Stochastic models in population biology and their deterministic analogs
Stochastic models in population biology and their deterministic analogs
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DOI：
10.1103/physreve.70.041902
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发表时间：
2004-10-01
影响因子：
2.4
通讯作者：
Newman, TJ
中科院分区：
文献类型：
--
作者：
McKane, AJ;Newman, TJ
我们引入了一类基于“斑块动力学”的随机种群模型。斑块的大小可能是不同的，这允许人们量化这些随机模型与各种平均场理论的偏离，这些平均场理论在斑块大小变得非常大时通常是有效的。这些模型可用于在空间和非空间环境中阐明广泛的生物过程。在这里，我们集中讨论两个物种之间的竞争。我们给出了补丁模型的数学分析，其中我们推导了竞争平均场方程的精确形式(及其在非空间情况下的一阶修正)，并给出了模拟结果。这些平均场方程在某些重要方面不同于那些通常以现象学为基础写下来的方程。我们的一般结论是，平均场理论对于空间模型比对于单个孤立的斑块更稳健。这是由于斑块间扩散导致的重复救援事件导致的空间环境中随机效应的稀释。然而，即使在空间环境中，由于适度的斑块大小而产生的离散效应也会导致与平均场理论的显著偏离。
We introduce a class of stochastic population models based on "patch dynamics." The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean-field theories, which are generally valid as the patch size becomes very large. These models may be used to formulate a broad range of biological processes in both spatial and nonspatial contexts. Here, we concentrate on two-species competition. We present both a mathematical analysis of the patch model, in which we derive the precise form of the competition mean-field equations (and their first-order corrections in the nonspatial case), and simulation results. These mean-field equations differ, in some important ways, from those which are normally written down on phenomenological grounds. Our general conclusion is that mean-field theory is more robust for spatial models than for a single isolated patch. This is due to the dilution of stochastic effects in a spatial setting resulting from repeated rescue events mediated by interpatch diffusion. However, discrete effects due to modest patch sizes lead to striking deviations from mean-field theory even in a spatial setting.