Phylogeny and biogeography of the Pleistocene Holarctic steppe and semi-desert goosefoot plant Krascheninnikovia ceratoides

•Uniformly diploid and uniformly tetraploid populations of K. ceratoides were found.•The ancestral area probably was in the region of Mongolia, northern China and Middle Asia.•The species spread from the ancestral area to the east (North America) and to the west (Europe).•The spread may be related to steppe and semi-desert expansion during Pleistocene glacial periods.