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On moment closures for population dynamics in continuous space

机译:关于连续空间中人口动态的矩封闭

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A first-order moment closure, the mean-field assumption that organisms encounter one another in proportion to their spatial average densities, lies at the heart of much theoretical ecology. This assumption ignores all spatial information and, at the very least, needs to be replaced by a second-order closure to gain understanding of ecological dynamics in spatially structured populations. We describe a number of conditions that a second-order closure should satisfy and use these conditions to evaluate some closures currently available in the literature. Two conditions are particularly helpful in discriminating among the alternatives: that the closure should be positive, and that the dynamics should be unaltered when identical individuals are given different labels. On this basis, a class of closures we refer to as 'power-2' turns out to provide a good compromise between positivity and dynamical invariance under relabellina. (C) 2004 Elsevier Ltd. All rights reserved.
机译:一阶矩闭合是有机体与其空间平均密度成正比的平均场假设,它是许多理论生态学的核心。这个假设忽略了所有空间信息,至少需要用二阶封闭代替,以了解空间结构种群的生态动态。我们描述了二阶闭包应满足的许多条件,并使用这些条件来评估文献中当前可用的一些闭包。区分备选方案时,有两个条件特别有用:封闭应该是肯定的,并且当相同的个体被赋予不同的标签时,动态应该保持不变。在此基础上,我们称之为“幂2”的一类闭包被证明在重新标记下的正性和动态不变性之间提供了很好的折衷方案。 (C)2004 Elsevier Ltd.保留所有权利。

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