Field theoretic techniques for macroecology and community assembly

由于人类活动，我们的世界正在经历快速变化。我的研究的首要目标是了解这些变化将如何影响生态社区，以及我们如何减轻它们的影响。为了实现这些目标，我将进一步发展我们对生态群落如何工作的理论理解，该项目的主要成果将是推导和测试关于生物多样性在不同空间尺度上的结构方式的新预测。考虑到典型生态群落的巨大复杂性，在任何易于处理的分析中都不可能包括每一个细节。因此，人们必须想出一个策略，只保留最相关的信息，这样我们就可以扔掉不重要的细节，但仍然可以做出准确的预测。史蒂芬·哈贝尔的中性理论是这种节俭策略的典型例子，它在几乎没有可调参数的情况下做出了令人惊讶的成功的生态预测。一个关键的输出被称为物种丰度分布，它告诉我们在一个生态群落中，在任何给定的种群规模下，我们平均应该找到多少物种。然而，在中性理论中，有三种重要的空间模式尚不可能做出分析预测。第一个是物种丰度分布如何随样本面积的变化-例如，随着样本面积的减少，我们预计会发现越来越多的稀有物种。但这种关系的确切预测形式是什么？我们还不知道。第二种模式被称为物种-面积关系，它准确地描述了所发现的物种数量应该如何随着样本面积的增加而增加。第三种模式被称为距离衰减，它告诉我们，作为地理分离的函数，我们应该预期两个群落有多少物种是共同的。我提出的研究的第一个主题将使用从我的理论物理博士背景中提取的田野理论技术，并结合我在生态学博士后工作期间开发的方法。使用这种方法的组合，我将在中性理论中为这三种模式产生新的、分析性的预测，这超出了迄今为止可用的计算机模拟。这些工具的应用在群落生态学的背景下是相当新颖的，并将打开跨越生命科学界面的互动的机会。我的研究的第二个主题将开始通过考虑一种被称为密度依赖的现象来增加这幅图的复杂性。密度依赖的影响是，当一个地区的人口规模增加，导致过度拥挤时，个人会发现在该地区更难生存，人口规模会回落。我将继续使用场论中的工具，特别是相互作用的场论来分析这个复杂的问题，并确定密度依赖对上面三种空间模式的影响。最后，我将用广泛的生态数据集测试我的新预测，这些数据跨越生命的领域，从树木到微生物。虽然宏观生物在生态学上有很长的历史，但微生物生态学尤其是一个年轻得多的领域-然而我们知道微生物在自然界的许多过程中都是必不可少的。现代分子技术使我们能够以前所未有的分辨率探索微生物生态，在一个庞大的同事网络的合作下，我将根据这些数据来检验我的预测。用新的生态数据来面对我的新分析方法，将使我能够就生态群落的运行规则得出重要的结论。

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.