It has recently become clear that many invasive species have evolved in situ via hybridization or polyploidy from progenitors which themselves are introduced species. For species formed by hybridization or polyploidy, genetic diversity within the newly formed species is influenced by the number of independent evolutionary origins of the species. For recently formed species, an analysis of genetic structure can provide insight into the number of independent origin events involved in the formation of the species. For a putative invasive allopolyploid species, the number of origins involved in the species formation, the genetic diversity present within these origins, and the level of gene flow between independent origins determines the genetic composition of the neospecies. Here we analyze the genetic structure of the newly formed allopolyploid species, Salsola ryanii, a tumbleweed which evolved within the last 20–100 years in California. We utilize the genetic structure analysis to determine that this new species is the result of at least three independent allopolyplodization events followed by gene flow between the descendants of independent origins.