Segment of a consensus directed acyclic graph. A typical segment of a directed acyclic graph representing the consensus map of one barley linkage group is shown. Each oval represents one bin of SNP markers, using POPA names for SNPs. Where an oval contains more than one SNP, it means that there was no evidence of recombination in any mapping population between those markers. The observed recombination frequencies between marker bins are shown. The exact order of marker bins cannot be solved with certainty unless markers are shared between maps. Recombination frequencies are often not proportional to physical distance, nor consistent, when comparing two or more maps from different mapping populations. Therefore directed acyclic graphs provide a more exact description of the limit of knowledge of the marker order than does a linear map derived using approximations based on recombination values. See the text for further discussion.