Heuristics for the Phylogeny Problem

A phylogeny is a tree that relates taxonomic units, based on their similarity over a set of characters. The problem of nding a phylogeny with the minimum number of evolutionary steps is one of the main problems in comparative biology. In this work, we study diierent heuristic approaches to the phylogeny problem under the parsimony criterion. New algorithms based on GRASP, VNS, and tabu search metaheuristics are proposed. All heuristics are implemented and compared under the same framework, leading to consistent and thorough comparative results. Computational results are reported for benchmark instances from the literature. 1. Phylogeny Problem. A phylogeny (or an evolutionary tree) is a tree that relates groups of species, populations of distinct species, populations of the same species, or homologous genes in populations of distinct species, indistinctly denoted by taxons 3, 32, 33]. Such relations are based on the similarity over a set of characters. Tree leaves represent the taxons under analysis, while interior nodes represent hypothetical (unknown) ancestors. Characters are independent attributes used to compare taxons. A character may represent e.g. a morphologial attribute or a position within a sequence of nucleotides. Each character take values on a nite set of possible states. For example, if some character describes a position in a sequence of nucleotides, then the possible states are \Adenine", \Cytosine", \Guanine", and \Timine". Each taxon is deened by their character states. Binary characters are those who have only two possible states, which represent the presence or the absence of some attribute. Instances of the phylogeny problem (with binary characters) are then characterized by 0-1 matrices, in which each element (i; j) corresponds to the state of character j within taxon i. Each row represents the characteristic vector of some taxon. Diierent criteria may be used in the evaluation of phylogenetic trees. Each state change along a branch of the phylogenetic tree is counted as an evolutionary step. The parsimony criterion states that the best phylogeny is the one that can be explained by the minimum number of evolutionary steps. It is frequently said that this criterion is the best one if the probability of character mutation is very small 22, 24, 31]. Given a set of taxons deened by a set of characters, the phylogeny problem (under parsimony) consists in nding a phylogeny with the minimum number of evolutionary steps. The phylogeny problem is one of the main problems in comparative biology.