Lior Pachter and Bernd Sturmfels will be offering this seminar in the fall,
Wednesdays, 3-5 PM, in 939 Evans.
Nota Bene: No meeting on Wednesday, August 27th.
Students may enroll for 2 units using CCN 55197.
Enrolled students will be expected to complete a research project.
Ruchira Datta and Ian Sammis are coordinating the seminar.
Please email Ruchira Datta if you want to be added to the mailing list,
which is archived here.

NEW! Josephine Yu, of the Polyhedra & Experiments group, has made an example of a higher-dimensional tree.

Here are some possible project ideas:

1. Experiment with PHYLIP, and look at Felsenstein's book.
2. Experiment with SPLITSTREE, and look at Huson's papers.
3. Section 7.6 in the book: GROUP-VALUED DISSIMILARITIES
4. Section 7.7 in the book: PERTURBING TREE METRICS
5. Section 8.7 "THE FELSENSTEIN ZONE": Extend Theorem 8.7.1 to |X| = 5.
6. Write a program (inefficient is fine for starters) which computes the DISTANCE BETWEEN two given metric TREES, starting from the description in [Billera-Holmes-Vogtmann] of the geodesics in the space of trees. Consult with Nina Amenta. Apply this program to some large multiple alignments in order to identify sequences under selection.
7. Study the paper [Evans/Speed, Annals of Statistics 1993] on the 3-PARAMETER KIMURA MODEL for trees and use 4TI2 to compute the Markov basis of the resulting toric model in some small cases.
8. Implement a k-dissimilarity map reconstruction algorithm.
9. Study Atteson's paper on the neighbor joining algorithm: "The Performance of Neighbor-Joining Methods of Phylogenetic Reconstruction" (Algorithmica Vol. 25) and describe the NJ map on the space of trees.
10. Study the Thorne-Kishino-Felsenstein model and related models by Mitchison and Holmes that allow for insertions and deletions.
11. Comparative Genomics via Phylogenetic Invariants for Jukes-Cantor Semigroups. (Blanchette and Sankoff).
12. Study the paper: Determining the Number and Structure of Phylogenetic Invariants by Thomas Hagedorn (Adv. Applied Math. 24 (1): 1--21)
    Abstract: The method of invariants is an important approach in biology for determining phylogenetic information which avoids the problems involving long branch lengths that plague other methods. In this paper, we verify the conjecture on the number of algebraic generators for the ideal of polynomial invariants. We also study rational and analytic invariants and prove several criteria concerning when it suffices to work with polynomial invariants.

Here are some interesting links:

Phylogenetics, a new book by Charles Semple and Mike Steel

Inferring Phylogenies, a new book by Joe Felsenstein

Mathematics of Evolution and Phylogeny, a recent conference in Paris;
the program includes links to the webpages of the speakers

Workshop on "Phylogenetic Combinatorics",
a conference that took place in Germany in 2002

Workshop on "Phylogenetic Combinatorics",
a conference that took place in Germany in 2001

Symposium on Combinatorial Methods in Biological Data Analysis,
a conference that took place in Germany in 2000

DIMACS Workshop on Mathematical Hierarchies and Biology
a conference that took place at Rutgers University in 1996;
the proceedings were published.

Phylogenies: An Overview,
by Susan Holmes

Maximum Likelihood on Four Taxa Phylogenetic Trees: Analytic Solutions,
by Benny Chor, our very own Amit Khetan, and Sagi Snir

Phylogenetic Invariants for the General Markov Model of Sequence Mutation,
by Elizabeth Allman and John Rhodes

Landscapes on Spaces of Trees,
by Oliver Bastert, Dan Rockmore, Peter F. Stadler, and Gottfried Tinhofer

Haplotyping as Perfect Phylogeny: A direct approach,
by Dan Gusfield

Phylogeny Numbers,
by Fred S. Roberts and Li Sheng

Bibliography of Systematics, Phylogeny, and Taxonomy,
compiled in 2000 by Joseph Malkevitch

Tim Sluckin, a mathematician and member of the
AHRB Centre for the Evolutionary Analysis of Cultural Behaviour

The Graph of Life, the April 2003 Puzzling Adventures column
by Dennis E. Shasha in Scientific American

and more phylogenetics everywhere...