Edgar A. Duéñez-Guzmán

Research

As part of a collaboration between Sergey Gavrilets and Jonathan Losos, a model to study adaptive radiation on Anolis lizards is being developed.

This is an individual-based model with explicitly genetics in a squared array of patches. For this model, the environment in each patch is considered as a two dimensional continuum describing the distribution of branch diameters at each heights. Each individual lizard has traits specifying the preference for a certain height and diameter as well as the particular strength of those preferences. To calculate mating preferences and crowding factors (carrying capacity) it is, thus, necessary to compute parametrized integrals with no known analytical solution.

My involvement on this project has been two-fold:

• Optimize (working with Michael Vose) the calculation of the integrals to achieve the required performance.
• Help with the implementation of an efficient parallel version of the model to run on NICS's supercomputer Kraken

With the talk integration of parametrized integrands, I presented our solution to the numerical integration problem at the Fifth International Conference of Applied Mathematics and Computation in Plovdiv, Bulgaria. We were able to obtain theoretical bounds for the relative error, and several orders of magnitude improvement in both performance and accuracy with respect to canned numerical integration routines like GSL , NAG and Maple. The article is available here, along with the presentation slides.

The implementation challenges of running this model in Kraken, and our approach at solving them were presented at the Cray Users Group conference in Atlanta, 2009. The article can be accessed here.