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Dimensions of Level-1 Group-Based Phylogenetic Networks
Elizabeth Gross1, Robert Krone2, Samuel Martin3
1Department of Mathematics, University of Hawai'i at Mānoa, Mānoa, HI, USA.
Bulletin of Mathematical Biology
|June 17, 2024
Summary
We developed a formula for the dimension of algebraic varieties representing evolutionary histories on phylogenetic networks with horizontal gene transfer or hybridization. This aids in understanding complex evolutionary models.
Area of Science:
- Evolutionary biology
- Algebraic geometry
- Computational phylogenetics
Background:
- Phylogenetic networks model complex evolutionary histories involving reticulate evolution.
- Markov models on these networks can be represented as algebraic varieties.
- Understanding the dimensions of these varieties is key to algebraic analysis.
Purpose of the Study:
- To derive a formula for the dimension of algebraic varieties associated with triangle-free level-1 phylogenetic networks.
- To explore applications of this dimension formula in evolutionary modeling and identifiability.
Main Methods:
- Utilizing algebraic geometry to study phylogenetic networks.
- Developing a formula for the dimension of codimension zero toric fiber products.
- Applying group-based evolutionary models to phylogenetic networks.
Main Results:
- A novel formula for the dimension of the variety of a triangle-free level-1 phylogenetic network under a group-based model.
- A dimension formula for codimension zero toric fiber products.
Conclusions:
- The derived formula provides a new tool for analyzing evolutionary models on phylogenetic networks.
- The results have implications for understanding parameter identifiability in evolutionary studies.
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