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

栖息地边缘变化的多物种模型中的持久性和传播速度

• 批准号: 1515875
• 负责人: Bingtuan Li
• 金额: $ 22.5万
• 依托单位: University of Louisville Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-15 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1515875&HistoricalAwards=false
• 关键词: Persistence; Spreading; Speeds; Multi; Species

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.

一个物种是否能够在环境中生存和传播是生态学中一个长期存在的基本问题。 最近，气候变化和景观转变使这个问题成为人们关注的焦点。 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已经发生了地理上的变化。 气候引起的变化可能以复杂的方式与人口统计过程相互作用，为影响物种种群增长和传播、长期动态和物种之间的相互作用奠定基础。 该项目旨在建立新的框架来分析不断变化的栖息地中物种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如何应对的问题。 它有助于提供越来越多的信息来识别濒临灭绝的物种，并预测持续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策略。 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，还致力于人力资源开发，注重研究生的培养和技能发展，为他们提供跨学科互动和探索的经验。 在该项目中，研究人员制定并分析了描述物种在变化的栖息地中的生长、相互作用和扩散的空间种群模型。 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-猎物模型，以及具有变化的栖息地边缘的半离散阶段结构空间模型，以强调改变栖息地适宜性在与现有物种相互作用的入侵物种的持久性和传播中的作用。 在这些模型中，栖息地范围的变化被纳入以行波形式传播的物种生长函数中。 对以下情况进行物种空间动态研究：（i）一个物种扩散到一个被常驻物种占据的不断变化的栖息地； (ii) 两个物种连续入侵一个开放的移动栖息地，并且较早的物种仍在扩大其空间范围的过程中。 开发了新技术来确定模型解在随时间扩展和移动的适当有界和无界空间间隔上的行为。 采用微分方程、积分方程和动力系统的方法来检测物种灭绝的条件，并确定持久存在的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。