Patchiness and Demographic Noise in Three Ecological Examples
Patchiness and Demographic Noise in Three Ecological Examples
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DOI：
10.1007/s10955-012-0506-x
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发表时间：
2012-09-01
影响因子：
1.6
通讯作者：
Levin, Simon A.
中科院分区：
文献类型：
--
作者：
Bonachela, Juan A.;Munoz, Miguel A.;Levin, Simon A.
理解空间聚集的前因后果是生态学中最基本的问题之一。聚集是种群个体之间相互作用产生的一种紧急现象，最多只能感知到其群体的局部密度。因此，考虑到个体层面的相互作用和波动对于正确描述人口是至关重要的。经典的决定论方程适用于描述总体的某些方面，但忽略了与个体离散性固有的随机性有关的特征。人口的随机方程确实通过人口噪声项解释了这些波动产生的影响，但由于其复杂性，它们可能很难处理(有时是不可能的)。即使它们可以写成简单的形式，但由于存在“平方根”固有噪声，它们仍然难以数值积分。在本文中，我们讨论了一种简单的方法，将人口随机性的影响添加到三个经典的确定性生态学例子中，在这些例子中，聚集起着重要的作用。我们使用最近引入的积分方案来研究所得到的方程，该积分方案特别设计用于将数值随机方程与人口统计噪声相结合。为了考察这些随机例子显示聚集的能力，我们发现这三个系统不仅表现出斑驳的构型，而且还经历了一个属于定向渗流普适类的相变。
Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense only-at most-local densities of their cohorts. Thus, taking into account the individual-level interactions and fluctuations is essential to reach a correct description of the population. Classic deterministic equations are suitable to describe some aspects of the population, but leave out features related to the stochasticity inherent to the discreteness of the individuals. Stochastic equations for the population do account for these fluctuation-generated effects by means of demographic noise terms but, owing to their complexity, they can be difficult (or, at times, impossible) to deal with. Even when they can be written in a simple form, they are still difficult to numerically integrate due to the presence of the "square-root" intrinsic noise. In this paper, we discuss a simple way to add the effect of demographic stochasticity to three classic, deterministic ecological examples where aggregation plays an important role. We study the resulting equations using a recently-introduced integration scheme especially devised to integrate numerically stochastic equations with demographic noise. Aimed at scrutinizing the ability of these stochastic examples to show aggregation, we find that the three systems not only show patchy configurations, but also undergo a phase transition belonging to the directed percolation universality class.