随机集合种群模型中的快模消除
Fast-mode elimination in stochastic metapopulation models
摘要：
我们调查的随机动力学的实体被限制在一组岛屿，它们之间的迁移。他们被认为是两种类型之一，除了迁移，他们也繁殖和死亡。属于这一类的系统在生物学和社会科学中很常见，出现在生态学、群体遗传学、流行病学、生物化学、语言学、观点动力学和其他领域。在所有这些情况下的控制方程是棘手的，因为他们做的多维福克-普朗克方程，或等价地，耦合的非线性随机微分方程与乘性噪声。我们开发了一种方法，利用分离的时间尺度之间的快速和缓慢的变量，以减少这些方程，使它们类似于一个单一的岛屿，这是经得起分析。这项技术是普遍适用的，但我们选择在群体遗传学的背景下讨论它，部分原因是由于选择而出现的额外特征。该方法背后的想法是简单的，其应用系统，并在一系列参数值的完整模型的模拟结果非常吻合。
英文摘要：
We investigate the stochastic dynamics of entities which are confined to a set of islands, between which they migrate. They are assumed to be one of two types, and in addition to migration, they also reproduce and die. Systems which fall into this class are common in biology and social science, occurring in ecology, population genetics, epidemiology, biochemistry, linguistics, opinion dynamics, and other areas. In all these cases the governing equations are intractable, consisting as they do of multidimensional Fokker-Planck equations or, equivalently, coupled nonlinear stochastic differential equations with multiplicative noise. We develop a methodology which exploits a separation in time scales between fast and slow variables to reduce these equations so that they resemble those for a single island, which are amenable to analysis. The technique is generally applicable, but we choose to discuss it in the context of population genetics, in part because of the extra features that appear due to selection. The idea behind the method is simple, its application systematic, and the results in very good agreement with simulations of the full model for a range of parameter values.
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