YST_Core_N550_1013locSNP data file for STRUCTURE and DAPC analysis of "CORE" data setYST_Full_N591_747locSNP data file for STRUCTURE and DAPC analysis of "FULL" data setYST_Outgroups_N392_440locSNP data file for STRUCTURE and DAPC analysis of "OUTGROUPS" data setYST_Core_N550_1013loc_BAPSSNP data file for BAPS analysis of "CORE" data setYST_Full_N591_747loc_BAPSSNP data file for BAPS analysis of "FULL" data setYST_Outgroups_N392_440loc_BAPSSNP data file for BAPS analysis of "OUTGROUPS" data setYST_Core_N550_1013loc_BayeScanSNP data file for BayeScan analysis of "CORE" data setYST_Core_N550_1013loc_BSYST_Full_N591_752loc_BayeScanSNP data file for BayeScan analysis of "FULL" data setYST_Full_N591_752loc_BSYST_Outgroups_N392_441loc_BayeScanSNP data file for BayeScan analysis of "OUTGROUPS" data setYST_Outgroups_N392_441locYST_Core_N550_HP-rare_8regSNP data file for HP-Rare analysis of "CORE" datasetYST_Core_N550_Arlequin_8regSNP data file for analysis of population genomic diversity and pairwise Fst in ArlequinStacks_commands_YST_3datasetsCommands used for denovo analyses of "FULL", "CORE", and "OUTGROUPS" datasets in STACKS 1.20.Stacks_commands.txtYST_EUR-AM_943loc_ABCSNP data file for DIYABC analysis of YST in both Eurasia and AmericasYST_NoPNW_5reg_943loc_rev.snpYST_EUR_1069loc_ABCSNP data file for DIYABC analysis of YST in three regions of Eurasia (western Europe, eastern Europe, and Asia)YST_EUR_3reg_1069loc_rev.snpYST_EUR-AM_943loc_BayeScanSNP data file for BayeScan analysis of data set used for DIYABC analysis of YST in both Eurasia and AmericasYST_NoPNW_943loc_singCAYST_EUR_1069loc_BayeScanSNP data file for BayeScan analysis of data set for DIYABC analysis of YST in EurasiaYST_EURonly_3reg_1069locMEC_15-1264_Sample_DataList of samples and sequencing run informationSample_codesSampling sites for seeds of yellow starthistle (*Centaurea solstitialis*) and related taxa, including sampling site information (nearest city, country/state, continent, latitude, and longitude), and year of collection. Location numbers correspond to locations depicted in Fig S1. CESO = *C. solstitialis*, CENE = *C. nicaeensis*, CEPA = *C. pallescens*, CEME = *C. melitensis*.

Identifying sources of genetic variation and reconstructing invasion routes for non-native introduced species is central to understanding the circumstances under which they may evolve increased invasiveness. In this study, we used genome-wide single nucleotide polymorphisms to study the colonization history of Centaurea solstitialis in its native range in Eurasia and invasions into the Americas. We leveraged this information to pinpoint key evolutionary shifts in plant size, a focal trait associated with invasiveness in this species. Our analyses revealed clear population genomic structure of potential source populations in Eurasia, including deep differentiation of a lineage found in the southern Apennine and Balkan Peninsulas and divergence among populations in Asia, eastern Europe, and western Europe. We found strongest support for an evolutionary scenario in which western European populations were derived from an ancient admixture event between populations from eastern Europe and Asia, and subsequently served as the main genetic ‘bridgehead’ for introductions to the Americas. Introductions to California appear to be from a single source region, and multiple, independent introductions of divergent genotypes likely occurred into the Pacific Northwest. Plant size has evolved significantly at three points during range expansion, including a large size increase in the lineage responsible for the aggressive invasion of California's interior. These results reveal a long history of colonization, admixture, and trait evolution in C. solstitialis, and suggest routes for improving evidence-based management decisions for one of the most ecologically and economically damaging invasive species in the western United States.