Spatial Ecology via Reaction-Diffusion Equations
Spatial Ecology via Reaction-Diffusion Equations
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发表时间：
2003-11
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通讯作者：
R. S. Cantrell;C. Cosner
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作者：
R. S. Cantrell;C. Cosner
前言。系列前言。1引言。1.1导言。1.2单一物种的非空间模型。1.3相互作用物种的非空间模型。1.3.1质量-作用和Lotka-Volterra模型。1.3.2质量-作用之外：功能响应。1.4空间模型：概述。1.5反应-扩散模型。1.5.1导出扩散模型。1.5.2通过相互作用粒子系统的扩散模型：光滑的重要性。1.5.3反应-扩散模型能告诉我们什么？1.5.4边、边界条件和环境异质性。1.6数学背景。1.6.1动力系统。1.6.2偏微分方程的基本概念：一个例子。1.6.3偏微分方程的现代方法：与线性代数和矩阵理论的类比。1.6.4椭圆算子：弱解、状态空间和映射性质。1.6.5作为动力系统的反应-扩散模型。1.6.6抛物方程的经典正则性理论。1.6.7最大原理和单调性。2单一物种的线性增长模型：通过特征值平均空间效应。2.1简单模型中的特征值、持久性和标度。2.1.1应用：物种-面积关系。2.2特征值的变分公式：考虑异质性。2.3简单线性模型中碎片化和平流/趋向性的影响。2.3.1碎片化。2.3.2平流/趋向性。2.4一个空间维度的图形分析。2.4.1有利生境斑块的最佳位置。2.4.2缓冲区和边界行为的影响。2.5特征值和正性。2.5.1平流模型。2.5.2时间周期性。2.5.3特征值和正性的附加结果。2.6与其他主题和模型的联系。2.6.1特征值、可解性和多重性。2.6.2其他模型类型：离散空间和时间。附录3.密度依赖的单物种模型。3.1平衡在单物种模型中的重要性。3.2平衡和稳定性：亚解和超解。3.2.1持续和灭绝。3.2.2最小补丁大小。3.2.3平衡的唯一性。3.3平衡和尺度：一个空间维度。3.3.1最小斑块大小的重新研究。3.4平衡的延续和分岔。3.4.1延续。3.4.2分岔结果。3.4.3讨论和结论。3.5单物种模型的应用和性质。3.5.1捕食者入侵如何影响临界斑块大小。3.5.2扩散和狭缝效应。3.5.3平衡的性质。3.6更一般的单物种模型。附录4持久性。4.1导论。4.1.1生态学概述。4.1.2 ODEModels举例。4.1.3一点历史观点。4.2持久性的定义。4.2.1生态持久性。4.2.2抽象持久性。4.3建立持久性的技术。4.3.1平均Lyapunov函数方法。4.3.2不环性方法。4.4不可入侵意味着共存。4.4.1不环性和ODE竞争模型。4.4.2反应-扩散模拟。4.4.3与特征值的连接。4.54.6生态永续性和平衡。4.6.1抽象永续性意味着生态永续性。4.6.2永续性意味着成分正平衡的存在。附录5超越持久性：更多持久性理论。5.1简介。5.2压缩性。5.3实用持久性。5.4边界瞬态轨道。5.5非自治系统中的持久性。5.6条件持久性。5.7消光结果。附录6反应-扩散模型的空间异质性。6.1绪论。6.2生境斑块内部的空间异质性。6.2.1空间隔离如何促进共存。6.2.2局部与全球竞争的一些差异。6.2.3生境斑块形状介导的共存。6.3边缘介导效应。6.3.1特征值注释。6.3.2外部生境退化导致生态保护区内部竞争逆转：边界条件的影响。6.3.3自然保护区的跨界补贴与竞争平衡。6.3.4病原体传播介导的竞争。6.4估算和后果。附录。7非单调系统。7.1简介。7.2捕食者介导的共存。7.3三物种竞争。7.3.1两个优势竞争者如何介导一个劣势竞争者的持久性。7.3.2 May- leonard例子的重述。7.4三个营养级模型。合同附件。参考文献。索引。
Preface. Series Preface. 1 Introduction. 1.1 Introductory Remarks. 1.2 Nonspatial Models for a Single Species. 1.3 Nonspatial Models For Interacting Species. 1.3.1 Mass-Action and Lotka-Volterra Models. 1.3.2 Beyond Mass-Action: The Functional Response. 1.4 Spatial Models: A General Overview. 1.5 Reaction-Diffusion Models. 1.5.1 Deriving Diffusion Models. 1.5.2 Diffusion Models Via Interacting Particle Systems: The Importance of Being Smooth. 1.5.3 What Can Reaction-Diffusion Models Tell Us? 1.5.4 Edges, Boundary Conditions, and Environmental Heterogeneity. 1.6 Mathematical Background. 1.6.1 Dynamical Systems. 1.6.2 Basic Concepts in Partial Differential Equations: An Example. 1.6.3 Modern Approaches to Partial Differential Equations: Analogies with Linear Algebra and Matrix Theory. 1.6.4 Elliptic Operators: Weak Solutions, State Spaces, and Mapping Properties. 1.6.5 Reaction-Diffusion Models as Dynamical Systems. 1.6.6 Classical Regularity Theory for Parabolic Equations. 1.6.7 Maximum Principles and Monotonicity. 2 Linear Growth Models for a Single Species: Averaging Spatial Effects Via Eigenvalues. 2.1 Eigenvalues, Persistence, and Scaling in Simple Models. 2.1.1 An Application: Species-Area Relations. 2.2 Variational Formulations of Eigenvalues: Accounting for Heterogeneity. 2.3 Effects of Fragmentation and Advection/Taxis in Simple Linear Models. 2.3.1 Fragmentation. 2.3.2 Advection/Taxis. 2.4 Graphical Analysis in One Space Dimension. 2.4.1 The Best Location for a Favorable Habitat Patch. 2.4.2 Effects of Buffer Zones and Boundary Behavior. 2.5 Eigenvalues and Positivity. 2.5.1 Advective Models. 2.5.2 Time Periodicity. 2.5.3 Additional Results on Eigenvalues and Positivity. 2.6 Connections with Other Topics and Models. 2.6.1 Eigenvalues, Solvability, and Multiplicity. 2.6.2 Other Model Types: Discrete Space and Time. Appendix. 3 Density Dependent Single-Species Models. 3.1 The Importance of Equilibria in Single Species Models. 3.2 Equilibria and Stability: Sub- and Supersolutions. 3.2.1 Persistence and Extinction. 3.2.2 Minimal Patch Sizes. 3.2.3 Uniqueness of Equilibria. 3.3 Equilibria and Scaling: One Space Dimension. 3.3.1 Minimum Patch Size Revisited. 3.4 Continuation and Bifurcation of Equilibria. 3.4.1 Continuation. 3.4.2 Bifurcation Results. 3.4.3 Discussion and Conclusions. 3.5 Applications and Properties of Single Species Models. 3.5.1 How Predator Incursions Affect Critical Patch Size. 3.5.2 Diffusion and Allee Effects. 3.5.3 Properties of Equilibria. 3.6 More General Single Species Models. Appendix. 4 Permanence. 4.1 Introduction. 4.1.1 Ecological Overview. 4.1.2 ODEModels as Examples. 4.1.3 A Little Historical Perspective. 4.2 Definition of Permanence. 4.2.1 Ecological Permanence. 4.2.2 Abstract Permanence. 4.3 Techniques for Establishing Permanence. 4.3.1 Average Lyapunov Function Approach. 4.3.2 Acyclicity Approach. 4.4 Invasibility Implies Coexistence. 4.4.1 Acyclicity and an ODE Competition Model. 4.4.2 A Reaction-Diffusion Analogue. 4.4.3 Connection to Eigenvalues. 4.5 Permanence in Reaction-Diffusion Models for Predation. 4.6 Ecological Permanence and Equilibria. 4.6.1 Abstract Permanence Implies Ecological Permanence. 4.6.2 Permanence Implies the Existence of a Componentwise Positive Equilibrium. Appendix. 5 Beyond Permanence: More Persistence Theory. 5.1 Introduction. 5.2 Compressivity. 5.3 Practical Persistence. 5.4 Bounding Transient Orbits. 5.5 Persistence in Nonautonomous Systems. 5.6 Conditional Persistence. 5.7 Extinction Results. Appendix. 6 Spatial Heterogeneity in Reaction-Diffusion Models. 6.1 Introduction. 6.2 Spatial Heterogeneity within the Habitat Patch. 6.2.1 How Spatial Segregation May Facilitate Coexistence. 6.2.2 Some Disparities Between Local and Global Competition. 6.2.3 Coexistence Mediated by the Shape of the Habitat Patch. 6.3 Edge Mediated Effects. 6.3.1 A Note About Eigenvalues. 6.3.2 Competitive Reversals Inside Ecological Reserves Via External Habitat Degradation: Effects of Boundary Conditions. 6.3.3 Cross-Edge Subsidies and the Balance of Competition in Nature Preserves. 6.3.4 Competition Mediated by Pathogen Transmission. 6.4 Estimates and Consequences. Appendix. 7 Nonmonotone Systems. 7.1 Introduction. 7.2 Predator Mediated Coexistence. 7.3 Three Species Competition. 7.3.1 How Two Dominant Competitors May Mediate the Persistence of an Inferior Competitor. 7.3.2 The May-Leonard Example Revisited. 7.4 Three Trophic Level Models. Appendix. References. Index.