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Analysis of Self-Similarity in Phylogenetic Trees
Mathematics and Statistics
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River streams, blood systems, fracture processes in solids, percolation of a liquid through a porous media are all modeled and studied using tree graphs. In many cases, such tree networks are self-similar, retaining their statistical structure on different levels of the hierarchy. The most studied particular class of self-similar trees is so-called Tokunaga model, which is a two-parameter model for trees with side branching. This project explores the self-similarity paradigm for the evolutionary “Tree of Life.” The primary goal of this project is to determine whether self-similarity, Tokunaga self-similarity and related Horton constraints apply to phylogenetic trees. The results of the project suggest that phylogenetic trees are self-similar, and satisfy the Horton constraints. We also find that phylogenetic trees are Tokunaga self-similar, though this result requires further analysis. Furthermore, our findings suggest that the existing conventional models for phylogenetic trees do not adequately describe their structure. The findings broaden the realm of the tree self-similarity concept and provide a useful modeling constraint on evolutionary trees.