The genus Avena (oats) contains diploid, tetraploid and hexaploid species that evolved through hybridization and polyploidization. Four genome types (named A through D) are generally recognized. We used GBS markers to construct linkage maps of A genome diploid (Avena strigosa x A. wiestii, 2n = 14), and AB genome tetraploid (A. barbata 2n = 28) oats. These maps greatly improve coverage from older marker systems. Seven linkage groups in the tetraploid showed much stronger homology and synteny with the A genome diploids than did the other seven, implying an allopolyploid hybrid origin of A. barbata from distinct A and B genome diploid ancestors. Inferred homeologies within A. barbata revealed that the A and B genomes are differentiated by several translocations between chromosomes within each subgenome. However, no translocation exchanges were observed between A and B genomes. Comparison to a consensus map of ACD hexaploid A. sativa (2n = 42) revealed that the A and D genomes of A. sativa show parallel rearrangements when compared to the A genomes of the diploids and tetraploids. While intergenomic translocations are well known in polyploid Avena, our results are most parsimoniously explained if translocations also occurred in the A, B and D genome diploid ancestors of polyploid Avena.