Georg-August-University Goettingen, J.F. Blumenbach Institute of Zoology and Anthropology, Berliner Str. 28, 37073 Goettingen, Germany.
Ecol Lett. 2011 Jan;14(1):29-35. doi: 10.1111/j.1461-0248.2010.01553.x. Epub 2010 Nov 11.
Robust critical systems are characterized by power laws which occur over a broad range of conditions. Their robust behaviour has been explained by local interactions. While such systems could be widespread in nature, their properties are not well understood. Here, we study three robust critical ecosystem models and a null model that lacks spatial interactions. In all these models, individuals aggregate in patches whose size distributions follow power laws which melt down under increasing external stress. We propose that this power-law decay associated with the connectivity of the system can be used to evaluate the level of stress exerted on the ecosystem. We identify several indicators along the transition to extinction. These indicators give us a relative measure of the distance to extinction, and have therefore potential application to conservation biology, especially for ecosystems with self-organization and critical transitions.
稳健的临界系统的特点是在广泛的条件下出现的幂律。它们的稳健行为可以用局部相互作用来解释。虽然这类系统在自然界中可能很普遍，但它们的特性还不是很清楚。在这里，我们研究了三个稳健的临界生态系统模型和一个缺乏空间相互作用的零模型。在所有这些模型中，个体在斑块中聚集，其大小分布遵循幂律，在外部压力增加时会瓦解。我们提出，与系统连接性相关的这种幂律衰减可以用来评估对生态系统施加的压力水平。我们在向灭绝的转变过程中确定了几个指标。这些指标为我们提供了一个与灭绝距离的相对度量，因此对保护生物学有潜在的应用，特别是对具有自组织和临界转变的生态系统。
