Hypothesis Testing With Rank Conditions in Phylogenetics.

Area of Science:

• Computational Biology
• Phylogenetics
• Bioinformatics

Background:

• Phylogenetic models describe sequence evolution across taxa.
• Four-taxon models utilize flattening matrices and rank conditions.
• Singular Value Decomposition (SVD) methods like SVDQuartets leverage these properties.

Purpose of the Study:

• To explore the SVD score as a statistical test for phylogenetic data.
• To assess if observed phylogenetic data align with a specific quartet tree model.
• To develop methods for hypothesis testing in phylogenetics using SVD scores.

Main Methods:

• Utilized singular value decomposition (SVD) on flattening matrices derived from sequence data.
• Developed a hypothesis testing framework using the SVD score as a test statistic.
• Approximated the distribution of the SVD score and derived upper bounds for p-values.

Main Results:

• The SVD score can be used to test phylogenetic hypotheses.
• Approximations for the SVD score distribution and p-value bounds were established.
• Hypothesis tests were applied to simulated phylogenetic data.

Conclusions:

• The SVD score offers a quantifiable method for evaluating phylogenetic tree hypotheses.
• The developed statistical framework provides a means to assess the fit of data to specific quartet trees.
• Findings have implications for interpreting rank-based inference methods in phylogenetics.