Phylogenetic Networks Based on the Molecular Clock Hypothesis

ABSTRACT

A classical result in phylogenetic trees is that a binary phylogenetic tree adhering to the molecular clock hypothesis exists if and only if the matrix of distances between taxa is ultrametric. The ultrametric condition is very restrictive. In this paper we study phylogenetic networks that can be constructed assuming the molecular clock hypothesis. We characterize distance matrices that admit such networks for 3 and 4 taxa. We also design two algorithms for constructing networks optimizing the least-squares fit.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.5 PATTERN RECOGNITION
      I.5.2 Design Methodology
          Subjects: Classifier design and evaluation

Additional Classification:
  E. Data
  E.1 DATA STRUCTURES
      Subjects: Trees

  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on matrices

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.6 Optimization
          Subjects: Least squares methods

  J. Computer Applications
  J.3 LIFE AND MEDICAL SCIENCES
      Subjects: Biology and genetics

General Terms:
Algorithms, Design

Keywords:
Phylogenetic Networks, molecular clock hypothesis, least-squares fit