Extinction in neutrally stable stochastic Lotka-Volterra models.
Extinction in neutrally stable stochastic Lotka-Volterra models.
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DOI：
10.1103/physreve.85.051903
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发表时间：
2010-01
期刊：
影响因子：
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通讯作者：
Alexander Dobrinevski;Erwin Frey
中科院分区：
文献类型：
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作者：
Alexander Dobrinevski;Erwin Frey
相互竞争的生物物种群体在进化选择力的非线性动力学和相互作用的随机性产生的随机波动之间表现出一种迷人的相互作用。对物种灭绝过程的理解是进化和生物多样性研究的关键组成部分，而导致物种灭绝的过程受到这两个因素的影响。本文研究了一类基于广义Lotka-Volterra系统的随机种群动力学模型。在基本确定性模型的中性稳定性的情况下，内在噪声对物种生存的影响是巨大的：它在与种群规模成比例的时间尺度上破坏相互作用的物种的共存。我们介绍了一种基于随机平均的新方法，它允许人们通过减少到低维有效动力学来定量地理解这种消光过程。这是对两个高度对称的模型进行解析，并可以推广到更复杂的情况。我们得到的消光概率分布和其他感兴趣的量与模拟结果非常吻合。
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.