THE IMPORTANCE OF BEING DISCRETE (AND SPATIAL)
THE IMPORTANCE OF BEING DISCRETE (AND SPATIAL)
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DOI：
10.1006/tpbi.1994.1032
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发表时间：
1994-12-01
影响因子：
1.4
通讯作者：
LEVIN, S
中科院分区：
文献类型：
--
作者：
DURRETT, R;LEVIN, S
我们考虑并比较了空间分布系统动力学建模的四种方法：平均场方法（由常微分方程描述），其中每个个体被认为具有与其他个体相互作用的相等概率;斑块模型，将离散个体分组为斑块，而无需额外的空间结构;反应扩散方程，其中无穷小个体分布在空间中;和相互作用的粒子系统，其中个体是离散的，空间被明确地处理。我们将这四种方法应用于空间分布种群中物种相互作用的三个例子，并比较它们的预测。每个都代表了关于生物学的不同假设，因此它们之间的比较具有生物学和建模意义。在第一种情况下，所有四种方法都同意，在第二个空间模型不同意与非空间的，而在第三个随机模型与离散的个人不同意与微分方程的基础上。我们进一步表明，与粒子系统相关联的极限反应扩散方程可以有不同的定性行为，从那些简单地增加扩散项的平均场方程。(C)1994年出版社出版。
We consider and compare four approaches to modeling the dynamics of spatially distributed systems: mean field approaches (described by ordinary differential equations) in which every individual is considered to have equal probability of interacting with every other individual; patch models that group discrete individuals into patches without additional spatial structure; reaction-diffusion equations, in which infinitesimal individuals are distributed in space; and interacting particle systems, in which individuals are discrete and space is treated explicitly. We apply these four approaches to three examples of species interactions in spatially distributed populations and compare their predictions. Each represents different assumptions about the biology and hence a comparison among them has biological as well as modeling implications. In the first case all four approaches agree, in the second the spatial models disagree with the nonspatial ones, while in the third the stochastic models with discrete individuals disagree with the ones based on differential equations. We show further that the limiting reaction-diffusion equations associated with particle systems can have different qualitative behavior from those obtained by simply adding diffusion terms to mean field equations. (C) 1994 Academic Press, Inc.