Genetic structure was studied using SNPs in approximate linkage equilibrium, which were obtained using the LD pruning algorithm in PLINK v.1.90p17 (link). This calculates pairwise R2 for all marker pairs in sliding windows with a size of 50 markers and an increment of 5 markers and removes the first marker of pairs, in which R2 < 0.5.
Analysis with the ADMIXTURE parametric model35 (link) was performed with a number of ancestral populations (K) ranging from 1 to 15. One thousand bootstrap replicates were run to estimate parameter standard errors. The most suitable number of K was selected in correspondence with the lowest cross‐validation (CV) error. Cultivars were assigned to one specific ancestral population when the membership coefficient qi for that cluster was >0.6. If not, they were considered admixed.
PCA on SNP data was performed using SVS v.8.8.3 (Golden Helix Inc.), and a three-dimensional plot was obtained using the top three components identified with default parameters of the additive model.
TreeMix (v1.12)36 (link) was used to infer splits and mixtures among Italian, French, Spanish, and U.S. germplasm, testing a model with no migration, and models with all the three possible migration events among the four populations. The “get_f()” R function was used to obtain the variance explained by each model.
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