Aggregated metapopulation lifetime statistics has been used to access stylized facts that might help identify the underlying patch-level dynamics. For instance, the emergence of scaling laws in the aggregated probability distribution of patch lifetimes can be associated to critical phenomena, in which the correlation length among system units tends to diverge. Nevertheless, an aggregated approach is biased by patch-level variability, a fact that can blur the interpretation of the data. Here, I propose a weakly-coupled metapopulation model to show how patch variability can solely trigger qualitatively different lifetime probability distribution at the aggregated level. In a generalized approach, I obtain a two-way connection between the variability of a certain patch property (e.g. carrying capacity, environment condition or connectivity) and the aggregated lifetime probability distribution. Furthermore, for a particular case, assuming that scaling laws are observed at the aggregated-level, I speculate the heterogeneity that could be behind it, relating the qualitative features the variability (mean, variance and concentration) to the scaling exponents. In this perspective, the application points to the possibility of equivalence between heterogeneous weakly-coupled metapopulations and homogeneous ones that exhibit critical behavior.

中文翻译：

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将元种群异质性与汇总的生命周期统计数据联系起来

聚合的元种群寿命统计数据已被用于访问可能有助于识别潜在补丁级动态的程式化事实。例如，补丁寿命的聚合概率分布中标度定律的出现可能与关键现象有关，其中系统单元之间的相关长度趋于发散。然而，聚合方法会受到补丁级别可变性的影响，这一事实可能会模糊数据的解释。在这里，我提出了一个弱耦合的元种群模型，以展示补丁可变性如何在聚合水平上单独触发质量上不同的生命周期概率分布。在一般的方法中，我获得了某个补丁属性（例如承载能力、环境条件或连通性）和聚合寿命概率分布。此外，对于特定情况，假设在聚合级别观察到标度定律，我推测其背后可能存在异质性，将定性特征、可变性（均值、方差和浓度）与标度指数相关联。从这个角度来看，该应用程序指出了异质弱耦合元群与表现出关键行为的同质元群之间存在等效性的可能性。