Spreading Speed, Traveling Waves, and Minimal Domain Size in Impulsive Reaction–Diffusion Models
Spreading Speed, Traveling Waves, and Minimal Domain Size in Impulsive Reaction–Diffusion Models
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DOI：
10.1007/s11538-012-9757-6
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发表时间：
2012-08
影响因子：
3.5
通讯作者：
M. Lewis;Bingtuan Li
中科院分区：
文献类型：
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作者：
M. Lewis;Bingtuan Li
物种的生长、死亡和扩散如何影响物种的传播和持续，构成了空间生态学的中心问题。我们提出了具有不同繁殖和扩散阶段的物种的脉冲反应扩散方程模型。这些模型可以描述季节性出生脉冲加上全年的非线性死亡和扩散。或者，它们可以描述季节性收获，加上非线性出生和死亡以及全年的扩散。季节性脉冲中的种群动态由离散映射来描述，该离散映射将脉冲结束时的种群密度作为脉冲开始时的种群密度的可能的非单调函数。扩散阶段的动力学由有界或无界区域中的非线性反应扩散方程控制。我们发展了一个空间显式的理论框架，将物种的生命率(死亡率或繁殖力)和扩散特征与物种的传播速度、行波速度以及物种持续生存的最小区域大小联系起来。我们给出了关于模型参数的传播速度的显式表达式，并证明了传播速度可以表征为一类行波解的最慢速度。我们还给出了使用模型参数的最小区域尺寸的显式公式。我们的结果显示了扩散系数，以及离散和连续时间增长和死亡的组合如何在各种生态情景下决定种群的扩散和持续动态。数值模拟结果验证了理论结果的正确性。
How growth, mortality, and dispersal in a species affect the species’ spread and persistence constitutes a central problem in spatial ecology. We propose impulsive reaction–diffusion equation models for species with distinct reproductive and dispersal stages. These models can describe a seasonal birth pulse plus nonlinear mortality and dispersal throughout the year. Alternatively, they can describe seasonal harvesting, plus nonlinear birth and mortality as well as dispersal throughout the year. The population dynamics in the seasonal pulse is described by a discrete map that gives the density of the population at the end of a pulse as a possibly nonmonotone function of the density of the population at the beginning of the pulse. The dynamics in the dispersal stage is governed by a nonlinear reaction–diffusion equation in a bounded or unbounded domain. We develop a spatially explicit theoretical framework that links species vital rates (mortality or fecundity) and dispersal characteristics with species’ spreading speeds, traveling wave speeds, as well as minimal domain size for species persistence. We provide an explicit formula for the spreading speed in terms of model parameters, and show that the spreading speed can be characterized as the slowest speed of a class of traveling wave solutions. We also give an explicit formula for the minimal domain size using model parameters. Our results show how the diffusion coefficient, and the combination of discrete- and continuous-time growth and mortality determine the spread and persistence dynamics of the population in a wide variety of ecological scenarios. Numerical simulations are presented to demonstrate the theoretical results.