Hadamard Phylogenetic Methods and the n-taxon process

Details Hadamard Phylogenetic Methods and the n-taxon process Hadamard Phylogenetic Methods and the n-taxon process

2008-06-09

arxiv.org/abs/0806.1378v1

Biology

Quantitative Biology

Populations and Evolution

20 pages, 2 figures

Scientific paper

The Hadamard transform of \cite{Hendy89a, 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.

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