Field theoretic techniques for macroecology and community assembly

Our world is undergoing rapid changes due to human activity. My research has the overarching goals of understanding how these changes will impact ecological communities, and how we may mitigate their effects. To achieve these goals, I will further develop our theoretical understanding of how ecological communities work, and the primary outcome of this project will be to derive and test new predictions for the way biodiversity is structured across different spatial scales. Given the tremendous complexity of a typical ecological community, it is impossible to include every single detail in any tractable analysis. One therefore has to come up with a strategy for keeping only the most pertinent information, so that we may throw away the details that don't matter but still make accurate predictions. Stephen Hubbell's Neutral Theory is the canonical example of this kind of parsimonious strategy, and it makes surprisingly successful ecological predictions while having very few adjustable parameters. One key output is known as the species abundance distribution, which tells us on average how many species we should expect to find with any given population size in an ecological community. However, there are three important spatial patterns for which it is not yet possible to make analytical predictions in Neutral Theory. The first is how this species abundance distribution changes with sample area---for example, we would expect to find more and more rare species as sample area is reduced. But what is the exact predicted form of this relationship? We don't yet know. The second pattern is known as the species-area relationship, which describes precisely how the number of species found should increase with sample area. And the third pattern is known as distance decay, which tells us how many species we should expect two communities to have in common, as a function of their geographical separation. The first theme of my proposed research will use field theoretical techniques drawn from my doctoral background in theoretical physics, in concert with methods developed during my postdoctoral work in ecology. Using this combination of approaches I will generate new, analytical predictions for these three patterns in Neutral Theory, going beyond the computer simulations available thus far. The application of these tools is quite novel in the context of community ecology, and will open up the opportunity for interaction across the life science interface.The second theme of my research will begin to add more complexity to this picture, by considering a phenomenon known as density dependence. The effect of density dependence is that when population size increases in a local region, leading to overcrowding, individuals find it harder to survive in that region and the population size drops back down. I will continue to use tools from field theory, with a particular focus on interacting field theories to analyze this complex problem, and to determine what difference density dependence makes to the three spatial patterns above.Finally, I will test my new predictions against a broad range of ecological datasets, stretching across life's domains, from trees down to microbes. While macroscopic organisms have a long history in ecology, microbial ecology in particular is a much younger field---and yet we know that microbes are essential to many processes in nature. Modern molecular techniques allow us to explore microbial ecology with unprecedented resolution, and with the collaboration of a large network of colleagues I will test my predictions against this data. Confronting my novel analytical methods with new kinds of ecological data will allow me to make draw important conclusions about the rules by which ecological communities play.