REU -- Mathematical Phylogenetics and the Space of Trees

Summer 2014

Instructor: Seth Sullivant, office: 3114 SAS Hall, email:

Graduate Student Mentor: Colby Long, office: 4123 SAS Hall, email:

Students: Mercedes Coleman, Cody Fitzgerald, Amber Holmes, Emily Smith

REU Products: Poster Final Project Report

Description: Phylogenetics is the area of biology concerned with inferring ancestral relationships between collections of taxa (e.g. species). An ancestral history of species is usually summarized by a phylogenetic tree. Phylogenetics is a rich area for interactions between mathematics and biology, and mathematical tools in phylogenetics include: discrete math, probability, statistics, algebra and geometry.

This REU will focus on the mathematical study of tree space. Tree space is a geometric object which consists of the set of all metric trees and with a natural distance measure comparing those trees. In many situations, different data sets or different methods for analyzing the same data can yield different trees. Given a collection of inferred trees, how do we compare them? Is there a natural notion of a consensus tree or an average tree? Tree space provides useful ways to address these questions, by phrasing the questions as geometric operations.

After spending a few days developing background on the mathematical aspects of phylogenetics, we will work on reading papers and identifying open problems to tackle.

Basic Reading:

Advanced Reading:

LateX Resources: