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Abstract
IntroductionA gene tree for a gene family is often discordant with the containing species tree because of its complex evolutionary course during which gene duplication, gene loss and incomplete lineage sorting events might occur. Hence, it is of great challenge to infer the containing species tree from a set of gene trees. One common approach to this inference problem is through gene tree and species tree reconciliation.ResultsIn this paper, we generalize the traditional least common ancestor (LCA) reconciliation to define a reconciliation between a gene tree and species tree under the tree homomorphism framework. We then study the structural properties of the space of all reconciliations between a gene tree and a species tree in terms of the gene duplication, gene loss or deep coalescence costs. As application, we show that the LCA reconciliation is the unique one that has the minimum deep coalescence cost, provide a novel characterization of the reconciliations with the optimal duplication cost, and present efficient algorithms for enumerating (nearly-)optimal reconciliations with respect to each cost.ConclusionsThis work provides a new graph-theoretic framework for studying gene tree and species tree reconciliations.
Highlights
A gene tree for a gene family is often discordant with the containing species tree because of its complex evolutionary course during which gene duplication, gene loss and incomplete lineage sorting events might occur
We show that the least common ancestor (LCA) reconciliation has the minimum duplication and loss cost [9,15], and the minimum deep coalescence cost
We present a novel characterization of the reconciliations with the optimal duplication cost, and develop efficient algorithms for enumerating optimal reconciliations with respect to each cost model
Summary
A gene tree for a gene family is often discordant with the containing species tree because of its complex evolutionary course during which gene duplication, gene loss and incomplete lineage sorting events might occur. One common approach to this inference problem is through gene tree and species tree reconciliation. It provides an unprecedented opportunity to infer phylogenetic trees from multilocus and genomics data. One approach to inferring phylogeny from multilocus data is to reconstruct a gene tree from each locus and to combine the resulting trees into a phylogeny, called the containing species tree. Given a gene tree for a gene family and a containing species tree, a reconciliation between them represents an evolutionary scenario of the gene family within the evolutionary history represented by the species tree [4]. To study gene duplication history, gene tree and species tree are reconciled to minimize the number of gene duplications and/or losses. It has been shown that the so-called least common ancestor (LCA) reconciliation has the minimum duplication and loss cost [9,15]
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