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Using Phylogenetic Analysis to Investigate Eukaryotic Gene Origin

Using Phylogenetic Analysis to Investigate Eukaryotic Gene Origin

Published on: August 14, 2018

Phylogenetic trees and Euclidean embeddings.

Mark Layer¹, John A Rhodes²

¹Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK, 99775, USA.

Journal of Mathematical Biology

|May 9, 2016

Summary

This summary is machine-generated.

A square root transformation of phylogenetic tree distances enables taxa embedding into Euclidean space. This method offers new insights and reinterprets tree-building algorithms like Neighbor-Joining (NJ).

Keywords:

Distance methods Multidimensional scaling Neighbor joining Phylogenetic trees

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Area of Science:

Phylogenetics
Computational Biology
Evolutionary Biology

Background:

A prior observation demonstrated that a square root transformation of distances on phylogenetic trees allows taxa embedding into Euclidean space.
The previous justification for this embedding relied on a diffusion model of continuous character evolution.

Purpose of the Study:

To provide a direct, elementary explanation for the square root transformation embedding of taxa into Euclidean space.
To offer substantial additional insight into the mathematical underpinnings of this embedding.
To utilize this embedding to reinterpret differences between Neighbor-Joining (NJ) and BIONJ tree-building algorithms.

Main Methods:

A direct mathematical derivation was used to explain the square root transformation embedding.
The derived embedding was applied to analyze and compare the NJ and BIONJ tree-building methods.

Main Results:

A clear, elementary explanation for the embedding of taxa into Euclidean space via square root transformation was established.
The embedding was shown to reflect underlying tree structures within the data.
Differences between NJ and BIONJ algorithms were reinterpreted through the lens of this Euclidean embedding.

Conclusions:

The square root transformation provides a powerful tool for visualizing and analyzing phylogenetic relationships in Euclidean space.
This embedding offers a novel perspective for understanding and comparing different phylogenetic tree construction algorithms.
The method highlights the geometric properties inherent in phylogenetic data.