A Tractable Variant Of The Single Cut Or Join Distance With Duplicated Genes

In this work, we introduce a variant of the Single Cut or Join distance that accounts for duplicated genes, in the context of directed evolution from an ancestral genome to a descendant genome where orthology relations between ancestral genes and their descendant are known. Our model includes two duplication mechanisms: single-gene tandem duplication and creation of single-gene circular chromosomes. We prove that in this model, computing the distance and a parsimonious evolutionary scenario in terms of SCJ and single-gene duplication events can be done in linear time. Simulations show that the inferred number of cuts and joins scales linearly with the true number of such events even at high rates of genome rearrangements and segmental duplications. We also show that the median problem is tractable for this distance.