#### Event Title

Efficient Quartet Systems: A New Systematic Approach to Supertree Reconstruction

#### Poster Number

28

#### Faculty Mentor

Joseph Rusinko, Ph.D.

#### College

College of Arts and Sciences

#### Department

Mathematics

#### Location

Richardson Ballroom

#### Start Date

24-4-2015 3:20 PM

#### End Date

24-4-2015 4:50 PM

#### Description

A phylogenetic tree is described by quartets that show where a split in the tree should occur. The number of compatible quartets that define a tree is the number of taxa on the tree to the fourth power. Scientists often want to combine multiple phylogenetic trees, or input trees, to derive a “supertree.” This is typically done by giving a collection of all the quartets that define the input trees to tree reconstruction software such as MaxCut. However, the number of compatible quartets that define a supertree is often too large for MaxCut to handle and contains a lot of conflicting quartets. Therefore, it would be helpful to find a subset of quartets which would return a correct input tree so that, when the quartet systems defining the input trees are combined, there are not too many quartets for MaxCut to consider and a correct supertree is returned. An efficient quartet system is a collection of quartets which distinguish unique paths across a phylogenetic tree. An efficient quartet system is found by first distinguishing each internal vertex on a phylogenetic tree with pairs of taxa and then consistently using these vertex-distinguishing pairs to create quartets that distinguish the paths of the tree. An efficient quartet system reduces the number of quartets used to reconstruct a tree and, additionally, returns the correct tree for multiple different topologies of trees.

Efficient Quartet Systems: A New Systematic Approach to Supertree Reconstruction

Richardson Ballroom

A phylogenetic tree is described by quartets that show where a split in the tree should occur. The number of compatible quartets that define a tree is the number of taxa on the tree to the fourth power. Scientists often want to combine multiple phylogenetic trees, or input trees, to derive a “supertree.” This is typically done by giving a collection of all the quartets that define the input trees to tree reconstruction software such as MaxCut. However, the number of compatible quartets that define a supertree is often too large for MaxCut to handle and contains a lot of conflicting quartets. Therefore, it would be helpful to find a subset of quartets which would return a correct input tree so that, when the quartet systems defining the input trees are combined, there are not too many quartets for MaxCut to consider and a correct supertree is returned. An efficient quartet system is a collection of quartets which distinguish unique paths across a phylogenetic tree. An efficient quartet system is found by first distinguishing each internal vertex on a phylogenetic tree with pairs of taxa and then consistently using these vertex-distinguishing pairs to create quartets that distinguish the paths of the tree. An efficient quartet system reduces the number of quartets used to reconstruct a tree and, additionally, returns the correct tree for multiple different topologies of trees.

## Comments

Presented at the MAA Joint Mathematics Meeting, January 2015, and the South Carolina INBRE Spring Symposium, February 2015

Supported by an NIH-INBRE grant from the National Center for Research Resources and the National Institute of General Medical Sciences