RUI: Stochastic Interactions: Understanding Invasion and Extinction in Ecological Systems

该项目的目标是开发数学和统计方法，以了解环境干扰或入侵物种如何影响连接在大型食物网中的群落。生物系统是非常复杂的，涉及不同尺度上的许多组件之间的多种相互作用。如何对生态群落进行分类，以解释它们如何共存和进化，一直是生物学家和生态学家感兴趣的话题。即使经过一个世纪的研究，完全理解观察到的物种入侵和灭绝所需的数学工具和模型仍然不存在。此外，很少有生态学研究考虑具有随机效应的数学模型。现实世界的系统天生就是嘈杂的，只有包含随机效应，才能正确理解生态社区。这项工作涉及与英国南极调查局的生态学家合作，创建一种以特定数据为基础的跨学科方法。研究成果将通过研讨会、在会议上的陈述以及在同行评议期刊上发表的文章来传播。该项目将培训本科生和研究生进行跨学科的数学研究。蒙特克莱尔州立大学的许多学生是STEM中代表性不足的群体(包括妇女和少数族裔)的成员，该研究计划将利用现有的支持这些学生的计划。该项目涉及使用理论、统计和计算方法来提高我们对大型生态系统模型如何响应随机相互作用和扰动的理解。特别令人感兴趣的是研究食物网中的初级和次级灭绝级联，以及食物网对入侵物种的易感性。通过考虑各种经验的和合成的食物网，并将完全动力学与随机性结合起来，这项工作将阐明哪些生态系统机制(例如，自我调节、相互作用强度、反馈环)有助于稳定食物网免受干扰。这项工作的三个主要组成部分是：(I)对随机系统进行全面的数值研究，以提高我们对随机入侵、初级灭绝和由此产生的次生灭绝级联的理解；(Ii)发展新的方法，利用连续马尔可夫链模型，在考虑物种之间的两两、三向和更高阶相互作用时，找到灭绝的最佳路径；以及(Iii)使用创新的渐近分析确定现有食物网对外来物种入侵的脆弱性。这一结果将有助于提高我们对生物多样性和生物群落的组织以及可能稳定或破坏生态系统稳定的因素的理解。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。

The goal of this project is to develop mathematical and statistical approaches to understand how environmental disturbances or invading species affect communities connected in large food webs. Biological systems are very complex, involving a multitude of interactions among many components at different scales. How ecological communities may be grouped to explain how they coexist and evolve has been a subject of intense interest among biologists and ecologists. Even after a century of research, the mathematical tools and models needed to fully understand observed species invasions and extinctions do not exist. Moreover, very few ecological studies have considered mathematical models with random effects. Real world systems are inherently noisy, and only by including random effects can one properly understand an ecological community. The work involves collaboration with ecologists based at British Antarctic Survey in the United Kingdom to create an interdisciplinary approach grounded in specific data. The outcome of the research will be disseminated through seminars, presentations at meetings, and publications in peer-reviewed journals. The project will train undergraduate and graduate students in interdisciplinary mathematical research. Many students at Montclair State University are members of underrepresented groups in STEM (including women and minorities), and the research program will leverage existing programs which support these students. The project involves the use of theoretical, statistical, and computational approaches to improve our understanding of how models of large ecological systems respond to stochastic interactions and perturbations. Of particular interest is the study of primary and secondary extinction cascades in food webs as well as the susceptibility of food webs to invasive species. By considering a variety of empirical and synthetic food webs and incorporating full dynamics with stochasticity, the work will shed light on which ecosystem mechanisms (e.g., self-regulation, interaction strengths, feedback loops) serve to stabilize food webs against perturbations. The three major components of the work are to: (i) perform comprehensive numerical studies of the stochastic systems to improve our understanding of stochastic invasion, primary extinction, and the resulting secondary extinction cascade; (ii) develop new approaches using continuous Markov chain models to find the optimal path to extinction when considering pairwise, three-way, and higher-order interactions between species; and (iii) determine the vulnerability of an existing food web to invasion by exotic species using innovative asymptotic analysis The results will be useful in improving our understanding of biodiversity and the organization of living communities as well as factors that can stabilize or destabilize ecosystems.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.