Efficient algorithms for inferring evolutionary trees

Abstract

In this paper, we examine two related problems of inferring the evolutionary history of n objects, either from present characters of the objects or from several partial estimates of their evolutionary history. The first problem is called the Phylogeny problem, and second is the Tree Compatibility problem. Both of these problems are central in algorithmic approaches to the study of evolution and in other problems of historical reconstruction. In this paper, we show that both of these problems can be solved by graph theoretic methods in linear time, which is time optimal, and which is a significant improvement over existing methods. PERFECT PHYLOGENYLet M be an n by m 0-1 matrix representing n objects in terms of m characters that describe the objects; cell (iJ) of M has a value of one if and only if object i has character j . A phylogenetic tree for M is a rooted tree T where each object is attached to exactly one leaf of T, where each of the m characters is associated with exactly one edge of the tree and where, for any leaf w of T, the characters associated with the edges along the unique path from the root to w exactly specify the character vector of the objects at leaf w. In the example in Figure 1. the first matrix M has a phylogenetic tree T, but the second matrix M' does not.The interpretation of a phylogenetic tree is that it gives an estimate of the evolutionary history (in terms of branching pattern, but not time) of the objects, based on the following biological assumptions:(1) The root of the tree represents an ancestral object that has none of the present m characters; that is, in the ancestral object, the state of each character is zero.(2) Each of the characters changes from the zero state to the one state exactly once, and never from the one state to the zero state.The key feature of a phylogenetic tree (without which there would be no interesting problem) is that each character is associated with exactly one edge

Beaches of Islands of Tractability: Algorithms for Parsimony and Minimum Perfect Phylogeny Haplotyping Problems

“…that they can be placed at the leaves of an evolutionary tree within which each site mutates at most once. Haplotype matrices admitting a perfect phylogeny are completely characterised [8] [9] by the absence of the forbidden submatrix…”

Simple Reconstruction of Binary Near-Perfect Phylogenetic Trees

“…He showed that the BPP problem can be solved in linear time [8]. The problem we consider is an extension called the binary near perfect phylogeny reconstruction (BNPP).…”

“…Input Assumptions: If no pair of characters in input I contains the fourgamete property, we can use Gusfield's elegant algorithm [8] to reconstruct a perfect phylogeny. We assume that the all zeros taxa is present in the input.…”

“…Only characters corresponding to non-isolated vertices can mutate more than once in any optimal phylogeny (a simple proof follows from Buneman graphs [16]). Since all characters of C \ M mutate exactly once, the algorithm constructs a perfect phylogeny on this character set using Gusfield's linear time algorithm [8]. The perfect phylogeny is unique because of Lemma 2.…”

Efficient Algorithms for Descendent Subtrees Comparison of Phylogenetic Trees with Applications to Co-evolutionary Classifications in Bacterial Genome

“…Numerous phylogenetic inference methods, e.g. maximum parsimony, maximum likelihood, distance matrix fitting, subtrees consistency, and quartet based methods have been proposed over the years [15,1,14,26,17,27,4]; furthermore, it is rather common to compare the same set of species w.r.t. different biological sequences or different genes, hence obtaining various trees.…”