Pair approximation for lattice models with multiple interaction scales
Pair approximation for lattice models with multiple interaction scales
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DOI：
10.1006/jtbi.2001.2322
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发表时间：
2001-06-21
影响因子：
2
通讯作者：
Ellner, SP
中科院分区：
文献类型：
--
作者：
Ellner, SP
对近似经常被证明是有效的，以获得定性信息的基于格的随机空间模型的人口，流行病和进化动力学。对近似是一种矩封闭方法，其中平均场描述由每种可能类型的相邻位置对的频率的近似方程补充。对近似相对于连续空间模型的矩闭合的限制是个体之间的所有交互模式（例如，后代的扩散、竞争或疾病传播：）被假定在由相互作用邻域的大小确定的单个空间尺度上操作。在本文中，我提出了一个多尺度对近似，它允许不同大小的邻居为每种类型的相互作用。为了说明和测试的近似，我考虑了一个空间单物种的logistic模型，其中的后代分散在一个出生的邻居和建立的个人有一个死亡率取决于人口密度在竞争的邻居，与这些邻居嵌套在其他。稳态方程的分析产生了几个定性预测，这些预测通过模型模拟得到证实，动态方程的数值解提供了对大晶格上随机模型瞬态行为的密切近似。因此，多尺度对近似提供了一个有用的中间标准对近似的一个单一的相互作用的邻居，和一套完整的矩方程的空间更详细的模型。(C)北京：科学出版社.
Pair approximation has frequently proved effective for deriving qualitative information about lattice-based stochastic spatial models for population, epidemic and evolutionary dynamics. Pair approximation is a moment closure method in which the mean-field description is supplemented by approximate equations for the frequencies of neighbor-site pairs of each possible type. A limitation of pair approximation relative to moment closure for continuous space models is that all modes of interaction between individuals (e.g., dispersal of offspring, competition, or disease transmission:) are assumed to operate over a single spatial scale determined by the size of the interaction neighborhood. In this paper I present a multiscale pair approximation which allows different sized neighborhoods for each type of interaction. To illustrate and test the approximation I consider a spatial single-species logistic model in which offspring are dispersed across a birth neighborhood and established individuals have a death rate depending on the population density in a competition neighborhood, with one of these neighborhoods nested inside the other. Analysis of the steady-state equations yields several qualitative predictions that are confirmed by simulations of the model, and numerical solutions of the dynamic equations provide a close approximation to the transient behavior of the stochastic model on a large lattice. The multiscale pair approximation thus provides a useful intermediate between the standard pair approximation for a single interaction neighborhood, and a complete set of moment equations for more spatially detailed models. (C) 2001 Academic Press.