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Combinatorics of Tandem Duplication Random Loss Mutations on Circular Genomes

The tandem duplication random loss operation (TDRL) is an important genome rearrangement operation in metazoan mitochondrial genomes. A TDRL consists of a duplication of a contiguous set of genes in tandem followed by a random loss of one copy of each duplicated gene. This paper presents an analysis of the combinatorics of TDRLs on circular genomes, e.g., the mitochondrial genome. In particular, results on TDRLs for circular genomes and their linear representatives are established. Moreover, the distance between gene orders with respect to linear TDRLs and circular TDRLs is studied. An analysis of the available animal mitochondrial gene orders shows the practical relevance of the theoretical results.