How Fitch-Margoliash Algorithm can Benefit from Multi Dimensional Scaling

Area of Science:

• Bioinformatics
• Computational Biology
• Evolutionary Biology

Background:

• Phylogenetic methods often represent genetic sequences as points in high-dimensional space.
• Studying evolutionary processes in these spaces involves challenges like the concentration of measured phenomena.

Purpose of the Study:

• To investigate the influence of high-dimensional space properties on phylogenetic reconstruction.
• To evaluate the Fitch-Margoliash algorithm, a Least Squares method, in this context.

Main Methods:

• Examined the relationship between Least Squares methods (Fitch-Margoliash) and Multi-Dimensional Scaling (MDS).
• Introduced concepts of "continuity" and "trustworthiness" to mitigate risks like "false neighborhoods" and "tears" in dimensionality reduction.
• Proposed new criteria for phylogeny construction.

Main Results:

• Least Squares methods for phylogeny are closely related to MDS.
• Identified "false neighborhood" and "tears" as key risks in dimensionality reduction for phylogenetics.
• Demonstrated that new criteria enhance distance preservation and robustness in phylogenetic trees.

Conclusions:

• Improvements in MDS can benefit Least Squares-based phylogenetic methods.
• Addressing dimensionality reduction risks is crucial for accurate evolutionary inference.
• The proposed criteria offer a more robust approach to building phylogenies, honoring Professor W.M. Fitch's legacy.