The ABCs of MGR with DCJ

We study the small phylogeny problem in the space of multichromosomal genomes under the double cut and join metric. This is similar to the existing MGR (multiple genome rearrangements) approach but it allows, in addition to inversion and reciprocal translocation, operations of transposition and block interchange. Empirically, with chloroplast and mammalian data sets, it finds solutions as good as or better than MGR when the latter operations are prohibited. Permitting these operations allows quantitatively better solutions where part of the reconstructed ancestral genomes may be included in circular chromosomes. We discuss the biological likelihood of transpositions and block interchanges in the mammalian data.