For the last fifteen years, my primary research interests have been in phylogenetics, and phylogenetic modeling. I am particularly interested in models of DNA site subsitution and the multispecies coalescent model describing the formation of gene trees within a rooted metric species tree.
Recently, with post-doc J. Mitchell and graduate student H. Banos, our group has implemented a new statistically consistent method of species network inference under the Network Multispecies Coalescent Model. The R package MSCquartets implements some statistical hypothesis tests for testing if quartets on gene trees might have arisen under the NMSC, and constructs a distance table for NANUQ, the species network topology estimator.
A current graduate student S. Yourdkhani is working to prove that the profile mixture model of Susko, Linker and Roger is identifiable using algebraic techniques. She has also worked with J. Rhodes creating a metric quartet distance on gene trees.
Just last summer I began collaborating with J. Degnan, M. Owen, and C. Solis-Lemus on further gene tree/species tree research with the help of an AIM SQuaRE grant. In recent years my research has been funded by the NIH and the NSF.
For a list of publications since I became interested in phylogenetics, click here, and visit the software link above for information on software development.
Interestingly, I got interested in mathematical biology, and phylogenetics in particular, as an outgrowth of a teaching project started by J. Rhodes and colleagues. This work resulted in the undergraduate textbook "Mathematical Models in Biology: An Introduction" published by Cambridge University Press in 2004. An electronic solutons manual and a list of known errata is available on request.
Salmon Problem: Determine the ideal defining the fourth secant variety of P^3 x P^3 x P^3.
Some details, including
a prize for its solution.
In 2007, I posed the salmon problem while at the IMA. This problem took on a wonderful life of its own.
If you have access to MathSciNet, seach on the phrase `salmon problem' to follow the thread.
Set theoretic version solved! Congratulations to Shmuel Friedland for solving the set-theoretic version of the problem (spring 2010)! Further progress by Dan Bates and Luke Oeding (2010). Still further progress by Friedland, Gross (April 2011). And Claudio Raciu (2012). And by Daleo and Hauenstein (2016).