The minimum evolution problem: Overview and classification

Molecular phylogenetics studies the hierarchical evolutionary relationships among organisms by means of molecular data. These relationships are typically described through a weighted tree, called phylogeny, whose leaves represent the observed organisms, internal vertices represent the intermediate ancestors, and the edges represent evolutionary relationships between pairs of organisms. Molecular phylogenetics provides several criteria to select a phylogeny among plausible alternative ones. Usually, such criteria can be expressed in terms of objective functions, and the phylogenies optimizing them are referred as optimal. One of the most important criteria is Minimum Evolution (ME) which states that the optimal phylogeny for a given set of organisms is the one whose sum of the edge weights is minimal. Finding the phylogeny satisfying the minimum evolution criterion involves the solution of an optimization problem, called Minimum Evolution Problem (MEP), notoriously NP-Hard. This article offers an overview of the minimum evolution problem, and discusses its specific versions arising from the literature.