Introduction

Wheat (Triticum aestivum L.) provides 20% of the total calories and 20% of plant-derived protein to the world population (Food and Agricultural Organization of the United Nations, 2010). However, the production levels need to be increased by 70% to meet the projected food requirements by 2050 (Ray et al. 2012). Even though progress has been made through conventional breeding approaches in increasing genetic gains of grain yield (GY) of spring bread wheat, it is less than 1% per year (Sharma et al. 2012; Aisawi et al. 2015; Crespo-Herrera et al. 2017). To meet the predicted demand, it is important to complement the conventional approaches through molecular breeding for complex traits (Reynolds and Langridge 2016). Even though GY is the most important trait in any plant breeding program, there still exists a large gap in understanding the genetic and molecular mechanism of the trait and its components (Valluru et al. 2014).

Linkage mapping and genome-wide association studies (GWAS) are two methods widely used to identify and understand the genetic basis of complex traits (Zhu et al. 2008). Grain yield is a complex trait determined by multiple quantitative trait loci (QTL) that interact with each other and with the environment (Sehgal et al. 2017). Genetic analysis to identify the genomic region for GY is often subjected to genotype-by-environment interaction (G × E) due to the complex nature of the trait. A recent study has shown the phenotypic plasticity for GY in the US Great Plains ranged from 1.3 to 5.3 Mg ha−1 (Grogan et al. 2016). To discover the genetic basis of grain yield it is important to have multi-environmental experiments conducted. In those studies, the identified QTL are constitutive—when consistently detected across most environments—or adaptive—when only detected in specific environmental conditions (Vargas et al. 1998).

Until a decade ago, QTL mapping was the first choice for genetic analysis to understand complex traits like GY (Quarrie et al. 1994, 2006; Kato et al. 1999; Kirigwi et al. 2007) but the trend has moved to GWAS due to less time required for population development and higher mapping resolutions (Zhang et al. 2010; Huang et al. 2010; Sukumaran et al. 2012). GWAS was used to identify genomic regions associated with GY and related traits in several populations (Sonah et al. 2015; Maccaferri et al. 2016; Valluru et al. 2017). Genomic regions related to plant development—phenology and plant height—were identified in chromosomes 1AL, 1BS, 2AL, 2BS, 2BL, 4BL, 5BL, and 6AL, with constitutive QTL on chromosomes 5BL and 6AL (Ain et al. 2015). Our previous study in temperate irrigated environments in Mexico identified genomic regions related to GY and yield components in chromosomes 5A (98 cM) and 6A (77–85 cM) (Sukumaran et al. 2015a).

Genes and QTLs associated with thousand grain weight (TGW) have been studied in bread wheat (Ramya et al. 2010; Zanke et al. 2014; Kumar et al. 2015; Simmonds et al. 2016; Brinton et al. 2017a). A region responsible for grain weight was fine mapped in chromosome 7D using introgression lines in winter wheat (Röder et al. 2008). However, the most studied gene affecting TGW in wheat is TaGW2-6A an orthologue of the OsGW2 gene, a RING-type E3 ubiquitin ligase in rice that influences grain width and weight (Su et al. 2011; Yang et al. 2012; Zhang et al. 2013; Jaiswal et al. 2015). This gene has two haplotypes—Hap-6A-A and Hap-6A-G—detected in the promotor region (Su et al. 2011). However, the superior effect of both haplotypes in different germplasms were reported. For instance, Hap-6A-A is superior allele in Chinese germplasm, increasing 3 g of TGW (Su et al. 2011) but another report suggested Hap-6A-G is the superior allele (Zhang et al. 2013). When this gene has an insertion in the eighth exon it reduces the protein sequence from 424 to 328 amino acids, it is responsible for large kernel in a European wheat variety (Yang et al. 2012). QTLs have been identified for grain number (GN), but none of them was studied in detail in spring wheat (Börner et al. 2002; Kuchel et al. 2007). A QTL mapping approach was used to identify a locus in chromosome 1B, which controls GN, and a locus in 7B associated with TGW without significant reduction in grain number (Griffiths et al. 2015). Overall, there has been little effort on dissecting the TGW and GN trade-off in spring wheat.

In general, GY is positively associated with GN, the positive association with TGW is less profound, and the two components themselves are usually negatively correlated. The aims of this study were (1) to identify genomic regions associated with GY, GN, and TGW in an elite spring wheat panel in diverse environments; (2) to identify sets of markers associated with GY and components that maximize the probability of identifying high GY wheat lines; and (3) identify specific markers for TGW and GN independent of GY, those can be used to maximize TGW and GN (e.g. increasing TGW while increasing GY and GN).

Materials and methods

Plant material

The plant material used in the study was the Wheat Association Mapping Initiative (WAMI) panel, which consisted of 287 spring bread wheat lines assembled from several of the CIMMYT’s wheat international nurseries distributed around the world; Elite Spring Wheat Yield Trials (ESWYT); Semi-arid Wheat Yield Trials (SAWYT), and High Temperature Wheat Yield Trials (HTWYT) (Lopes et al. 2012). In the WAMI panel, several studies were conducted; GWAS for GY and yield components in temperate irrigated environments (Sukumaran et al. 2015a), genomic regions for adaptation to density (Sukumaran et al. 2015b), identification of earliness per se (eps) locus (Sukumaran et al. 2016), markers for grain yield in moisture stress environments (Edae et al. 2014), QTLs for spike ethylene (Valluru et al. 2017), and candidate gene association mapping for drought tolerance (Edae et al. 2013). The population structure of the panel is loosely based on 1B.1R translocation as well as pedigree of lines, e.g. lines crossed with and derived from elite lines like Pastor, Weebil, and Baviacora are in high frequency in this panel (Lopes et al. 2015; Sukumaran et al. 2015a). The WAMI population has a low range of phenology; range of 9 days for heading and 35 cm for plant height, when grown under temperate irrigated conditions in Mexico (Lopes et al. 2015; Sukumaran et al. 2015a).

Phenotyping

The WAMI population was phenotyped in 31 major wheat growing areas in Bangladesh, India, Pakistan, Nepal, Sudan, and Mexico in 2009–2010 and 2010–2011 growing seasons (Lopes et al. 2012, 2015; Sukumaran et al. 2015b). We used a subset of the data—ten environments—from this, based on heritability estimates (Table 1); Bangladesh Agricultural Research Institute (BARI), Joydebpur, Indian Agricultural Research Institute (IARI), Indore (India I), National Wheat Research Program (NWRP) Bhairahawa, Rupandehi (Nepal B), National Agricultural Research Centre (NARC), Islamabad, (PAK I), Sudan Wad Medani (Sudan W), and CIMMYT’s experimental station, Campo Experimental Normal E. Borlaug (CENEB), Sonora Mexico (Mex), where I, D, H, and HD denotes, irrigated, drought, heat, and heat + drought conditions, respectively. These environments were diverse in terms of rainfall, heat stress, drought stress, and solar radiation patterns (Sukumaran et al. 2017). Minimum and maximum temperatures and coordinates of the environments were described in earlier publications (Sukumaran et al. 2016). The experimental design at each site was an α-lattice with two replications. Blocks were arranged based on the heading date of the materials. Checks were included as entry number 50, 100, 150, and 200 to verify any planting errors.

Table 1 Descriptive statistics of the traits collected on the WAMI panel in ten different environments in the years 2010 and 2011
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Several traits were recorded and among them three traits were analyzed in the present study: GY, GN, and TGW using standard protocols (Sayre et al. 1997; see Pask et al. 2012). At most locations, plants were sown on flat beds generally of 2.5–3.0 m length with 4–6 rows (20–25 cm between rows) providing total harvestable area > 3 m2 (Reynolds et al. 2017). Grain number was estimated from GY and TGW. Days to heading (DH) was recorded when 50% of the spikes in a plot had emerged from the boot leaf (Zadoks stage 59) from days of emergence and was used as a co-variate in the analyses (Zadoks et al. 1974). The phenotypic data for each environment and trait, as well as the genomic data, is available from the link http://hdl.handle.net/11529/10714.

Genotyping and statistical analysis

Genotyping of the panel with the 90 K Illumina Infinitum SNP array and SNP processing are described in an earlier publication (Sukumaran et al. 2015a). In short, genetic data of 38K SNPs was processed for monomorphic markers, missing values (< 5%), and minor allele frequency (> 10%) that resulted in 28K SNPs for GWAS. Several markers related to the genes for vernalization, photoperiod, plant height, and 1B/1R translocation were scored in the WAMI panel (Sukumaran et al. 2017). The genes with known position in the panel were: Vrn-A1 (5A) (Yan et al. 2003), Ppd-B1 (2B), and Rht-B1 (4B) (Ellis et al. 2002), earliness per se (Eps-D1) (Zikhali et al. 2014; Sukumaran et al. 2016), and TaGW2-6A (Simmonds et al. 2016) identified through blind association analysis, where marker score was used as a phenotype.

Analysis of variance (ANOVA) was conducted in SAS using the PROC MIXED commands. Genotypes, environments, and genotype-by-environment interaction (G × E) were considered as random factors in the model in estimating the Best Linear Unbiased predictions (BLUPs) for each environment and in combined analysis using META-R (Vargas et al. 2013). Principal component analysis of the data was performed using the R package “FactoMineR” (Lê et al. 2008) and correlations between the environments were estimated using the R package “corrplot” (Wei and Simko 2017). For the individual environment analyses, the following model was used:

$$Y_{ijk} = \mu + R_{i} + B_{j} \left( {R_{i} } \right) + G_{k} + {\text{Cov}} + \varepsilon_{ijk} ,$$

where Y is the trait of interest, μ is the mean effect, R i is the effect of the ith replicate, B j (R i ) is the effect of the jth incomplete block within the ith replicate, G k is the effect of the kth genotype, Cov is the effect of the covariate, and ε ijk is the error associated with the ith replication, jth incomplete block, and kth genotype, which is assumed to be normally and independently distributed, with mean zero and variance σ 2. Broad sense repeatability (H 2) was estimated as

$$H^{2} = \frac{{\sigma_{\text{g}}^{2} }}{{\sigma_{\text{g}}^{2} + \sigma_{\text{e}}^{2} /r}},$$

where \(\sigma_{\text{g}}^{2}\) and \(\sigma_{\text{e}}^{2}\) are genotype and environment variance and r is the number of replications.

For a combined analysis across all environments, the following model used for the estimation of BLUPs;

$$Y_{ijk} = \mu + L_{i} + R_{j} \left( {L_{i} } \right) + B_{k} \left( {L_{i} R_{j} } \right) + G_{l} + L_{i} \times G_{l} + {\text{Cov}} + \varepsilon_{ijk} ,$$

where the new terms L i and L i  × G l are the effects of the ith environment and the G × E, respectively. For the combined analysis the H 2 was estimated as,

$$H^{2} = \frac{{\sigma_{\text{g}}^{2} }}{{\sigma_{\text{g}}^{2} + \sigma_{\text{ge}}^{2} /l + \sigma_{\text{e}}^{2} /rl}},$$

where \(\sigma_{\text{ge}}^{2}\) is the genotype by environment interaction variance and l is the number of environments.

Genome-wide association analysis

GWAS were performed on the BLUPs for each trait from the combined analyses of ten environments. We followed the unified mixed model approach (Yu et al. 2006; Zhang et al. 2010) as well as the generalized linear models incorporated in the TASSEL 5.0 software (Bradbury et al. 2007) to test for marker trait associations (MTAs). To account for population structure, principal components (PC1–5) from the principal component analysis of the genotypic data, Q matrix (Q1–5) derived from the STRUCTURE software (Pritchard and Rosenberg 1999; Falush et al. 2003, 2007), and non-metric multi-dimensional scaling (nMDS1–5) (Zhu and Yu 2009) were used. In addition, kinship matrix (K) calculated using SPARGeDi (Hardy and Vekemans 2002) and coefficient of parentage matrix (COP) was used as random factor in the mixed model. We fitted several different models—including generalized linear models—accounted only fixed effects—and mixed linear models—accounted population structure and family relatedness—(i.e. simple model, Q1–5, K, COP, Q1–5 + K, Q1–5 + COP, PC1–5 + K, PC1–5 + COP, nMDS1–5 + K, and nMDS1–5 + COP) using the analysis options (Yu et al. 2006) in TASSEL. Best model to estimate the marker effects and marker traits associations were decided based on the quantile–quantile plots of p values from each model fitting; the model that is close to the 1:1 ratio as the best model (Yu et al. 2006). The threshold to call marker-trait associations significant was based on the p value where a drastic deviation of the expected p values from the observed p values was observed (Sukumaran et al. 2015a). To define a genomic region as QTL, linkage disequilibrium (LD) was estimated for the region with several significant MTAs.

Candidate-gene association mapping

We also performed candidate gene based association analysis with all the known genes in this panel. Random 600 SNPs at least 5 cM apart and distributed in the genome were used as background markers. The candidate genes along with these markers were analyzed to identify significant association with the phenotypes. Similar to GWAS, several models—linear and mixed—were fitted and the best model—determined by the Q–Q plots—was used to identify the MTAs. In addition, the effect of haplotype TaGW2-6A, which was identified to be associated with TGW from earlier studies, was tested on the BLUPs of TGW from combined analysis of the environments. We also tested the effect of this haplotype on TGW in ten individual environments using t test and results were reported.

Marker effects and best combinations of significant markers for grain yield

We used step-wise forward and backward regression to identify the best marker combinations for each trait (Schulthess et al. 2017). Multiple regression was performed with the Q matrix and significant markers for each trait to estimate the likelihood-ratio-based R 2 (LRR 2) (Sun et al. 2010) for each marker. LRR 2 estimation avoids the effect of intercept that potentially have confounding effect on the variation explained by each marker. In addition, all significant markers for GY, TGW, and GN were fitted together in the step-wise regression models and multiple regression models to identify the optimum combination of makers and to estimate the marker effects for GY. These analyses were performed using the custom-made scripts in R software.

Results

Agronomic variation and repeatability estimates

Among the 31 environments phenotyped for grain yield, ten environments with moderate to high H 2 values were used for the analyses. The average yield of the WAMI panel from all environments was 3.81 t/ha with a range of 2.51 t/ha in Nepal B11 to 6.48 t/ha in Mex I10. The highest heritability estimate for GY was observed in Mex H10 and Mex I10 (0.75) with a mean H 2 of 0.67 among all environments. The average TGW was 33.45 g and varied from 29.36 g in Mex HD10 to 43.58 g in Mex I10. The highest H 2 estimate for TGW (0.96) was observed in Mex I10 and the lowest was in Pak I10 (0.72). GN was estimated from GY and TGW and it varied from 767.88 grains per m−2 in Nepal B11 to 17,554 grains per m−2 in Ind I11. The H 2 estimate for GN ranged from 0.48 (Nepal B11) to 0.85 (Mex h10) (Table 1). The H 2 values across environments for GY, TGW, and GN were 0.68, 0.95, and 0.42, respectively. The mean values across environments were 3.81 t/ha, 33.4 g, 3739.1, for GY, TGW, and GN (Table 2).

Table 2 ANOVA for the combined analysis of environments for each trait where the WAMI population was grown in 2010 and 2011 (see Table 1)
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Correlations between the traits and environments

Among environments, the highest correlation coefficients (r) was observed for TGW, followed by GN, and GY. The highest correlation for GY was observed between Mex H10 and Mex HD10 (r = 0.65). The Mexican environments had moderate to high r with most other environments. The lowest correlations among environments were observed with Sudan W10 and Pak I10 for GY. In Sudan W10, GY showed negative correlations with BGLD J11 and Mex HD10. The correlations for GN between the environments followed a pattern similar to GY with highest correlation between Mex I10 and Mex D10 (r = 0.68). Seven environments (BGLD J11, Nepal B11, Sudan W10, Mea H10, Mex HD10, Mex D10, and Mex I10) showed correlations (r > 0.30). TGW, the highest heritability trait showed the highest r (0.86) between Mex HD10 and Mex H10. Most environments were highly correlated for TGW and the lowest r value being 0.36 between Pak I10 and BGLD J11 (Fig. 1). The r value between GY and TGW was (r = 0.21), between GY and GN was (r = 0.56), and between GN and TGW was (r = − 0.50). In general, GN was positively correlated with GY than TGW in all environments.

Fig. 1
figure 1

Phenotypic correlations of the traits a grain yield, b thousand grain weight, and c grain number between the locations. Blue shades indicate significance at α < 0.001. Refer to table one for abbreviations (color figure online)

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GWAS results

GWAS was conducted in TASSEL using GLM and MLM models (Fig. 2). For most of the traits, PC3 + K matrix was the best model and showed less deviation of the expected values from the observed values in the Q–Q plots.

Fig. 2
figure 2

GWAS results as Manhattan plot for a grain yield, b grain weight and c grain number on the combined BLUPs of WAMI data collected in 2010 and 2011 in 10 environments. Blue lines indicate the GWAS threshold of 0.001 (color figure online)

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Grain yield

GWAS of the combined environment BLUPs detected 27 MTAs in six chromosomes—2A, 3B, 4A, 4B, 5A, and 7A—associated with GY that explained 4–7% of the variation of the trait with p values < 0.001 (Supplementary Table 1). The MTAs could be localized into ten genomic regions based on LD; 2A (106 cM), 3B (86 cM), 3B (91 cM), 3B (95 cM), 3B (115 cM), 4A (151 cM), 4B (66–68 cM), 6A (77–85 cM), and 7A (35 cM) (Table 3). We further explored the 3B and 6A regions and found that, the markers in chromosome 3B at 86, 91, 95, and 119 cM are in high LD, with r 2 = 1, indicating a large QTL for GY in chromosome 3B from 86 to 119 cM (Supplementary Fig. 1). LD estimates in the chromosome 6A region from 77 to 85 cM indicated the presence of an LD block in 77–81 cM region, but on individual environment analysis markers at 85 cM were also associated (Supplementary Fig. 2). A blind association analysis of the TaGW2-6A haplotype indicted the possible location of the TaGW2 gene in chromosome 6A (77–78 cM).

Table 3 Most significant genomic regions associated with grain yield and thousand grain weight based on combined GWAS of environments
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Thousand grain weight

We identified 34 MTAs for TGW from combined analysis of environment BLUPs in chromosomes; 1B, 2A, 2B, 3B, 3D, 5A, 6A, 6B, and 7D (Supplementary Table 2). Based on LD analysis, these MTAs corresponded to 15 QTLs—1B (141–148, and 164 cM), 2A (143 cM), 2B (20–26 cM), 2B (96–99 cM and 145 cM, 3B (51 cM), 3D (48 cM), 5A (26, 60, and 98 cM), 6A (77–85 cM), 6B (113 cM), and 7D (55 and 78 cM), located in nine chromosomes (Table 3). The Vrn-A1 gene in chromosome 5A (90 cM) had significant effect on flowering time in an earlier study (Sukumaran et al. 2015a), but the present locus associated with TGW is in chromosome 5A at 98 cM. LD analysis indicated these loci are not in high LD, which suggests that these are separate loci (Supplementary Fig. 3).

Grain number

For GN, we identified 31 significant MTAs in twelve chromosomes; 1A, 1D, 2B, 3A, 3B, 4B, 5A, 5B, 5D, 6A, 6D, and 7A (Supplementary Table 3). LD analysis of the significant MTAs narrowed the significant loci into 13 QTLs on chromosomes 1A (130 cM), 1D (51 cM) 2B (96–99 cM), 3A (15 cM), 3B (99 cM), 4B (81 cM), 5A (98 cM), 5B (3–4 cM), 5D (203 cM), 6A (141 cM), 6D (77 cM), and 7A (120 and 135 cM) (Table 4).

Table 4 Most significant genomic regions associated with grain number (m−2) based on combined GWAS of environments
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Common markers and trade-off for grain weight and grain number

A comparison of the GWAS results for all traits identified four common regions associated with multiple traits. A common locus for GY and TGW was located in chromosome 6A (77–85 cM). A common QTL for GY and GN was detected in chromosome 3B (99 cM). Common loci for GN and TGW were in chromosome 5A (98 cM) and 2B (96 cM) (Fig. 3).

Fig. 3
figure 3

Venn diagram illustrating the common genomic regions for grain yield, grain weight, and grain number for the combined data from 10 environments. Subscript numbers indicate the centi morgan (cM) position of marker-trait associations in a chromosome based on the 90 K consensus map. The arrows indicates positive (↑) or negative (↓) additive effects of minor alleles

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We also estimated the effect of these loci on GY, TGW, and GN. The locus in 6A (85 cM) had positive effect on GY, TGW, and GN with an allele substitution effect of 4.7, 1.7, and 2%, respectively. The locus on chromosome 3B (99 cM) had an allelic substitute effect of 3.0, − 4.5, and 3.1% for GY, TGW, and GN, respectively. The locus on chromosome 2B (96 cM) had a positive allelic substitution effect on GY (0.2%) and TGW (7.16%), but negative effect on GN (− 2.2%). The locus in chromosome 5A (98 cM) had positive effect on GY (0.18%) and GN (1.54%), but negative effect on TGW (− 2.85%) (Fig. 4).

Fig. 4
figure 4

Effect of four loci in chromosomes 6A (77–85 cM), 3B (99 cM), 2B (96 cM), and 5A (98 cM) associated with multiple traits a grain yield, b grain weight, and c grain number based on the means of all environments. The alleles were represented by 0 and 2 for each SNP

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Marker combinations and effects

We also identified the optimum marker combination that explained highest variation for GY, TGW, and GN using step-wise regression (Supplementary Tables 4, 5, and 6) and multiple regression analyses. Five marker combinations—IWA2963 (4B), IWB2774 (3B), IWB52628 (6A), IWB51659 (4B), and IWB72516 (2A)—explained 27% of the variation for GY based on multiple regression analysis, where as the population structure (Q3) explained 7% (Table 5). The marker IWA2963 (4B) explained 12% of the variation in GY based on LRR 2 and the other three markers explained 15% of the variance. The combination of 10 markers—IWB65271 (1B), IWB18267 (7D), IWB40900 (3B), IWA6949 (5A), IWB65783 (6A), IWB23810 (3D), IWB686 (5A), IWB32380 (2B), IWB2414 (2B), and IWB42660 (2B)—explained 31% of the variation for TGW, where as Q3 explained 28%. Multiple regression analysis identified the combination of 11 markers—IWB24502 (6D), IWB6365 (3A), IWB53601 (6A), IWB50952 (1A), IWB63867 (7A), IWB53861 (5D), IWB15488 (1D), IWB686 (5A), IWB68969 (7A), IWB9095 (3B), and IWB49242 (2B)—that explained 37% of the variation for GN. The population structure (Q3) explained 3% of the variation for GN.

Table 5 Multiple regression analysis of the significant markers; variance explained by each model (R 2) and likelihood-ratio based R 2 (LRR 2) for each additional marker for grain yield (GY), grain weight (TKW), and grain number (GN)
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We also fitted all significant MTAs for GY, TGW, and GN in step-wise regression to identify the most effective marker combination for GY (Supplementary Table 6). Multiple regression analysis identified a combination of 12 markers—IWB2774 (3B), IWB52628 (6A), IWB50952 (1A), IWA6949 (5A), IWB53601 (6A), IWB65783 (6A), IWB63656 (3A), IWB51659 (4B), IWB15488 (1D), IWB18267 (7D), IWB49242 (2B), and IWB686 (5A)—that explained 35% of the variation for GY, Q3 explaining 9% (Table 6).

Table 6 Multiple regression analysis of the makers associated with grain yield considering all traits: model R 2 and likelihood ratio based R 2 (LRR 2) for each additional marker in the model
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Analysis of marker by environment interaction using step-wise regression of the 12 significant markers on the BLUPs for grain yield in each environment indicated variation in the marker effects. The markers directly associated with GY—IWB2774 (3.35%) and IWB52628 (3.02%)—explained highest variation for GY on average than markers indirectly associated for GY, i.e. markers identified for TGW and GN (Table 7). The highest LRR 2 values for a marker was in MexI10 environment, IWB2774 explaining 12.01% variation for GY. Total variation explained by the twelve markers were highest in MexI10 (24.08%) followed by MexHD10 (21.24%).

Table 7 Marker by environment interaction of the twelve markers as percentage of variation explained for grain yield and variation explained by population structure (Q 3 ) matrix for grain yield in respective environments
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Association of known genes with the traits

We did candidate gene-based association mapping of several known genes. Results indicated that Rht-B1 and Vrn-D1a were associated with grain yield with a p value of < 0.001. Other genes were not significantly associated with any of the traits when a p value threshold of 0.001 was used. A blind association mapping—using marker score as trait—for the TaGW2-6A polymorphism in the WAMI population identified the location of the gene in chromosome 6A at 77–78 cM. However, in the combined analysis of BLUPs for TGW, the locus we identified was at 77 cM but individual analysis the locus was at 85 cM. A t-test of the TaGW2-6A haplotypes—Hap-6A-A and Hap-6A-G—with the phenotypic data of all individual environments indicated that the SNP is significantly associated with TGW in only two environments (Supplementary Table 9). The p value from t test was significant in Mex H10 (p = 0.002) and Nepal B10 (p = 0.02) at significant level of α = 0.05. In addition, the TaGW2-6A Hap 6A-G haplotype was superior in Mexico D10 but TaGW2-6A Hap-6A-A haplotype was superior in Nepal B10. In all other environments, the marker effect was not significant as denoted by standard error in bar plot (Supplementary Fig. 4).

Discussion

In the present study, we identified several MTAs for GY, TGW, and GN using large-scale multi-environment data in spring wheat. We observed that the combined analysis of environments had high heritability estimates and increased the power to detect causative loci. Large-scale multi-environment studies are associated with high G × E, which prompted us to reduce the environments from 31 to 10 based on heritability estimates of the traits. In our previous study, we successfully followed the same approach for flowering time where we used 19 environments with high heritability estimates and identified earliness per se (eps-D1) locus in CIMMYT spring wheat germplasm (Sukumaran et al. 2016). Phenotypic correlations between the environments for each trait were high, indicating the importance of research conducted at Mexican environments that is applicable several countries (Braun et al. 1996). TGW showed the highest correlation between the environments similar to our earlier study (Sukumaran et al. 2017).

The locus in chromosome 6A (77–85 cM) was associated with GY and TGW. We have detected the same locus important for GY, GN, and GW in temperate irrigated conditions in Cd. Obregon, Mexico in an earlier study (Sukumaran et al. 2015a). A QTL in chromosome 6A associated with TGW, GY, and green canopy duration was identified earlier in winter wheat and might be similar in spring wheat (Simmonds et al. 2014). Candidate gene based association mapping of the TaGW2-6A haplotype did not show significant association between the gene and TGW on BLUPs from combined analysis of environments. We observed the significant effect of this marker on TGW in two out of ten environments, and it was opposite in those environments. In Mex HD 10, the TaGW2-6A Hap-6A-G was superior whereas in Nepal the TaGW2-6A Hap-6A-A was superior. Taken together, it indicates that the effect of the gene is dependent on the environment and probably there could be another gene controlling the expression TaGW2-6A. Our study indicated that this gene does not show consistent and significant association with grain weight across different environments; however, it is close to the causative loci for TGW variation.

In addition to the 6A locus for GY and TGW, a common MTA for TGW and GN was detected in 5A at 98 cM. This locus was also associated with GN and TGW in temperate irrigated environments (Sukumaran et al. 2015a). A GWAS study using the 90 K SNP array in spring wheat also identified a similar genomic region associated with GY (Ain et al. 2015). Recently, a stable QTL on chromosome 5A associated with 6.9% increase in grain weight was identified which lead to 4% longer grains and 1.5% wider grains (Brinton et al. 2017b). The QTL contributes to increased pericarp cell length, thus contributing to grain weight We believe this might be the same locus in spring wheat and winter wheat but need to be further explored.

A chromosome 3B genomic region associated with grain yield was also reported in multiple studies (Bonneau et al. 2013; Lopes et al. 2013; Edae et al. 2014; Sukumaran et al. 2015a). The locus identified in chromosomes 3B (86–99 cM) was associated with multiple traits (GY, maturity, and chlorophyll content at vegetative state) in the temperate irrigated environments (Sukumaran et al. 2015a). An earlier study had identified MTAs on chromosome 3B at 70 cM for adaptation to density in the same WAMI panel (Sukumaran et al. 2015b). A QTL with large effect for GY was also identified in chromosome 3B using a different genetic map (Bonneau et al. 2013, 2017).

We will propose these four candidate regions in chromosomes 2B (96 cM), 3B (99 cM), 5A (98 cM), and 6A (77–85 cM) for further gene discovery and validation that is associated with the trade-off for grain weight and grain number. In general, it is possible to increase GY by increases in GN, but increases in GN is associated with decreased TGW. From our study, we found loci that are associated with a positive association between GY, TGW and GN.

Stepwise regression and multiple regression analysis identified the optimum combination significant markers for the traits. The additive effect of markers decreases as more number of markers are added to the model. We used population structure in the multiple regression model to avoid the overestimation of the marker effects from regression analysis. Likelihood ratio based R2 was estimated for each marker based on the marker substitution effect from multiple regression analysis (Sun et al. 2010). The best marker combinations for traits explained 27, 31, and 33% for GY, TGW, and GN, respectively. However, our analysis to find the optimum combination of markers found a marker based model that could explain 32% of GY, indicating a combination of makers for GY, TGW, and GN is important to select for GY in a breeding program, instead of marker for GY alone (27%). This indicated that the markers that are not directly related to the trait also has an effect on the trait and much of the variation is not explained when grain yield is dissected directly (Reynolds and Langridge 2016).

We also compared markers associated with GY, TGW, and GN with earlier studies. The MTA on chromosome 4B (66–68 cM) were close to the Rht-B1 locus in chromosome 4B (56 cM) identified by blind association analysis of Rht-B1 score. Candidate gene-based association analysis confirmed the association of Rht-B1 with grain yield (Supplementary Table 8). The MTA in chromosomes 2A (106 cM), 4A (151 cM), and 7A (35 cM) are novel loci associated with GY. Further analysis of the TGW MTAs showed the locus on chromosome 1B at 141–168 cM is close to the 1B/1R translocation from blind association analysis (Lopes et al. 2015). The locus in chromosome 7D (78 cM) was close to Vrn-D3 locus (91 cM) but we expect them to be different based on LD. The MTAs on 2A (143 cM), 2B (20, 26, and 145 cM), 3B (51 cM), 3D (148 cM), 5A (26 and 60 cM), and 6B (113 cM) for TGW are novel. Apart from the common loci for GN and other traits, the MTAs detected in chromosomes 1A (130 cM), 1D (51 cM), 3A (15 cM), 4B (81 cM), 5B (3–4 cM), 5D (203 cM), 6A (141 cM), 6D (77 cM), and 7A (135 cM) are novel in this population.

GWAS is a powerful technique to identify the genomic regions associated with traits of interest, but often with confounding effects of population structure in genetic analyses which was negotiated by the use of models accounting for population structure and familial relatedness (Zhu et al. 2008;Yu et al. 2006; Zhang et al. 2010). We compared the genomic regions detected in the study with previous studies on the same panel and with already known genes/QTLs detected. We identified four loci to be associated with GY and its components in chromosomes 2B, 3B, 5A, and 6A. Among them, the loci in chromosome 6A and 2B showed positive allelic substitution effect for GY and TGW. In many cases, GY is not strongly associated with TGW. Any positive association between GY, TGW, and GN is a perfect scenario for increasing overall GY by increasing GN and TGW.

Conclusions

Genome-wide association analysis identified several key genomic regions associated with grain yield and yield components. Among them, four of them showed a trade-off between thousand grain yield, grain weight, and grain number. A comparison of variation explained by markers associated with trait per se and its components indicated that higher variation is explained by the combination of markers for trait per se and its components. The genomic regions identified in the present study can be used for MAS and need to be further studied to fine map or clone genes.