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Phylogenetic Networks

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Part of the Foundations for Undergraduate Research in Mathematics book series (FURM)

Abstract

Phylogenetics is the study of the evolutionary relationships between organisms. One of the main challenges in the field is to take biological data for a group of organisms and to infer an evolutionary tree, a graph that represents these relationships. Developing practical and efficient methods for inferring phylogenetic trees has led to a number of interesting mathematical questions across a variety of fields. However, due to hybridization and gene flow, a phylogenetic network may be a better representation of the evolutionary history of some groups of organisms. In this chapter, we introduce some of the basic concepts in phylogenetics and present related research projects on phylogenetic networks that touch on areas of graph theory and abstract algebra. In the first section, we describe several open research questions related to the combinatorics of phylogenetic networks. In the second, we describe problems related to understanding phylogenetic statistical models as algebraic varieties. These problems fit broadly in the realm of algebra, but could be more accurately classified as problems in algebraic statistics or applied algebraic geometry.

Notes

Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant No. DMS-1616186 and Grant No. DMS-1620109.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.University of Hawai‘i at MānoaHonoluluUSA
  2. 2.The College of WoosterWoosterUSA
  3. 3.Hobart and William Smith CollegesGenevaUSA

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