Developing an axiomatic theory of evolution

现代进化理论是建立在一套复杂的数学模型的基础上的，这些模型描述了种群如何随着时间的推移而变化，并相互分化。虽然这组模型非常成功，但它并没有产生一个统一的数学进化理论，因为每个模型都是基于不同的简化假设。因此，我们并不清楚不同的模型是如何相互关联的，而且一些真正的进化过程对于这个理论体系来说是不可见的，因为它们没有被任何特定的模型所处理。这个项目的目标是发展一个单一的数学进化理论体系，它只基于我们知道是正确的假设，它将统一现有的模型，并允许研究当前理论无法解决的进化过程。这个项目将产生两个重要的后果。首先，这项工作将为研究以前难以研究的情况下的进化动力学提供工具，例如非常小的种群，那些处于高度不稳定的环境中的种群，以及那些生活在具有可变迁移率的零星环境中的种群。这些种群最有可能经历物种形成或灭绝。其次，这项工作将阐明进化论的数学统一性，既加深了我们对进化如何运作的理解，又巩固了进化生物学作为一门建立在普遍数学规则基础上的科学。研究生和博士后研究人员将接受数学进化生物学方面的培训，特别是在向非数学观众展示他们的研究时。结果将发表在开放获取期刊上，PI计划建立一个网页，将所有出版物与该项目的非技术摘要链接起来。

Modern evolutionary theory is based on a set of sophisticated mathematical models that describe how populations change over time and diverge from one another. While this collection of models has been very successful, it has not produced a unified mathematical evolutionary theory, since each model is based on different simplifying assumptions. It is thus not clear how the different models relate to one another, and some real evolutionary processes are invisible to this body of theory because they are not addressed by any particular model. The goal of this project is to develop a single body of mathematical evolutionary theory that is based only on assumptions that we know to be true, and that will both unify the existing models and allow study of evolutionary processes that current theory fails to address.This project will have two important consequences. First, the work will provide tools for investigating evolutionary dynamics in cases that have previously been hard to study, such as very small populations, those in highly unstable environments, and those living in patchy environments with variable migration rates. These populations are most likely to experience either speciation or extinction. Second, this work will illuminate the underlying mathematical unity of evolutionary theory, both deepening our understanding of how evolution works, and solidifying evolutionary biology as a science grounded in universal mathematical rules. Graduate students and postdoctoral researchers will be trained in mathematical evolutionary biology, and particularly in presenting their research to non-mathematical audiences. Results will be published in open access journals and the PI plans a webpage that links all publications with a non-technical summary of the project.