The Structural Asymmetry and Scaling of Phylogenetic Trees Open Access

Abstract

Understanding the patterns and processes of evolution is very challenging. Because they carry inherent information about evolution, phylogenetic trees become a prevalent tool in evolutionary biology. In this work, we studied large-scale phylogenetic trees in terms of tree asymmetry and distribution of branch length. We used two indicators: the ratio of the size of smaller child clade to the size of parent clade and the ultrametric distances between two consecutive nodes. By comparing with a random null model and a critical model, we found that both the topology and timing of trees are scale-invariant and could be described by a power law distribution. This scale-invariance suggests that similar forces drive the evolution over a large range of scales. However, the observed patterns of several trees are better described by the null tree from the Markov process. Future works could attempt to explain this deviation.

Table of Contents

Table of Contents

1.Introduction...................................................................................................... 1

1.1 Definitions about phylogenetic trees........................................................... 2

1.2 The critical model by Boettcher and Paczuski.......................................... 4

1.3 the markov model............................................................................................. 5

1.4 Asymmetric Tree structure............................................................................ 6

1.5 Ultrametricity.................................................................................................. 9

2. Methods.............................................................................................................. 12

2.1 Newick tree format........................................................................................ 12

2.2 data................................................................................................................... 13

2.3 implementation................................................................................................ 14

2.4 Asymmetric Tree structure.......................................................................... 14

2.5 Ultrametric distances................................................................................... 15

3. Results and Discussion.............................................................................. 15

3.1 Tree topology.................................................................................................. 15

3.2 Ultrametric distances................................................................................... 18

4. references........................................................................................................ 25

5. appendix.............................................................................................................. 31

About this Honors Thesis

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School	Emory College
Department	Physics
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Physics, Theory Biology, Ecology Biology, Evolution and Development
Keyword	memory Phylogenetic tree scale-free binary tree ultrametric power law evolution
Committee Chair / Thesis Advisor	Stefan Boettcher, Emory University
Committee Members	Effrosyni Seitaridou, Emory University Daniel Weissman, Emory University

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