Gene Tree Correction by Leaf Removal and Modification: Tractability and Approximability

The reconciliation of a gene tree and a species tree is a well-known method to understand the evolution of a gene family in order to identify which evolutionary events (speciations, duplications and losses) occurred during gene evolution. Since reconciliation is usually affected by errors in the gene trees, they have to be preprocessed before the reconciliation process. A method to tackle with this problem aims to correct a gene tree by removing the minimum number of leaves (Minimum Leaf Removal). In this paper we show that Minimum Leaf Removal is not approximable within factor b logm, where m is the number of leaves of the species tree and b > 0 is a constant. Furthermore, we introduce a new variant of the problem, where the goal is the correction of a gene tree with the minimum number of leaf modifications. We show that this problem, differently from the removal version, is W[1]-hard, when parameterized by the number of leaf modifications.

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