###### Academic background

Ph.D. University of California, Berkeley, Energy and Resources, December 2004

M.S. University of Illinois, Urbana-Champaign, Physics, 1999

AB Columbia University, Physics, 1994

###### Research interests

In my lab we study community ecology, focusing on the influence of interspecific competition on community structure, and what insights patterns of community structure might provide about the mechanisms by which competing species coexist. Competitive coexistence fascinates us because the biodiversity occurring in nature is puzzling given the expectation that among competing species, the best one should simply win. Also, the mechanisms of coexistence likely have an important influence on the functioning and stability of ecosystems, and role of biodiversity in that functioning and stability. We also have other interests beyond competition.

We focus on developing theory, but, especially in our work on competition, in developing theory we often aim specifically to improve ecologist's ability to gain empirical insight into communities in nature. We derive more refined empirical expectations, which better take into account system complexities. We also carry out theoretical studies aimed at informing how empirical approaches might be better carried out. Finally, we develop mathematical machinery for calculating theoretically relevant properties of specific systems. We also at times carry out empirical work, or collaborate with others on empirical work. Our theoretical work involves both mathematical and computational approaches. Our empirical work is largely focused on plant communities, especially forests.

###### Competition and community structure research activities:

**1) Development of fundamental aspects of niche theory**

The classical answer to the question of how competing species coexist in nature is that species coexist stably by differing from each other in some way that lessens the competitive influence of species on each other compared to their influence on themselves. The classical "niche theory" arising from this idea also suggests that, among a set of competing species, not only must there be differences between species, but these differences must be "large enough" if coexistence is to occur--i.e. there are system-specific "limits to similarity". However, there is actually a great deal of mathematical development needed still to make these concepts fully rigorous and general. High on the to do list is to fully reformulate these principles for coexistence that is not only stable but also robust to variation in environmental parameters. Furthermore, we want to be able to calculate the robustness of coexistence in particular systems. In my lab we are working to make these fundamental aspects of niche theory more rigorous, general, and applicable to particular systems.

**2) Development of neutral theory as a quantitative process-based null model in ecology, and development of stochastic niche theory**

Lately ecologists have wondered about an alternative to the classical "niche theory" answer to how species coexist. Instead of being different enough to stably coexist, perhaps species are simply similar to one another in fitness in a given environment, and hence persisting there together for a long period of time. The recently proposed "neutral" theory of ecology is aimed at describing the structure of such non-stable, purely fitness-equalized, communities. In this case community structure is shaped entirely by dispersal and stochasticity in the birth, death, and speciation and extinction processes. Neutral theory may be an accurate description of some coexistence, especially in highly diverse systems. However, it has the potential to play a more important role in community ecology, similar to the role an analogous theory has played in evolutionary biology, as a quantitative process-based null model whose rejection indicates the presence of processes of interest, in this case niche differentiation and habitat filtering.

However, it has not yet lived up to this potential. When the neutral model fits data, it seems a stochastic niche model might do just as well. When the neutral model fails, it may be only because it simplifies demographic details unrelated to niches. In my lab we are carrying out the theory development needed to construct more informative tests of neutral theory. This includes: a) identifying what aspects of the complexity influencing dispersal and demographic stochasticity should be included in the neutral models we test, b) gaining insight into what sorts of departures niche differentiation will lead to in patterns of community structure when acting in concert with dispersal limitation and demographic stochasticity (this is the "stochastic niche theory" part), and how detectable those departures are, and c) thinking carefully about how tests of neutral theory might be constructed in such a way that meaningful departures can be more easily detected, and working to carry out such tests on tropical forest data sets.

**3) Overcoming challenges in linking trait patterns with niche processes, especially for forest communities**

Recently there has been a drive among community ecologists to understand coexistence of species in communities in terms of the ‘functional traits’ they exhibit, meaning traits that impact the performance of organisms. Functional traits provide a more tangible, physical picture that may lead to insight into structural similarities across communities of a given type, and are critical for connecting vegetation dynamics with ecosystem properties. Ecologists have been looking for patterns of dispersion and evenness in the distribution of species in functional traits as a sign that niche differentiation is enabling coexistence.

We think functional trait approaches to community ecology are an exciting line of research. Our focus has been on the theoretical basis for the patterns being looked for. Most of these recent studies cite limiting similarity theory as their inspiration. But there are some important disconnects between that theory and empirical expectations of trait patterning. There is also the issue of whether the traits ecologists are choosing to study are actually important for competition, and hence traits that we would expect niche differentiation along, and how to go about selecting such traits. We have been working to highlight and synthesize the disconnects between theory and empiricism, and are studying mechanistic stochastic niche models to refine empirical expectations. We are also developing an approach to more rigorously link differentiation in specific traits to coexistence mechanisms they might drive, and beginning to carry it out for the George Reserve forest, by linking tree traits to aspects of demographic performance in a mechanistic model of competition for light. Along the way we are also further developing models of competition for light to better understand the demographic tradeoffs that can allow for stable coexistence for this resource. Finally we are interested in the potential for functional trait patterning to provide insight into the ecology of invasive species, and have begun to consider how it might do so for a particular example, the invasion of autumn-olive Elaeagnus umbellate of the George Reserve forest.

###### Other research interests:

We are interested in other topics in community ecology as well. Being interested in community structure as a window into process, we also study community structure in its own right. We focus on identifying key aspects of the spatial and abundance distribution of species shaping community or "macroecological" patterns (the patterns you see when you take a coarse-grained look at ecological systems, potentially at large scales). We are also interested in the application of spatial scaling patterns of diversity for estimating extinction rates from habitat loss and fragmentation and climate change. We also have an interest in the evolution of species interactions in a spatial context, and ultimately in how spatial structure influences the evolutionary assembly of whole food webs and their resulting stability properties. Finally, another current interest is in the role of competition and other factors in species' range shifts under climate change, in particular the replacement of one mouse species by the other (Peromyscus maniculatis gracilis by P. leucopus) at their range boundaries in Michigan.

###### Teaching

**BIOLOGY/ENVIRONMENT 281 General Ecology**

An undergraduate course providing a broad introduction to ecology. Required for EEB and Program in the Environment majors and meets the Group II course requirement for biology and general biology majors.

**EEB 408: Modeling for Ecology and Evolutionary Biology**

Course motivation and overall goals: The ability to translate between qualitative hypotheses and their more exact expression in the form of mathematical equations, and to analyze these equations to determine behavior under those hypotheses, are becoming essential skills for all biologists. Biology students do not always have the time to take the multitude of math courses needed to gain modeling skills, and there is value to learning at least basic modeling skills directly in the context motivating the biology student. The key goals of this course are to teach students how to:

1) understand and develop basic mathematical models of ecological and evolutionary phenomena, and

2) analyze those mathematical models using a combination of “pencil and paper” and computational approaches.

The course will assume only a background in calculus and at least one advanced class in ecology and evolutionary biology or related fields.

More specifically, the course will teach students to read, derive, and analyze simple continuous and discrete time models of biological systems (especially ordinary differential equations and simple recursion relations). Time permitting, additional topics may include stochastic models and assumptions behind some more complex model formulations. As examples we will use classical ecology and evolutionary biology models, with the examples chosen driven to some degree by student's interests. The course will also teach students some basic skills in Mathematica for analyzing and simulating the models discussed in the class. The course will involve lab and homework assignments, exams, and a project in which the student develops and analyzes a model in there area of interest.

Textbook: "A Biologist's Guide to Mathematical Modeling in Ecology and Evolution" by Sarah P. Otto and Troy Day.

Audience: Advanced undergraduate and beginning graduate students studying ecology and evolutionary biology or related fields.