Hadamard Phylogenetic Methods and the n-taxon process

2008/06/09 by David Bryant, Bryant, David · 1 citation
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · #FOS: Biological sciences #Genetic diversity and population structure #Genomics and Phylogenetic Studies #Plant and animal studies #Populations and Evolution (q-bio.PE)

paper · pdf · doi:10.48550/arxiv.0806.1378

openalex publication_date 2008/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Hadamard transform of \citeHendy89a, Hendy89 provides a way to work with stochastic models for sequence evolution without having to deal with the complications of tree space and the graphical structure of trees. Here we demonstrate that the transform can be expressed in terms of the familiar \bP[\bt] = e^\bQ[\bt] formula for Markov chains. The key idea is to study the evolution of vectors of states, one vector entry for each taxa; we call this the n-taxon process. We derive transition probabilities for the process. Significantly, the findings show that tree-based models are indeed in the family of (multi-variate) exponential distributions.

Cited by

• Convergence-Divergence Models: Generalizations of Phylogenetic Trees Modeling Gene Flow Over Time

Related

• Approximate Bayesian computation for Markovian binary trees in phylogenetics
• Dimensional reduction for the general Markov model on phylogenetic trees
• A semialgebraic description of the general Markov model on phylogenetic trees
• Phylogenetic invariants: straightforward from the general Markov to equivariant models
• Phylogenetic mixtures and linear invariants for equal input models