I received my Ph.D degree in 1999 from the Program in Applied Mathematics at the University of Arizona. I was awarded a National Science Foundation Postdoctoral Research Fellowship in 2000 and used it to work with Alan Hastings at the University of California in Davis for two years before taking an assistant professorship in Ecology and Evolutionary Biology at the University of Tennessee in Knoxville in 2002. I joined the faculty here at the University of Michigan in 2005 where I hold joint appointments in the Department of Mathematics and the Center for the Study of Complex Systems.
Broadly speaking, I am interested in the dynamics of ecological systems. I write and analyze mathematical models of particular biological systems in order to understand observed patterns and make predictions. My research foci include (1) the role of seasonality in shaping population dynamics, (2) the dynamics of host-pathogen systems including rabies, cholera, measles, and whooping cough, (3) population cycles, (4) laboratory microcosms as model systems, (5) statistical methods for nonlinear, stochastic systems with measurement error, and (5) dynamical approaches to phylogenetic comparative analysis. More generally, I am deeply interested in the development and analysis of new biological models for concrete systems.
I am engaged in a number of research projects. These include (1) a study of the ecological influences affecting rabies infection in bats, (2) a study aimed at understanding the role of decadal-scale climatic fluctuations in determining the incidence and severity of cholera outbreaks, (3) the development of generally-applicable mathematico-statistical techniques to bring nonlinear stochastic models of biological process into direct confrontation with time-series data, (4) a study aimed at disentangling the complex interactions of humans with their environment using anthropological and biological data from Sanak Island, off Alaska, and (5) the development of new techniques for phylogenetic comparative analysis based on a direct modeling approach. I am currently seeking students and postdocs interested in participating in any of these studies or in related areas.
NEW: Bio 202 Mathematics of Life, an Introduction to Quantitative Biology
WHO: Lower-division biology-bound or biology-curious students. In particular, the course welcomes students who may find the traditional mathematics sequence intimidating and/or for whom the relevance of the traditional sequence to biology is unclear. Majors of relevance include Biology, PitE, General Biology, EEB, MCDB, Microbiology, Plant Biology, premedicine, and pre-health.
WHY: This course gives majors in biology and related fields the opportunity to master the quantitative skills — including the elements of logic, statistics, probability, dynamics, data visualization, and scientific computing — needed to excel in the increasingly quantitative biological and bio-medical sciences. This course will satisfy the Quantitative Analysis 2 requirement for Program in Biology majors (i.e., it will substitute for Calculus II). It does not satisfy the prerequisites of higher math courses.
HOW: The course will be taught in an intensive, workshop/lab format, with short topical lectures, in-class discussions, and challenging exercises with opportunities for personalized guidance from the instructors. Instead of examinations or graded homework, students will track their progress via a graded notebook and perfect their ability to solve problems and communicate solutions through edited drafts of short papers based on challenging problems in biology. The course will cover the elements of statistics, data visualization, dynamics, probability, and scientific computing.
Read more and see the Course Guide.
Bio/Environ 281 General Ecology:
The course introduces the basic concepts and principles of ecology as applied to the study of individuals, populations, and communities of both plants and animals.
Course topics include:
the roles of physical and biotic factors influencing the distribution and abundance of organisms; the dynamics of population growth; species interactions including competition, predation, mutualism; the structure of ecological communities; ecological succession; and applications of ecology to problems of environment and resource management.
The course is a suitable prerequisite for intermediate and advanced courses in ecology.
EEB/Math 466 Mathematical Ecology:
Mathematical models are the backbone of ecological theory; they form the basis for modern approaches to understanding, managing, and predicting the dynamics of ecological systems. This course provides an overview of the major classes of ecological models, with an emphasis on ecological dynamics. We will focus on principles guiding the formulation of models and on the mathematical techniques that can be used to analyze them. We will examine deterministic and stochastic models, structured and unstructured models, single- and multiple-species models. Because ecological systems are typically nonlinear, we cannot often "solve" model equations: we employ techniques of nonlinear analysis, stochastic analysis, and numerical analysis to obtain results. This course will introduce many of these techniques in the context of ecological theory.
An additional goal of the course is to develop students' skills in the use of mathematical software. We will make extensive use of Matlab and R for numerical computations and Mathematica for symbolic computation.
Applied math and advanced ecology students interested in the use of mathematical models and theoretical, statistical, and computational ecology. The techniques introduced in the course will be useful to students from many disciplines, including chemical engineering, economics, natural resources, public health, and so on.
EEB 401 Interrogating Data with Models:
Ecologists are frequently taught statistical recipes that can be used to analyze data, e.g., correlation, regression, analysis of variance. These classical methods have been designed with analytical tractability foremost in mind. The assumptions on which they depend are such that they typically afford only an oblique perspective on the specific ecological questions we wish to answer. This is a pity, since hard-won data are effectively squandered when we can ask only crude questions of them.
EEB 800 Theoretical Ecology Seminar