A Tractable Variant of the Single Cut or Join Distance with Duplicated Genes

The Rooted SCJ Median with Single Gene Duplications

“…Evolutionary Model. In this work, following [10], we consider a model of directed evolution in which, when comparing two genomes, we assume one, denoted by A, is a trivial genome and an ancestor of the other genome, denoted by D.…”

“…Problem Statements. In [10], Feijão et al introduced the directed SCJ-TD-FD (d-SCJ-TD-FD) distance problem that asks to compute the minimum number of SCJ, TD and FD operations needed to transform A into D, denoted by d DSCJ (A, D). They showed that this problem is tractable and that the distance can be computed using a simple set-theoretical formula, extending naturally the distance formula for the SCJ with no duplication model.…”

“…A first median problem was also introduced in [10], the directed SCJ-TD-FD (d-SCJ-TD-FD) median problem, defined as follows: given D 1 , . .…”

“…In [23] it was shown that in an evolutionary model including SCJ and whole-chromosome duplications, the pairwise distance problem is tractable. More recently, we introduced a variant of SCJ including single-gene duplications where the distance between an ancestral genome and a descendant genome can be computed, when orthology relations between the descendant and ancestral genes are provided [10]. We also showed that a directed median problem where the median is the ancestor of k given genomes is tractable, again by reduction to a MWM problem.…”

“…. D k , and we are looking for a median M , whose gene content and orthology relation to the given genomes are provided, that minimizes the sum of the directed distances between A and M , and M and the D i s, in the distance model defined in [10]. In Sect.…”