Persistence and Spreading Speeds in Multi-Species Models with A Shifting Habitat Edge

物种能否在环境中生存和传播，是生态学中一个根本性的、长期存在的问题。最近，气候变化和景观转换将这个问题提上了议事日程。由于气候变化的过程，许多物种适合种群增长的栖息地在地理上发生了转移。气候引起的变化可能以复杂的方式与种群人口过程相联系，为影响物种种群的增长和扩散、长期动态和物种之间的相互作用奠定了基础。该项目旨在产生新的框架，用于分析物种在不断变化的栖息地中的持久性和传播速度。它解决了生态系统如何受到气候变化的影响以及生态系统未来可能如何应对的问题。它有助于越来越多的信息，确定高灭绝风险的物种，并预测在持续的气候变化下入侵物种的传播。该项目的成果有助于改进应对自然资源管理挑战的战略。该项目进一步促进了数学家和生物学家之间的跨学科合作，以解决单一学科无法解决的问题。此外，它还有助于人力资源开发，侧重于研究生的培训和技能发展，并为他们提供跨学科互动和探索的经验。在这个项目中，研究人员制定并分析了描述物种在不断变化的栖息地中的生长、相互作用和扩散的空间种群模型。其目标是了解并准确描述气候变化如何影响生物入侵过程。研究了多物种反应扩散竞争模型和捕食者-食饵模型，以及具有移动生境边缘的半离散阶段结构空间模型，以强调生境适宜性变化在入侵物种与现有物种相互作用的持续和传播中的作用。在这些模型中，栖息地范围的变化被纳入作为行波传播的物种生长函数中。研究了如下情况下的物种空间动态：(I)一个物种扩散到一个迁徙的栖息地，由一个常驻物种占据；(Ii)两个物种连续入侵一个开放的迁徙栖息地，而较早的物种仍在扩大其空间范围的过程中。发展了新的技术来确定模型解在适当的有界和无界空间区间上的行为，这些空间区间在时间上扩展和移动。方法利用微分方程组、积分方程组和动力学系统来检测物种灭绝的条件，并确定持续物种在空间中的传播速度。这项研究的结果也对研究波传播的其他学科产生了影响。

Whether or not a species can persist and spread in an environment is a fundamental and long-standing question in ecology. Recently, this question has been brought to the forefront by climate change and landscape conversion. Due to the processes of climate change, habitat regions suitable for population growth of many species have been shifting geographically. Climatically induced shifts may interface with population demographic processes in complex ways, setting the stage for impacts on species population growth and spread, long-term dynamics and interactions between species. This project aims to produce new frameworks for the analysis of persistence and spreading speeds of species in a shifting habitat. It addresses the question of how ecosystems are being affected by climate change and how ecosystems might respond in the future. It contributes to the growing body of information identifying species at a high risk for extinction and predicting the spread of invasive species under ongoing climate change. The outcomes of the project help improve strategies for coping with challenges of natural resource management. This project further stimulates interdisciplinary collaboration between mathematicians and biologists to address issues beyond the reach of single disciplines. In addition, it contributes to human resources development, focusing on training and skill development of graduate students, and providing them with experience in interdisciplinary interaction and exploration. In this project, the investigator formulates and analyzes spatial population models that describe species growth, interactions, and dispersal in shifting habitats. The goal is to understand and accurately describe how climate change affects biological invasion processes. Multi-species reaction-diffusion competition models and predator-prey models, as well as semi-discrete stage-structured spatial models with a shifting habitat edge, are studied to emphasize the role of changing habitat suitability in persistence and spread of an invasive species interacting with an existing species. In these models, shifts in habitat ranges are incorporated in species growth functions that propagate as traveling waves. Species spatial dynamics are investigated for the following cases: (i) one species spreads into a shifting habitat preoccupied by a resident species; and (ii) two species consecutively invade an open shifting habitat and the earlier species is still in the process of expanding its spatial range. New techniques are developed to determine the behaviors of solutions of the models on appropriate bounded and unbounded spatial intervals that expand and shift in time. Methods from differential equations, integral equations, and dynamical systems are employed to detect conditions under which species go extinct and to determine spreading speeds of persisting species in space. The results of this research also have impacts in other disciplines where wave propagation is studied.