Dispersal in Ecological Models: From Patches to Landscapes

这项研究的目的是为了从理论上更好地理解生物的运动模式如何与它们运动的景观结构相互作用，从而影响物种的持久性和相互作用以及生态群落的组成。为此，研究人员将开发和分析分散生物体种群动态的数学模型。这些模型将是反应扩散系统的概括，将包含基于这些系统的生态模型中通常不存在的特征。生态学中的标准反应-扩散模型描述了居住在单一统一环境中的种群，并假设扩散完全是随机的，不受环境特性或其他生物存在的限制。研究人员将研究的模型将描述依赖于环境条件的扩散，发生在斑块状的景观中，和/或随时间变化。为了捕捉这些特征，模型将纳入机制和结构，如密度相关的扩散和边界条件，沿环境梯度的平流，随时间变化的边界条件，空间变化系数，以及由长距离扩散连接的多个斑块。纳入这些特征的动机是为了更实际地描述诸如生境破碎化和全球变化的影响等环境变化对人口的影响。为了分析这些模型，研究人员将使用常微分方程和偏微分方程、动力系统和非线性泛函分析的方法。一些建模假设将导致具有新特征的模型，这将需要开发新的数学思想和方法。该项目的目标是创建和应用数学模型，描述生物的运动模式如何影响其种群的增长或下降，以及它们如何与其他生物相互作用。这些模型将以方程式为基础，这些方程式包含诸如移动速度等因素，这些因素涉及对景观特征（如栖息地类型之间的边缘）的反应，或受到其他生物存在的影响。这些特征一般不存在于现有的生态学空间模型中。这些模型将描述居住在由不同生境类型混合组成的斑驳环境中的种群。这种环境通常是由人类活动造成的，如城市化、农业和自然保护区的建立。研究空间效应如何威胁或帮助维持生物多样性，或影响作物、害虫和生物防治剂等重要生物类型之间的相互作用，可能会提供见解，从而改善保护、土地管理、病虫害控制和城市规划等领域的决策。

The goal of the research is to gain a better theoretical understanding of how the patterns of movement of organisms interact with the structure of the landscape through which they move and thereby influence the persistence and interactions of species and the composition of ecological communities. To do that the investigators will develop and analyze mathematical models for the population dynamics of dispersing organisms. The models will be generalizations of reaction-diffusion systems that will incorporate features not usually present in ecological models based on those systems. Standard reaction-diffusion models in ecology describe populations inhabiting a single uniform environment and assume that dispersal is purely random and is not conditional on properties of the environment or the presence of other organisms. The models that the investigators will study will describe dispersal that depends on environmental conditions, occurs in patchy landscapes, and/or is variable in time. To capture those features the models will incorporate mechanisms and structures such as density-dependent diffusion and boundary conditions, advection along environmental gradients, boundary conditions that change over time, spatially varying coefficients, and multiple patches linked by long distance dispersal. The motivation for incorporating such features is to obtain more realistic descriptions of the ways in which populations can be affected by modifications of the environment such as habitat fragmentation and the effects of global change. To analyze the models the investigators will use methods from ordinary and partial differential equations, dynamical systems, and nonlinear functional analysis. Some of the modeling assumptions will lead to models with novel features that will require the development of new mathematical ideas and methods. The objective of the project is to create and apply mathematical models that describe how the movement patterns of organisms affect how their populations grow or decline and how they interact with other organisms. The models will be based on equations which incorporate factors such as movement rates that involve responses to features of the landscape such as edges between habitat types or are influenced by the presence of other organisms. Those features are not generally present in existing spatial models in ecology. The models will describe populations inhabiting patchy environments consisting of mixtures of different habitat types. Such environments often result from human activities such as urbanization, agriculture, and the creation of nature reserves. Investigating how spatial effects can threaten or help maintain biodiversity or affect interactions between important types of organisms such as crops, pests, and biological control agents may provide insights that will lead to improved decision making in areas such as conservation, land management, pest and disease control, and urban planning.