Relationship between genealogies and biophysical processes during spatial growth.

项目总结/摘要 种群动态是生物医学中许多紧迫问题的核心。不管我们是检查 流行病，微生物组或癌症，我们需要了解人口如何增长，传播， 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 的人口。此外，多样性的模式往往是唯一可用的线索， 推动人口动态的因素。尽管我们花了很多精力来描述 固定种群的多样性（混合良好和空间结构） 在不断增长的种群中的进化过程是非常有限的。我们最近的研究发现， 增长动态中看似无害的变化可以从根本上改变人口 在空间扩张中进化。为了理解这种现象，我们开发了强大的 理论工具，导致发现标准中隐藏的普适类 群体遗传学的反应扩散模型初步数据强烈支持 假设每个普遍性类都有一个独特的系谱结构。此外，中立 在某些空间扩张的种群中，进化似乎产生了与 那些在快速适应良好的混合人群，这表明，一些共同的签名， 我们需要重新审视选择。第一个目标是进一步发展这一理论，并在 数值模拟第二个目的是研究家谱的普遍行为 受普通生物物理过程的影响，这在标准单组分中被忽略 反应扩散模型具体来说，我们将把进化动力学理论扩展到 包括机械压力的影响，营养扩散，以及响应于 环境梯度第三个目标是建立基因之间的联系， 多样性和生长不稳定性，产生典型的人口形态。综合起来看， 这些研究方向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。这种能力对于我们打击 癌症、抗生素耐药性和流行病。数学创新发展于 这项工作的过程也应该在广泛的应用中是有用的，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.