Relationship between genealogies and biophysical processes during spatial growth.

项目摘要/摘要 种群动态是生物医学中许多紧迫问题的核心。无论我们看的是 流行病、微生物群或癌症，我们需要了解人口是如何增长、传播和 进化。这些过程的结果在很大程度上受生态和遗传多样性的控制。 人口中的一部分。此外，多样性的模式往往是关于 推动人口动态的因素。尽管花了很多精力来刻画 固定种群的多样性(混合良好和空间结构良好)对 不断增长的种群的进化过程要有限得多。我们最近的研究发现 增长动力中看似无害的变化可以从根本上改变人口 在空间扩张的过程中进化。为了理解这种现象，我们开发了强大的 理论工具，这些工具导致在标准中发现隐藏的通用类 群体遗传学的反应-扩散模型。初步数据有力地支持了 假设每个普适性类别都有独特的谱系结构。此外，中性的 在一些空间扩展的种群中的进化似乎产生了相同的系谱 那些快速适应良好混合种群的人，这表明一些共同的特征 需要重新考虑选拔的问题。第一个目标是进一步发展这一理论，并在 数值模拟。第二个目标是研究家谱的普遍行为 受普通生物物理过程的影响，而在标准的单组分中忽略了这些过程 反应扩散模型。具体地说，我们将把我们的进化动力学理论扩展到 包括机械压力、营养物质扩散和运动的影响 环境梯度。第三个目标是建立基因和基因之间的联系 产生典型种群形态的多样性和增长不稳定性。加在一起， 这些研究路线将为解释空间分辨的基因数据和使用 它可以预测和控制进化的过程。这样的能力对于我们打击 癌症、抗生素耐药性和流行病。数学上的创新是在 这项工作的过程在广泛的应用中也应该是有用的，因为反应- 扩散模型在化学、生物学和医学中有许多用途。

Project Summary / Abstract Population dynamics are central to many pressing problems in biomedicine. Whether we look at epidemics, microbiome, or cancer, we need to understand how populations grow, spread, and evolve. The outcome of these processes is largely controlled by ecological and genetic diversity of the population. Moreover, the patterns of diversity are often the only available cues about the factors that drive population dynamics. Although a lot of effort went into characterizing the diversity of stationary populations (both well-mixed and spatially structured) the understanding of evolutionary processes in growing populations is much more limited. Our recent work found that seemingly innocuous changes in the growth dynamics can fundamentally alter how populations evolve during spatial expansions. To understand such phenomena, we developed powerful theoretical tools, which lead to the discovery of hidden universality classes in the standard reaction-diffusion models of population genetics. Preliminary data strongly supports the hypothesis that each universality class has a unique structure of genealogies. Moreover, neutral evolution in some spatially expanding populations seems to produce genealogies identical to those in rapidly-adapting well-mixed populations, which suggests that some common signatures of selection need to be revisited. The first aim is to develop this theory further and test it in numerical simulations. The second aim is to examine how the universal behavior of genealogies is affected by common biophysical process, which are neglected in standard one-component reaction-diffusion models. Specifically, we will extend our theory of evolutionary dynamics to include the influence of mechanical pressure, nutrient diffusion, and movement in response to environmental gradients. The third aim is focused on establishing a connection between genetic diversity and growth instabilities that produce typical population morphologies. Taken together, these lines of research will lay the groundwork to interpret spatially-resolved genetic data and use it to predict and control the course of evolution. Such capabilities are essential for our fight against cancer, antibiotic resistance, and epidemics. The mathematical innovations developed in the course of this work should also be useful across a wide set of applications because reaction- diffusion models find numerous uses in chemistry, biology, and medicine.