these testing sites were used routinely to select lines for release as varieties, and for crossing them to generate new prebreeding lines (Reynolds and Langridge 2016). Physiological breeding is aimed at improving wheat productivity through complex physiological traits. These traits are often controlled by genes with small effects; if they can be proven to be of value in the breeding program, they are more effectively selected using genomic selection methods than using MAS.
Several models have been proposed for the genomic prediction schemes; however, it is important to test them on diverse environmental data before using them in the breeding program. Models 6 and 7 were the best models, for they had the highest average prediction ability values for the CV1 and CV2 scenarios for GY among all environments. Here, we evaluated seven models (some with the G·E term), and concluded that these models can predict GY with moderate to high levels of prediction ability, whereas less complex traits, such as GW, can be predicted without including any interaction terms in the model.
The results of this study agree with those of a recent study on Zn and Fe grain concentration in spring wheat (Velu et al. 2016). Models that include G·E interaction terms showed higher prediction accuracies. Also, prediction ability was generally associated with trait heritability, as in earlier reports (Muranty et al. 2015). The highest prediction ability was for GW, which is a high heritability trait in the WAMI panel (Sukumaran et al. 2015a). Another observation was that, for some environments, M3 gave high prediction ability for GW in the CV1 scenario, whereas model M2 was the best in CV2. In this study, we evaluated the correlation between genomic-and pedigree-based estimated breeding values, with phenotypic data from field trials. With a reasonable number of molecular markers, and incorporating G·E terms in the models, higher prediction ability was obtained for the "genomic" component when compared to pedigree-based prediction models (Burgueño et al. 2011). This was also dependent on trait heritability, as GW had higher prediction ability values even when using M3 (Muranty et al. 2015).
Genotypic values of lines in several environments were predicted using genomic prediction models; when compared across environments, the highest prediction ability was recorded at environments in Cd. Obregon (Mexico) for GY, GN, GW, and TTF. Relatively good climate, as well as optimal management of the Cd. Obregon site, are big factors influencing heritability of yield and prediction ability; sites with high heritability have higher prediction ability. However, our analysis also showed that there is no linear association between heritability and prediction ability values; nevertheless, prediction ability could be a function of H 2 values and other parameters (Spindel et al. 2015). Another factor that could increase genomic prediction ability is incorporating high-dimensional environmental covariates (Jarquin et al. 2014;Pérez-Rodríguez et al. 2015). Recent studies on wheat have shown that GS selection could reshape wheat breeding because it produces higher genetic gains than conventional breeding (Bassi et al. 2016).

Conclusions
Genotype · environment prediction models in genomic selection and pedigree-based selection can help accelerate breeding cycles for complex traits such as grain yield in multi-environmental trials. Traditionally, breeders have depended on phenotypic selection for generation advancement. Results of the present study show that GS is a complementary method to phenotypic selection with medium-to-high prediction ability values. Genomic prediction of GY, and other traits in spring wheat lines evaluated in a large and diverse number of international environments, indicated that sites in Mexico and India could be key sites for genomic-assisted breeding. A set of wheat lines not observed in several site-year combinations were predicted with correlations of 0.3-0.5 in Mexico and India (CV1) for models that included genomic and pedigree interaction with environments. When some of these lines were observed in some environments, this correlation increased to 0.45-0.53 (CV2).
For less complex traits, such as GW, the prediction ability of lines not observed in sets of environments increased to about 0.6 for Mexican environments (CV1). Sets of wheat lines observed in some environments, but not in others, were predicted with correlations of up to 0.8 in Mexican and India environments (CV2) for genomic-enabled prediction models including (or not) genomic and pedigree interactions with environments. n

Figure B1
Comparison between heritability values and the correlation between observed and predicted values for the best and worst models in predicting trait GY in different environments for two cross-validation scenarios: (A) CV1 (the best and worst models were M7 and M1, respectively), and (B) CV2 (the best and worst models were M7 and M1, respectively).

APPENDIX B APPENDIX A
Volume 7 February 2017 | Genomic Prediction G·E Interaction in Wheat | 493 Figure B2 Comparison between heritability values and the correlation between observed and predicted values for the best and worst models in predicting trait GW in different environments for two cross-validation scenarios (A) CV1 (the best and worst models were M3 and M1, respectively) and (B) CV2 (the best and worst models were M6 and M1, respectively).

Figure B3
Comparison between heritability values and the correlation between observed and predicted values for the best and worst models in predicting trait GN in different environments for two cross validation scenarios: (A) CV1 (the best and worst models were M6 and M1, respectively) and (B) CV2 (the best and worst models were M6 and M1, respectively).

Figure B4
Comparison between heritability values and the correlation between observed and predicted values for the best and worst models in predicting trait TTF in different environments for two cross-validation scenarios: (A) CV1 (the best and worst models were M5 and M1, respectively) and (B) CV2 (the best and worst models were M7 and M1, respectively).