Abstract

We consider the following basic problem in phylogenetic tree construction. Let $\mathcal{P} = \{T_1, \ldots, T_k\}$ be a collection of rooted phylogenetic trees over various subsets of a set of species. The tree compatibility problem asks whether there is a tree $T$ with the following property: for each $i \in \{1, \dots, k\}$, $T_i$ can be obtained from the restriction of $T$ to the species set of $T_i$ by contracting zero or more edges. If such a tree $T$ exists, we say that $\mathcal{P}$ is compatible. We give a $\tilde{O}(M_\mathcal{P})$ algorithm for the tree compatibility problem, where $M_\mathcal{P}$ is the total number of nodes and edges in $\mathcal{P}$. Unlike previous algorithms for this problem, the running time of our method does not depend on the degrees of the nodes in the input trees. Thus, it is equally fast on highly resolved and highly unresolved trees.

Highlights

  • Building a phylogenetic tree that encompasses all living species is one of the central challenges of computational biology

  • The tree compatibility problem asks whether there exists a phylogenetic supertree T for the set of species k i=1

  • A phylogenetic tree is a rooted tree T where every internal node has at least two children, along with a bijection λ that maps each leaf of T to an element of a set of species, denoted by L(T )

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Summary

Introduction

Building a phylogenetic tree that encompasses all living species is one of the central challenges of computational biology. The resulting trees are synthesized into a single phylogeny – a supertree – for the combined set of species This approach, proposed in the early 90s [2, 15], has been used successfully to build large-scale phylogenies (see, e.g., [3, 10]). The tree compatibility problem asks whether there exists a phylogenetic supertree T for the set of species k i=1. We present an algorithm that solves the compatibility problem for rooted trees in O(MP log MP ) time, where MP is the total number of vertices and edges in the trees in P. This running time is independent of the degrees of the internal nodes of the input trees

Previous Work
Our Contributions
Contents
Phylogenetic Trees
Profiles and Compatibility
The Triplet Graph
Testing Compatibility
Implementation
Discussion
Full Text
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