Fig. 5

The DCJ distance does not care about mixing components, but the rank distance never mixes them. Here we see two series of operations transforming a fictitious genome A into a fictitious genome B. Both genomes have two chromosomes, one containing genes a and b, and the other containing genes c and d. (Top) This series of operations involves an integration, two inversions, and an excision of a circular piece. Notice how it mixes the two chromosomes right after the first operation. The total DCJ score of this series is 4, which is optimal for DCJ. However, the total rank score for this series is 8, which is not optimal for rank. (Bottom) This series of operations involves a linearization, two inversions, and a circularization. Notice that this process actually mutates each chromosome independently, without mixing them. Its total DCJ score is 4, which is optimal for DCJ. Its rank score is 6, which is optimal for rank. Therefore, as far as DCJ is concerned these two scenarios are equivalent, but for the rank distance only the bottom one is optimal