Dimensions of Group-Based Phylogenetic Mixtures.

Area of Science:

• Evolutionary biology
• Algebraic statistics
• Computational geometry

Background:

• Phylogenetic mixture models are crucial for understanding evolutionary processes.
• These models are geometrically represented by joins of toric varieties.
• Nondefectiveness of these varieties is key for parameter identifiability.

Purpose of the Study:

• To determine conditions under which phylogenetic join varieties are nondefective.
• To advance combinatorial identifiability for group-based phylogenetic mixture models.
• To extend understanding of nondefectiveness in evolutionary models.

Main Methods:

• Analyzing group-based Markov models of evolution.
• Investigating properties of toric varieties and their joins.
• Applying algebraic geometry to phylogenetic models.

Main Results:

• Established nondefectiveness for a significant number of phylogenetic join varieties.
• Demonstrated nondefectiveness for group-based models with r trees and n leaves when n is greater than or equal to 2.
• Provided improved bounds for claw trees and computational evidence for small n.

Conclusions:

• Nondefectiveness is a common property for many phylogenetic join varieties.
• The findings contribute to the combinatorial identifiability of phylogenetic mixture models.
• This research bridges evolutionary modeling with advanced geometric and algebraic techniques.