Gene tree correction for reconciliation and species tree inference

Abstract

Background: Reconciliation is the commonly used method for inferring the evolutionary scenario for a gene family. It consists in "embedding" inferred gene trees into a known species tree, revealing the evolution of the gene family by duplications and losses. When a species tree is not known, a natural algorithmic problem is to infer a species tree from a set of gene trees, such that the corresponding reconciliation minimizes the number of duplications and/or losses. The main drawback of reconciliation is that the inferred evolutionary scenario is strongly dependent on the considered gene trees, as few misplaced leaves may lead to a completely different history, with significantly more duplications and losses. Results: In this paper, we take advantage of certain gene trees' properties in order to preprocess them for reconciliation or species tree inference. We flag certain duplication vertices of a gene tree, the "non-apparent duplication" (NAD) vertices, as resulting from the misplacement of leaves. In the case of species tree inference, we develop a polynomial-time heuristic for removing the minimum number of species leading to a set of gene trees that exhibit no NAD vertices with respect to at least one species tree. In the case of reconciliation, we consider the optimization problem of removing the minimum number of leaves or species leading to a tree without any NAD vertex. We develop a polynomial-time algorithm that is exact for two special classes of gene trees, and show a good performance on simulated data sets in the general case.

Correcting gene tree by removal and modification: Tractability and approximability

“…NAD nodes are considered as potential results of errors in a gene tree, since each NAD node represents a contradiction between the structure of a gene tree and a species tree that is not directly explainable by gene duplications. Motivated by this observation, some recent approaches aim to correct a gene tree by modifying its structure via polytomy refinement [21] or by removing misplaced leaves/labels [22].…”

“…The combinatorial approach considered in [22,23], asks for the minimum number of leaves/labels to be removed so that the computed gene tree does not contain NAD nodes. In [22,23], the complexity of two combinatorial problems related to the removal of leaves/labels (Minimum Leaf Removal and Minimum Label Removal) has been investigated.…”

“…In [22,23], the complexity of two combinatorial problems related to the removal of leaves/labels (Minimum Leaf Removal and Minimum Label Removal) has been investigated. In [23] the two problems have been shown to be APX-hard, even when each label has at most two occurrences in the gene tree.…”

“…NAD nodes are considered as potential results of errors in a gene tree, since each NAD node represents a contradiction between the structure of a gene tree and a species tree that is not directly explainable by gene duplications. Motivated by this observation, some recent approaches aim to correct a gene tree by modifying its structure via polytomy refinement [21] or by removing misplaced leaves/labels [22].The combinatorial approach considered in [22,23], asks for the minimum number of leaves/labels to be removed so that the computed gene tree does not contain NAD nodes. In [22,23], the complexity of two combinatorial problems related to the removal of leaves/labels (Minimum Leaf Removal and Minimum Label Removal) has been investigated.…”

“…Motivated by this observation, some recent approaches aim to correct a gene tree by modifying its structure via polytomy refinement [21] or by removing misplaced leaves/labels [22].…”