Diffusion, Directed Movement, Spatial and Temporal Heterogeneity in Population Dynamics
种群动态中的扩散、定向运动、时空异质性
基本信息
- 批准号:1714487
- 负责人:
- 金额:$ 25.05万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2017
- 资助国家:美国
- 起止时间:2017-07-01 至 2021-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
"Competition-exclusion" principle in evolution and ecology was first proposed by Darwin. In modern era, understanding "biodiversity" has become a central theme in plant ecology, and it has been observed that "spatial heterogeneity" plays an important role in biodiversity. On the other hand, diffusion has been used extensively and successfully in modeling various phenomena in nature and science. In this project, the Principal Investigator and his collaborators in ecology and biology, will continue to explore the effect of dispersal in heterogeneous environment which has led to a re-examination of the fundamental concept of "carrying capacity" and its relation to "intrinsic growth rates" in population dynamics. Both mathematical theories and rigorous biological experiments involving yeast will be used. Other related issues, such as temporal variations, will also be investigated.In this project, the main theme is to understand the consequences of interactions between diffusion (dispersal of species) and spatial, as well as temporal, variations in environment. An important element in this understanding is the intricate relation between the fundamental concepts of "carrying capacity" and "intrinsic growth rates". Those will be studied - first by biological experiments (which have been inspired by mathematical theories) and then by new mathematical models created to describe those experiments. The concavity or convexity of the relation between the two quantities would play an important role in population dynamics. Mathematically, what biological experiments suggest is to replace the classical (single) logistic equation for a single species population by a system containing an extra equation governing the "renewable" resources. This seems to be much closer to reality, and will change the well-known Lotka-Volterra system for two competing species to a much more challenging one, a new system of 3 equations with renewable resources. In this project, we will study these new systems thoroughly.
进化论和生态学中的“竞争-排斥”原理是由达尔文首先提出的。现代植物生态学研究的主题是“生物多样性”,空间异质性在生物多样性中起着重要作用。另一方面,扩散已被广泛和成功地用于模拟自然和科学中的各种现象。在这个项目中,首席研究员和他的生态学和生物学合作者将继续探索在异质环境中扩散的影响,从而重新审视人口动态中“承载能力”的基本概念及其与“内在增长率”的关系。数学理论和严格的生物实验,涉及酵母将被使用。本项目的主题是了解扩散(物种的扩散)与环境的空间和时间变化之间相互作用的后果。这种理解的一个重要因素是“承载能力”和“内在增长率”这两个基本概念之间的复杂关系。这些将被研究-首先通过生物实验(这是由数学理论启发的),然后通过新的数学模型来描述这些实验。这两个量之间的关系的凸性或凸性将在种群动力学中起重要作用。从数学上讲,生物学实验表明,用一个包含管理“可再生”资源的额外方程的系统来取代单一物种种群的经典(单一)逻辑斯谛方程。这似乎更接近现实,并将著名的两个竞争物种的Lotka-Volterra系统改变为一个更具挑战性的系统,一个新的可再生资源3方程系统。在这个项目中,我们将深入研究这些新系统。
项目成果
期刊论文数量(3)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Wei-Ming Ni其他文献
The uniqueness of indefinite nonlinear diffusion problem in populaton genetics
群体遗传学中不定非线性扩散问题的独特性
- DOI:
- 发表时间:
2016 - 期刊:
- 影响因子:0
- 作者:
Fang Li;Kimie Nakashima;Wei-Ming Ni;Fang Li and Kimie Nakashima;中島主恵 - 通讯作者:
中島主恵
Stability and uniqueness of multi-layered solutions
多层解决方案的稳定性和唯一性
- DOI:
- 发表时间:
2013 - 期刊:
- 影响因子:0
- 作者:
Fang Li;Kimie Nakashima;Wei-Ming Ni;Fang Li and Kimie Nakashima;中島主恵;Kimie Nakashima - 通讯作者:
Kimie Nakashima
On the natural extensions of dynamics with a Siegel or Cremer point
关于具有西格尔或克里默点的动力学的自然延伸
- DOI:
10.1080/10236198.2012.681780 - 发表时间:
2012 - 期刊:
- 影响因子:0
- 作者:
Linlin Su;Kimie Nakashima;Wei-Ming Ni;Kimie Nakashima;Kimie Nakashima;Kimie Nakashima;Kimie Nakashima;Kimie Nakashima;C. Cabrera and T. Kawahira - 通讯作者:
C. Cabrera and T. Kawahira
Preface [Special issue dedicated to the late Professor Rou-Huai Wang on the occasion of his 90th birthday]
序言【纪念已故王柔怀教授九十岁生日特刊】
- DOI:
- 发表时间:
2016 - 期刊:
- 影响因子:0
- 作者:
K.C. Chang;M.Y. Chi;Wei-Ming Ni;Z.Q.Wu - 通讯作者:
Z.Q.Wu
非線形解析と可積分系の数理
可积系统的非线性分析和数学
- DOI:
- 发表时间:
2010 - 期刊:
- 影响因子:0
- 作者:
Linlin Su;Kimie Nakashima;Wei-Ming Ni;Kimie Nakashima - 通讯作者:
Kimie Nakashima
Wei-Ming Ni的其他文献
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{{ truncateString('Wei-Ming Ni', 18)}}的其他基金
Diffusion in Heterogeneous Environments
异构环境中的扩散
- 批准号:
1210400 - 财政年份:2012
- 资助金额:
$ 25.05万 - 项目类别:
Standard Grant
Concentration Phenomena in Pattern Formation
图案形成中的集中现象
- 批准号:
0653043 - 财政年份:2007
- 资助金额:
$ 25.05万 - 项目类别:
Continuing Grant
Concentration Phenomena in Diffusion and Cross-Diffusion Systems
扩散和交叉扩散系统中的集中现象
- 批准号:
0400452 - 财政年份:2004
- 资助金额:
$ 25.05万 - 项目类别:
Continuing Grant
Diffusion and Cross-Diffusion in Pattern Formation
图案形成中的扩散和交叉扩散
- 批准号:
9988635 - 财政年份:2000
- 资助金额:
$ 25.05万 - 项目类别:
Continuing Grant
Mathematical Sciences: Diffusion, Cross-Diffusion and Spike Layers
数学科学:扩散、交叉扩散和尖峰层
- 批准号:
9705639 - 财政年份:1997
- 资助金额:
$ 25.05万 - 项目类别:
Standard Grant
Mathematical Sciences: Nonlinear Partial Differential Equations and Systems
数学科学:非线性偏微分方程和系统
- 批准号:
9401333 - 财政年份:1994
- 资助金额:
$ 25.05万 - 项目类别:
Continuing Grant
Mathematical Sciences: Semilinear Partial Differential Equations and Systems
数学科学:半线性偏微分方程和系统
- 批准号:
9101446 - 财政年份:1991
- 资助金额:
$ 25.05万 - 项目类别:
Continuing Grant
Mathematical Sciences: Conference on Nonlinear Diffusion Equations and Their Equilibrium States, University of Wales,Wales, England, August 20-30, 1989
数学科学:非线性扩散方程及其平衡态会议,威尔士大学,英国威尔士,1989 年 8 月 20-30 日
- 批准号:
8815183 - 财政年份:1989
- 资助金额:
$ 25.05万 - 项目类别:
Standard Grant
Mathematical Sciences: Semilinear Elliptic Equations and Systems
数学科学:半线性椭圆方程和系统
- 批准号:
8801587 - 财政年份:1988
- 资助金额:
$ 25.05万 - 项目类别:
Continuing Grant
Mathematical Sciences: Semilinear Elliptic Equations and Systems
数学科学:半线性椭圆方程和系统
- 批准号:
8601246 - 财政年份:1986
- 资助金额:
$ 25.05万 - 项目类别:
Standard Grant
相似国自然基金
晶态桥联聚倍半硅氧烷的自导向组装(self-directed assembly)及其发光性能
- 批准号:21171046
- 批准年份:2011
- 资助金额:55.0 万元
- 项目类别:面上项目
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