DMS-EPSRC Eco-Evolutionary Dynamics of Fluctuating Populations

一个基本的科学难题是理解多样性的起源和合作的进化，这可以通过理解由竞争物种组成的种群的稳定性来理解。它直接解决了深层次的社会关切，如维护濒危生态、有效防止生物多样性的丧失和遏制抗菌素耐药性的上升。为此，必须研究波动种群的生态进化动力耦合，即(I)种群数量、组成和每个物种特征的随机内部变异性和(Ii)环境条件的突然、渐进或重复的外部变化对生态系统进化的相互依存和综合影响。这项跨学科的研究位于生物学、数学、物理学、统计学和计算机科学的交界处，将结合这些领域迄今很少一起使用的一套先进的理论和数学工具。它将在一个国际合作中进行，由美国国家科学基金会数学科学部和英国工程和物理科学研究理事会共同资助，并为利兹大学的一名博士后研究员和弗吉尼亚理工大学的一名研究生提供高级培训。预计在基本理解复杂相互作用系统，特别是在内在噪声和环境变异性的共同影响下自发模式形成的概念和技术方面取得进展，并将在英国利兹和弗吉尼亚州布莱克斯堡交替组织的量身定做的研讨会上传播给科学界。虽然种群动力学传统上忽略波动，并考虑静态和均匀的环境，但随机发生的出生或死亡事件以及外部环境变化引起的人口噪声在及时理解种群的生态进化动力学方面发挥着关键作用。迄今为止，人们对外部环境变异性和内部人口噪声之间的相互依存关系知之甚少，但这一点非常重要，例如在微生物群落中，因为微生物群落往往容易受到突然和极端环境变化的影响。特别是，对受外部因素变化影响的不同大小和组成的种群进行建模，对于充分了解微生物抗生素耐药性的演变至关重要。标准的理论技术，如平均场近似或系统大小展开，不能直接使用，需要新的数学方法。将发展一套新的理论方法，基于并结合演化和非线性动力学、确定性和随机偏微分方程组、基于代理的计算机模拟和来自非平衡统计物理的工具，如动力学标度理论、临界现象的重整化群方法和连续统场理论下的随机动力学的数学表示。我们的目标是设计和定量描述复杂程度不断提高的生物相关进化模型，该模型既包含了切换的环境特征，又充分考虑了潜在的随机性。这些理论进展将被用来为实验室实验产生直接可测试的预测，以进一步探索人口噪声和环境变异性如何共同影响集体特征的出现，并影响物种共存和它们的空间模式组织。该项目由MPS数学科学部(DMS)通过数学生物学计划和LS-生物技术风险基金联合资助，材料研究部(DMR)通过凝聚态物质和材料理论计划联合资助。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

A fundamental scientific puzzle is understanding the origin of diversity and the evolution of cooperation, which can be understood through understanding the stability of populations composed of competing species. It directly addresses deep societal concerns, such as the maintenance of endangered ecologies, the effective prevention of the loss of biodiversity, and stemming the rise of antimicrobial resistance. To this end, one must address the coupled eco-evolutionary dynamics of fluctuating populations, namely the interdependence and combined effects of (i) random internal variability in population numbers, composition, and each species’ traits and (ii) sudden, gradual, or repetitive external changes in environmental conditions on the evolution of an ecological system. This transdisciplinary research is situated at the interface of biology, mathematics, physics, statistics, and computer science and will combine a set of advanced theoretical and mathematical tools from these fields that so far have rarely been utilized together. It will be pursued in an international collaboration, funded jointly through National Science Foundation – Division of Mathematical Sciences and the U.K. Engineering and Physical Sciences Research Council, and provide advanced training for a postdoctoral research fellow at the University of Leeds and a graduate student at Virginia Tech. Conceptual and technical advances in the basic understanding of complex interacting systems in general, and specifically of spontaneous pattern formation under the combined influence of intrinsic noise and environmental variability, are anticipated, and will be disseminated to the scientific community at tailored workshops to be organized alternatingly at Leeds, U.K. and Blacksburg, Virginia.While population dynamics traditionally ignores fluctuations and considers static and homogeneous environments, demographic noise arising from randomly occurring birth or death events as well as external environmental variations play a crucial role in understanding the eco-evolutionary dynamics of a population in time. The interdependence of external environmental variability and internal demographic noise is poorly understood to date, but it is of eminent importance, for example in microbial communities, which are often subject to sudden and extreme environmental changes. In particular, modelling populations of varying size and composition subject to changing external factors is crucial to gain a full understanding of the evolution of microbial antibiotic resistance. Standard theoretical techniques, like mean-field approximations or system-size expansions cannot be straightforwardly used, and new mathematical approaches are needed. A suite of novel theoretical methods, based on and combining evolutionary and nonlinear dynamics, deterministic and stochastic partial differential equations, agent-based computer simulations, and tools from non-equilibrium statistical physics such as dynamical scaling theory, renormalization group approaches to critical phenomena, and mathematical representations of stochastic kinetics in terms of continuum field theories, will be developed. The goal is to design and quantitatively characterize biologically relevant evolutionary models of increasing levels of complexity, which incorporate both switching environmental features and fully account for the underlying stochasticity. These theoretical advances will be utilized to generate directly testable predictions for laboratory experiments to further explore how demographic noise and environmental variability conjointly influence the emergence of collective features and affect species coexistence and their organization into spatial patterns.This project is jointly funded by the MPS Division of Mathematical Sciences (DMS) through the Mathematical Biology Program and the LS-BioTech Venture Fund, and the Division of Materials Research (DMR) through the Condensed Matter and Materials Theory program.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.