To define a relevant number of genetic groups in 632 worldwide bread wheat landraces and to assign lines to genetic groups, we used haplotypes defined above and the algorithm implemented in STRUCTURE software (35). We assumed a single domestication event and restricted our analysis to the correlated frequency model (36). We set other parameters at their default values using the admixture model and infer ALPHA option. We used a 10,000 burn-in period and 10,000 iterations. Allele frequencies in each of the K clusters (from 2 to 15) were estimated, and the percentage of genome derived from each cluster was estimated for each accession. Pairwise differentiation indexes FST (37) were calculated with the hierfstat R package (38) to estimate the distances between groups.

Geographical projections of PCoA axes or admixture matrixes were obtained using a Kriging method. Kriging is an interpolation method that relies on a model where the covariance matrix of admixture coefficients or principal coordinate scores exponentially decreases with distance (39). The spatial prediction is based on a Gaussian model. It supposes that the covariance matrix is stationary. The one we used is implemented in TESS3 (40).

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