An Algorithm for Constructing Principal Geodesics in Phylogenetic Treespace

Area of Science:

• Phylogenetics
• Computational Biology
• Data Visualization

Background:

• Phylogenetic analyses often yield multiple trees, posing challenges for summarization and visualization.
• Traditional methods like consensus trees offer limited insights into sample variability.
• Existing techniques such as consensus networks and multidimensional scaling have been applied to tree samples.

Purpose of the Study:

• To develop a novel stochastic algorithm for constructing a principal geodesic in treespace.
• To create a method analogous to principal component analysis for summarizing phylogenetic tree samples.
• To visualize variations in tree topology and branch lengths within a sample.

Main Methods:

• A stochastic algorithm searches parameter space to find a principal geodesic.
• The geodesic minimizes the sum of squared projected distances of tree data points.
• The method is analogous to principal component analysis for tree samples.

Main Results:

• The principal geodesic effectively summarizes the most variable features of tree samples, including topology and branch lengths.
• Visualization as an animation of smoothly changing trees provides intuitive insights.
• The methodology was successfully illustrated using experimental and simulated data sets.

Conclusions:

• The principal geodesic offers a powerful new way to understand and visualize samples of phylogenetic trees.
• This method provides greater insight into tree samples compared to previous approaches.
• A Java package, GeoPhytter, is available for constructing and visualizing principal geodesics.