Brachypodium distachyon (n=5) is a diploid and has been widely used as a genetic model. Brachypodium stacei (n=10) and B. hybridum (n=15) are species that are related to B. distachyon, leading to a theory that they are part of a polyploid series based on x = 5. Several lines of evidence suggest that this hypothesis is incorrect and that the genomes of the three taxa may have evolved by a more complex process. We constructed an optical whole-genome BioNano genome (BNG) map for each species and pairwise aligned the maps together. The maps confirmed that B. distachyon and B. stacei are both diploid, in spite of B. stacei having twice as many chromosomes as B. distachyon, and that B. hybridum is an allopolyploid formed from hybridization between B. distachyon and B. stacei. This study also demonstrated the use of BNG maps in the detection of structural variants among the genomes and their quantification.