Orthology Relation and Gene Tree Correction: Complexity Results

Abstract

Tree-oriented methods for inferring orthology and paralogy relations between genes are based on reconciling a gene tree with a species tree. On the other hand, many tree-free methods, mainly based on sequence similarity, are also available. The link between orthology relations and gene trees has been formally considered recently from the angle of reconstructing phylogenies from orthology relations. Here, we rather consider this link from a correction point of view. While a gene tree induces a set of relations, the converse is not always true, as a set of relations is not necessarily in agreement with any gene tree. How can we minimally correct an infeasible set of relations? On the other hand, given a gene tree and a set of relations, how to minimally correct a gene tree in order to fit the set of relations? In this paper, various objective functions are considered for the minimality criterion, among them the Robinson-Foulds distance between the initial and corrected gene tree. All considered problem variants are shown to be NP-complete.