 et al. 2004;Fu et al. 2005;Zhang et al. 2008). The rescaled genetic map from Wang et al. (2014) was used to indicate map locations of these SNPs. The Tagger function of Haploview v4.2 (Barrett et al. 2005) was used to select informative SNPs. To infer population structure, we used 1090 highly informative, non-redundant representative SNPs (tagSNPs) selected using the tagger function r 2 = 0.25, and for the calculation of the kinship matrix, we used 5563 non-redundant SNPs using the tagger function r 2 = 1.0.
Genetic diversity (D) of each subpopulation was calculated with the same 5563 SNPs using the formula: where p is the frequency of the i allele at the l locus and L is the number of loci (Weir 1996). D was calculated using SNPs with less than 10% missing values. Calculations were done using different minor allele difference levels (MAFs > 0.1, > 0.05, nd > 0) to facilitate comparisons with previous studies. Population structure was estimated using STRU CTU RE 2.3.4 (Pritchard et al. 2000), as described by Maccaferri et al. (2015). Four hypothetical subpopulations were determined as most likely proxies of the population structure, and the corresponding Q-matrices (4 × 262) of population membership coefficients were obtained. The STRU CTU RE plot was drawn using a modified version of the R script STRU CTU RE PLOT (Ramasamy et al. 2014). Population structure was also explored by principal component analysis (PCA) using the R package "ade4" (Dray and Dufour 2007).
To quantify the genetic variation explained by sowing times at the places where the lines were originated, we performed an analysis of molecular variance (AMOVA) using the R package "pegas" with 1000 permutations and Euclidean distance as genetic distance (Paradis 2010). Lines from CMT, UCD and other Mediterranean climates were classified as developed under fall sowing (DuF), whereas those from UIA, WAS, UMN, SDK and other high-latitude regions were classified as developed under spring sowing (DuS). Eighteen lines were excluded from this analysis because we did not have sufficient information (Table S1).

Linkage disequilibrium
Linkage disequilibrium (LD) between markers on each chromosomes was calculated in Tassel v4.3 (Bradbury et al. 2007). The critical r 2 value, beyond which LD was considered to be due to genetic linkage, was determined by taking the parametric 95th percentile of the squareroot-transformed r 2 data of unlinked markers (genetic distance > 50 cM) (Breseghello and Sorrells 2006). The scatter plot of r 2 versus genetic distance (cM) was fitted using a nonlinear model described by Remington et al. (2001) in R (R Core Team 2017). This model estimates LD (r 2 ) using recombination rate and effective population size, and adjusts for a low level of mutation and sample size (Sved 1971;Hill and Weir 1988;Remington et al. 2001). The R function nls (nonlinear least squares method) was used to fit the model. The intersection of the r 2 threshold and the fitted regression was used to estimate the average extent of LD for the complete genome, the three genomes and the individual chromosomes.

Genome-wide association study
The adjusted traits and the filtered SNPs were used for GWAS using the compressed mixed linear model approach Zhang et al. 2010) carried by Tassel v5 (Bradbury et al. 2007) with the implemented EMMA (Kang et al. 2008) and P3D (Zhang et al. 2010) algorithms to reduce computing time. Heterozygous genotypes were treated as missing values in the analysis. The kinship matrix (K matrix) was calculated in Tassel v.4 using the 5563 non-redundant SNPs, and the population structure matrix (Q matrix) from the STRU CTU RE analysis described above. The Q + K mixed linear model (MLM) was used for all traits based on comparisons of different methods as described in Maccaferri et al. (2015).
From the GWAS for each trait, we first selected SNPs that were significant (P < 0.05, marker-wise) in at least three of the five environments, with at least one environment with highly significant differences (P < 0.01). All the SNPs that satisfied these criteria are presented in File S1. Within this primary subset, we then selected those QTL that were also significant (P < 0.05) in at least one of the biparental populations in at least two environments. These SNPs are designated hereafter as "validated SNPs" in File S1. SNPs that passed the primary criteria and were in LD at r 2 > 0.2 were grouped together as one QTL, and the SNP with the most significant effect was selected as the representative SNP of the QTL. QTL for different traits that overlap in any of the markers in their, respectively, LD groups were considered colocated.
The probability of an SNP being significant by chance simultaneously for three GWAS and two biparental population experiments was estimated to be less than 6.25E−08 (0.0 5 × 0.05 × 0.01 × 0.05 × 0.05). Based on this number, the probability of at least one error in the 22,226 SNPs was estimated as 1 − (1 − 6.25E−08) 22,226 = 0.0014 (per trait). This formula assumes that all the tests are independent, which is not the case for many linked SNPs. If we consider only the 5563 nonredundant SNPs, the probability of one or more false positives among the validated SNPs is estimated to be less than 0.0003 per trait. In summary, the combination of these five selection criteria results in a very stringent selection criterion for the validated SNPs.
Real QTL that were not segregating in the biparental populations or that were not detected because of the small number of lines used per population could be lost using the above criteria. To avoid this, we selected a second set of SNPs that were not validated in the biparental populations but that were highly significant (P < 0.01) in the GWAS in at least four environments (three for KNS and SNS that were not evaluated in Obregon). The probability of an SNP being significant by chance in this subset was estimated to be less than 5.5E−05 (or 5.5E−03 for KNS and SNS, using the 5563 non-redundant SNPs). These QTL, henceforth "highly significant non-validated QTL," are highlighted in File S1 but are not discussed in detail in this study.

Population structure analysis reflected geographic origin
Results from STRU CTU RE indicated that the 262 wheat lines (Table S1) used in the present study can be grouped into four populations identified by different colors in Fig. 1a, mostly reflecting the geographic origin of the lines. The close relationship between the wheat lines from SDK and UMN is evident in both the STRU CTU RE and principal component analyses (PCA, Fig. 1b). The CMT and UCD lines overlap in the first principal component (PC1) and are partially separated by the second principal component (PC2). A slight differentiation between these programs is also evident in the STRU CTU RE analysis, where CMT lines showed a higher proportion of the population identified in yellow, whereas UCD showed a higher proportion of the population identified in red. Accessions from UIA and WAS were in the same region of PC1 and were differentiated only by PC2 (Fig. 1b). In the STRU CTU RE analysis, genotypes from UIA were mainly a mixture of the populations identified by the red and purple colors, whereas genotypes from WAS were mainly from the population identified in red (Fig. 1a). The group classified as "Other" was a complex mixture of populations, in agreement with their multiple sources (Fig. 1a).
We then classified the accessions into two subgroups based on sowing time at the regions where they were developed (Table S1). The first subgroup included 151 lines developed under fall-sowing (DuF) conditions (UCD, CMT, and OTHER accessions from Mediterranean regions). The second subgroup included 93 lines developed under spring sowing (DuS) conditions (SDK, UMN, UIA, WAS, and OTHER accessions from high latitudes). Eighteen lines were not classified (Table S1). The analysis of molecular variance (AMOVA) showed that sowing time at the place of origin accounted for 4.1% of the total molecular variation, breeding programs within sowing times accounted for 11.7% of the variation, and accessions within breeding programs accounted for the remaining 84.2% (Table 1).
ANOVAs between DuS and DuF accessions, using environments as blocks, showed that DuS accessions headed earlier (3.25 d, P = 0.0015), were taller (6.31 cm, P < 0.0001) and had lower grain yields (436.7 kg/ha, P = 0.0002) than DuF accessions. This last result is not surprising, given that DuF accessions were developed in environments more similar to the ones used in this study than DuS accessions. The reduced grain yield of DuS accessions was associated with decreases in both grain weight (0.5 mg, P = 0.025) and grain number (1.2 grains, P = 0.027), as well as higher levels of water stress (NWI3,