Developing a statistically powerful measure for quartet tree inference using phylogenetic identities and Markov...

Area of Science:

• Computational Biology
• Phylogenetics
• Evolutionary Biology

Background:

• Phylogenetic inference methods based on phylogenetic invariants and Markov invariants have garnered renewed interest.
• These methods utilize polynomial functions of sequence site patterns for tree reconstruction.
• The relationship and practical utility of these invariant-based approaches for phylogenetic inference remain unclear.

Purpose of the Study:

• To unify and compare phylogenetic and Markov invariants within a common framework, focusing on binary sequence data and quartets.
• To develop and evaluate novel invariant-based phylogenetic inference methods satisfying desirable statistical properties.
• To assess the performance of these new methods against existing approaches.

Main Methods:

• Developed a common framework for analyzing phylogenetic and Markov invariants for binary sequence data.
• Defined three key statistical properties for invariant-based phylogenetic methods: reordering invariance, Markov process stability, and continuous-time dependence.
• Proposed a statistically bias-corrected Markov invariants approach and extended phylogenetic invariants to satisfy the defined properties.

Main Results:

• A simulation study revealed that the proposed bias-corrected Markov invariants method is highly effective for phylogenetic inference.
• The binary case uniquely allows Markov invariants to be expressed as linear combinations of phylogenetic invariants.
• For models with more than two states (e.g., DNA sequences), phylogenetic invariants alone cannot satisfy all three statistical properties.

Conclusions:

• The bias-corrected Markov invariants method offers a powerful and statistically sound approach to phylogenetic inference.
• The distinct mathematical relationship between Markov and phylogenetic invariants in the binary case has significant implications.
• Phylogenetic invariants alone are insufficient for satisfying all desired statistical properties in multi-state models, highlighting the importance of Markov invariants.