An algebraic analysis of the two state Markov model on tripod trees

TL;DR

This paper provides a comprehensive algebraic analysis of the two-state Markov model on tripod trees, identifying conditions for model inference from data and extending these results to more complex quartet trees, aiding phylogenetic reconstruction.

Contribution

It fully analyzes the two-state Markov model on tripod trees, establishing conditions for inference and extension to quartet trees, which advances understanding in phylogenetic modeling.

Findings

Derived conditions for model inference from observations.

Identified when extensions to quartet trees are possible.

Discussed cases where extensions fail.

Abstract

Methods of phylogenetic inference use more and more complex models to generate trees from data. However, even simple models and their implications are not fully understood. Here, we investigate the two-state Markov model on a tripod tree, inferring conditions under which a given set of observations gives rise to such a model. This type of investigation has been undertaken before by several scientists from different fields of research. In contrast to other work we fully analyse the model, presenting conditions under which one can infer a model from the observation or at least get support for the tree-shaped interdependence of the leaves considered. We also present all conditions under which the results can be extended from tripod trees to quartet trees, a step necessary to reconstruct at least a topology. Apart from finding conditions under which such an extension works we discuss example cases for which such an extension does not work.