从公司到殖民地：生态系统中帕累托分布的起源
From companies to colonies: The origin of Pareto-like distributions in ecosystems
摘要：
最近的集群分布在各种生态系统的研究揭示了帕累托统计的空间殖民地的大小。这些结果得到了支持的细胞自动机模拟，产生强大的关键性的内源性模式形成的基础上的正反馈。我们表明，这种自组织的临界性是比例效应定律的一种表现，这一定律首先是在企业规模的背景下发现的。映射到马尔可夫生灭过程的随机模型，转移率与集群大小呈线性关系。这种映射提供了一个补丁统计和生态系统的动态之间的连接，不同的殖民地的“第一次通过时间”出现作为一个强大的工具，区分内源性和外源性的集群机制。即将发生的灾难性变化（如荒漠化）表现在空间殖民地的稳定性的急剧变化，因为集群消失的机会取决于其大小，而不是线性的。
英文摘要：
Recent studies of cluster distribution in various ecosystems revealed Pareto statistics for the size of spatial colonies. These results were supported by cellular automata simulations that yield robust criticality for endogenous pattern formation based on positive feedback. We show that this self-organized criticality is a manifestation of the law of proportionate effect, first discovered in the context of business firm size. Mapping the stochastic model to a Markov birth-death process, the transition rates are shown to scale linearly with cluster size. This mapping provides a connection between patch statistics and the dynamics of the ecosystem; the "first passage time" for different colonies emerges as a powerful tool that discriminates between endogenous and exogenous clustering mechanisms. Imminent catastrophic shifts (like desertification) manifest themselves in a drastic change of the stability properties of spatial colonies, as the chance of a cluster to disappear depends logarithmically, rather than linearly, on its size.
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