Consensus genetic maps: a graph theoretic approach

A genetic map is an ordering of genetic markers constructed from genetic linkage data for use in linkage studies and experimental design. While traditional methods have focused on constructing maps from a single population study, increasingly maps are generated for multiple lines and populations of the same organism. For example, in crop plants, where the genetic variability is high, researchers have created maps for many populations. In the face of these new data, we address the increasingly important problem of generating a consensus map an ordering of all markers in the various population studies. In our method, each input map is treated as a partial order on a set of markers. To find the most consistent order shared between maps, we model the partial orders as directed graphs. We create an aggregate by merging the transitive closure of the input graphs and taking the transitive reduction of the result. In this process, cycles may need to be broken to resolve inconsistencies between the inputs. Tlie cycle breaking problem is NP-hard, but the problem size depends upon the scope of the inconsistency between the input graphs, which will be local if the input graphs are from closely related organisms. We present results of running the resulting software on maps generated from seven populations of the crop plant Zea Mays.