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

一个物种能否在环境中持续生存和传播是生态学中一个基本而长期存在的问题。 最近，气候变化和景观转换使这个问题成为最重要的问题。 由于气候变化的过程，适合许多物种种群增长的栖息地区域在地理上发生了变化。 气候引起的变化可能以复杂的方式与种群的人口统计过程相互作用，为影响物种的种群增长和扩散、长期动态和物种之间的相互作用奠定基础。 该项目旨在为分析物种在不断变化的栖息地中的持久性和传播速度提供新的框架。 它讨论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。 它有助于提供越来越多的信息，以确定面临灭绝高风险的物种，并预测在持续气候变化的情况下入侵物种的蔓延。 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，它有助于人力资源开发，重点是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，研究人员制定和分析空间种群模型，描述物种的生长，相互作用和扩散在不断变化的栖息地。 目标是了解和准确描述气候变化如何影响生物入侵过程。 研究了多种群反应扩散竞争模型、捕食者-被捕食者模型以及具有移动生境边缘的半离散阶段结构空间模型，强调了生境适宜性变化在入侵物种与现存物种相互作用的持久性和扩散中的作用. 在这些模型中，栖息地范围的变化被纳入物种生长函数，传播的行波。 物种的空间动态进行了研究，为以下情况：（一）一个物种蔓延到一个移动的栖息地，由一个居民种全神贯注;（二）两个物种连续入侵一个开放的移动栖息地和较早的物种仍在扩大其空间范围的过程中。 新技术的发展，以确定适当的有界和无界的空间间隔，扩大和转移的时间模型的解决方案的行为。 从微分方程，积分方程和动力系统的方法来检测条件下物种灭绝，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.