Abstract
Genomic maps often do not specify the order within some groups of two or more markers. The synthesis of a master map from several sources introduces additional order ambiguity due to markers missing from some sources. We represent each chromosome as a partial order, summarized by a directed acyclic graph (DAG), to account for poor resolution and missing data. The genome rearrangement problem is then to infer a minimum number of translocations and reversals for transforming a set of linearizations, one for each chromosomal DAG in the genome of one species, to linearizations of the DAGs of another species. We augment each DAG to a directed graph (DG) in which all possible linearizations are embedded. The chromosomal DGs representing two genomes are combined to produce a single bicoloured graph. From this we extract a maximal decomposition into alternating coloured cycles, determining an optimal sequence of rearrangements. We test this approach on simulated partially ordered genomes and on marker data from maize and sorghum chromosomal maps.
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