Mathematical investigation of changes in stability of dynamically evolving ecosystems

动态演化的生态系统稳定性变化的数学研究

• 批准号: 2440651
• 金额: --
• 依托单位: University of York
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2440651
• 关键词: Mathematical; investigation; changes; stability; dynamically

Much research has been conducted on the local stability of large ecosystem models, with analytic results primarily reliant on random matrix theory. Essentially this approach assumes a static configuration of species in an ecosystem and asks whether such a system would be stable to small perturbations in species abundances. However, the abundance of, and interactions between, species in ecosystems are known to evolve over time. These evolutionary forces are likely to have an impact on ecosystem stability. Following recent work on the evolution of small (low-dimensional) ecosystems [1], there is scope to extend the techniques developed to the high dimensional systems that normally fall under the purview of random matrix theory. By combining these two approaches, one opens up the potential for an analytical understanding of how ecosystem stability might change over ecological and evolutionary scales. As addressed, the influence of statistical patterns in interaction structure on ecosystem stability has been studied at ecological time scales [2] in which species properties are fixed in time. However in evolving systems species are subject to mutation. This not only leads to changes in species properties, but also to the generation of within-species variation. A consequence of this is that the dimension of the dynamical system can change. One of the primary mathematical challenges of this study will therefore be to modify standard analytical approaches that use random matrix theory to account for this unusual dynamical behaviour. In doing so we aim to bridge the gap between existing approaches which have until now been constrained to considering high-dimensional systems at ecological timescales on the one hand, or low-dimensional systems at evolutionary timescales on the other. [1] "Population size changes and extinction risk of populations driven by mutant interactors" HJ Park, Y Pichugin, W Huang, A Traulsen Physical Review E 99 (2), 022305 (2019)[2] "The ecology of the microbiome: networks, competition, and stability" KZ Coyte, J Schluter, KR Foster Science 350 (6261), 663-666 (2015)

关于大型生态系统模型的局部稳定性已经进行了大量的研究，分析结果主要依赖于随机矩阵理论。基本上，这种方法假定生态系统中物种的静态配置，并询问这样的系统是否会对物种丰度的微小扰动保持稳定。然而，众所周知，生态系统中物种的丰度和相互作用是随着时间的推移而演变的。这些进化力量可能会对生态系统的稳定性产生影响。在最近关于小型(低维)生态系统进化的工作[1]之后，有机会将开发的技术扩展到通常属于随机矩阵理论范围内的高维系统。通过将这两种方法结合起来，就有可能对生态系统稳定性如何在生态和进化规模上发生变化进行分析理解。如上所述，在物种属性在时间上固定的生态时间尺度上，研究了相互作用结构中的统计模式对生态系统稳定性的影响。然而，在进化的系统中，物种容易发生突变。这不仅会导致物种属性的变化，还会导致物种内变异的产生。这样做的一个结果是动力系统的维度可以改变。因此，这项研究的主要数学挑战之一将是修改使用随机矩阵理论来解释这种不寻常的动态行为的标准分析方法。通过这样做，我们的目标是弥合现有方法之间的差距，这些方法到目前为止一直被限制为一方面在生态时间尺度上考虑高维系统，另一方面在进化时间尺度上考虑低维系统。[1]《微生物群落的生态：网络、竞争和稳定》，KZ Coyte，J Schluter，KR Foster Science 350(6261)，663-666(2015年)