# DIMACS Seminar on Math and CS in Biology

## Title:

An Exploration in Phylogenetic Space or How I Learned to Love the Tree

## Speaker:

- Dr. Peter Smouse
- Center for Theoretical and Applied Genetics
- Cook College, Rutgers University

## Place:

- DIMACS Seminar Room, CoRE Building, Room 431
- Busch Campus, Rutgers University

## Time:

- 3:00 PM
- Monday, April 24, 1995

## Abstract:

We have been exploring minimum spanning trees (MSTs) in a context
of human evolution, as determined for the mtDNA genome. There is
enough ambiguity in the data set, due to homoplasic mutation, that the
number of MSTs (each a maximally parsimonious solution) is truly vast,
far too many to evaluate exhaustively. In the process of exploring the
"tree space", we discover that "good trees" share several features:
(1) they are all quite similar (and I will present a method of
quantifying what I mean by the term "similar"); (2) they all resemble
the data closely (and I will present a way of gauging that); (3) they
minimize the sums of squared distances among all possible pairs of
entries, measured along the tree. While the enumeration problem is
Np-hard, defining the class of "good trees" is not difficult, and the
class occupies a portion of tree space that we might be able to
delineate effectively. The geometry of the problem, and how it
intersects with the graph theory, lends itself to such standard
techniques as principal coordinates analysis, quadratic programming,
and so on. Quite apart from the mathematical points, we learn
interesting things about translating the data into tree form and what
that means and what it doesn't mean.

Document last modified on April 24, 1995