## What I do

My work addresses fundamental questions in population, community, and evolutionary ecology. I am most interested in questions to do with system dynamics (changes over time) and the processes that drive them. Accordingly, much of my work uses a combination of mathematical modeling and experiments in tractable model systems such as laboratory microcosms. I use mathematical models because ecological and evolutionary systems are complex and nonlinear. It's impossible to develop and test rigorous hypotheses without mathematical help. I use microcosms because their high control and replicability allows powerful, rigorous experiments that would not otherwise be possible. For instance, in microcosms we often can isolate the effects of a single process on system dynamics, which may well be impossible in nature.

My lab is currently funded by an NSERC Discovery Grant.

## Synchrony and stability in metacommunities

This is a collaboration with David Vasseur. The aim of this project is to explain two common, important features of natural communities: stability and synchrony. Stability refers to the fact that most populations in most places persist for many generations without wild oscillations in abundance, despite environmental fluctuations. Synchrony refers to the fact that spatially-separated populations of the same species, and coexisting populations of different species, often fluctuate synchronously. This is problematic from a theoretical perspective, because theory suggests that synchrony and stability are rarely compatible. David and I are developing and testing realistic (i.e. stochastic, nonlinear) models of spatial community dynamics (metacommunity dynamics) to tease apart the links between synchrony and stability.Publications: Vasseur & Fox 2007 Ecol. Lett., Vasseur & Fox 2009 Nature, Fox et al. 2011 Ecol. Lett.

## Character convergence

This is another collaboration with David Vasseur. Exploitative competition is known to drive evolutionary divergence in resource use traits, thereby promoting adaptive radiation. However, divergence is expected only under competition for nutritionally-substitutable resources (e.g., different prey species). Plants, algae, and microbes often compete for essential resources (e.g., different nutrients), and herbivores often compete for complementary resources (e.g., different plants that vary in their protein:carbohydrate ratio). Our models show that competition for non-substitutable resources can select for convergence in resource use traits. Interestingly, character convergence also promotes, or at least does not inhibit, stable ecological coexistence. Hubbell's verbal argument that character convergence leads to neutral stability does not stand up to mathematical scrutiny.Publications: Fox & Vasseur 2008 Am. Nat., Vasseur & Fox 2011 Am. Nat.

## General theory of biodiversity and ecosystem function

Species extinctions and invasions can alter the rate or level of ecosystem functions like primary productivity, nutrient cycling, and decomposition. I am developing a general theory of how changes in biodiversity affect one important class of ecosystem functions. This framework is based on the Price Equation, originally developed in evolutionary biology to partition the fundamental mechanisms of evolutionary change. There are deep analogies between the mechanisms by which species evolve, and the mechanisms by which species gain and loss affect ecosystem function. One important implication of this work is that not all ecosystem functions can be incorporated within the same theoretical framework.Publications: Fox 2006 Ecology, Fox & Harpole 2008 Ecology, Hector et al. 2009, Fox 2010 Oikos, Fox and Kerr in press Oikos

## Quantifying the effects of coexistence mechanisms

Ecologists know surprisingly little about the relative importance of different kinds of coexistence mechanisms in nature. Bill Nelson and I are collaborating on a project to quantify the strength of coexistence mechanisms indirectly, by examining their dynamical effects. Using statistical tools drawn from population genetics, we are analyzing time series of algal and zooplankton communities to quantify how close coexisting species are to equal 'fitness' on average, and how much their relative fitnesses fluctuate over time. This quantitative information helps to narrow down the range of coexistence mechanisms consistent with the observed dynamics.Publications: Fox et al. 2010 Ecology