SAQ: semi-algebraic quartet reconstruction method

TL;DR

SAQ is a new phylogenetic quartet reconstruction method based on semi-algebraic descriptions, capable of handling complex models with rate heterogeneity and performing well even when assumptions are violated.

Contribution

The paper introduces SAQ, a novel algebraic approach for quartet reconstruction that is consistent with general Markov models and robust to model violations.

Findings

Outperforms existing methods on simulated data under the general Markov model.

Maintains high accuracy even when data violate model assumptions.

Effective for phylogenetic analysis with rate heterogeneity.

Abstract

We present the phylogenetic quartet reconstruction method SAQ (Semi-algebraic quartet reconstruction). SAQ is consistent with the most general Markov model of nucleotide substitution and, in particular, it allows for rate heterogeneity across lineages. Based on the algebraic and semi-algebraic description of distributions that arise from the general Markov model on a quartet, the method outputs normalized weights for the three trivalent quartets (which can be used as input of quartet-base methods). We show that SAQ is a highly competitive method that outperforms most of the well known reconstruction methods on data simulated under the general Markov model on 4-taxon trees. Moreover, it also achieves a high performance on data that violates the underlying assumptions.