Research Interests.

In general, I am deeply interested in ecological dynamics because they have so much to tell us about biology underlying them. I am interested in modeling particular systems, in analyzing particular models, and in developing general methods for modeling and analysis. I am presently pursuing several research projects.

Dynamics of cholera in India and Bangladesh.

From the theoretical point of view, this is an interesting system, for several reasons. Since the intrinsic dynamics of cholera are strongly seasonal and nonlinear, the stochastic models of cholera dynamics are quite interesting. Also, there exist large amounts of high-quality data on cholera incidence and mortality. A major goal of this research is to attempt to disentangle the intrinsic long-time-scale dynamics of cholera from the effects of extrinsic climatic drivers such as slow changes in monsoonal patterns and the El Niño-Southern Oscillation. This is an NSF-funded research project, under the auspices of the Ecology of Infectious Diseases program. I am doing this work in collaboration with a number of other researchers, here at UM (including Mercedes Pascual), at Princeton, in Washington DC, and abroad.

New methods for statistical inference using nonlinear, stochastic models with measurement error and incomplete information.

I am very excited about this project, which is about developing general-purpose methods for estimating parameters and doing model selection on nonlinear stochastic processes. Ecological processes are nonlinear and are stochastic, yet until recently, statistical approaches for dealing with such models have not existed.

Direct modeling approaches to phylogenetic comparative analysis.

In this project, which is again funded by an NSF grant, my colleague Marguerite Butler (University of Hawai'i) and I are developing and applying new methods for directly modeling the stochastic processes hypothesized to be active in the evolution of quantitative characters. We have developed some statistical software to aid in the analysis. I am enthused about this project because the basic approach can be extended in a large number of interesting and important directions.

I would welcome any student with excellent quantitative skills and a sharp mind to work on any or all of these projects. I feel certain that each of them will have a big impact on the field. Of course, I am also always willing to have a good student who wants to work on projects of his or her own as well. I accept students through three programs: Ecology & Evolutionary Biology (EEB), Applied Interdisciplinary Mathematics (AIM), and Mathematics. For more information on these programs, go to

• Ecology & Evolutionary Biology (www.eeb.lsa.umich.edu/eeb/graduates/),
• Applied & Interdisciplinary Mathematics (www.math.lsa.umich.edu/aim-grad/), or
• Mathematics (www.math.lsa.umich.edu/graduate/).