加权食物网能量传输网络的标度行为
Scaling Behaviors of Weighted Food Webs as Energy Transportation Networks
摘要：
食物网可以看作是一个能量传输网络，网络中每条边的权值表示两个物种之间的能量通量。通过对21个经验加权的食物网能量流网络的研究，我们发现了一些普遍存在的标度行为。为每个顶点$i$定义的两个随机变量$A_i$和$C_i$代表$i$的总通量（也称为顶点强度）和总间接效应或能量存储，发现它们分别遵循指数为$α\approx 1.32$和$β\approx 1.33$的幂律分布。另一个缩放行为是幂律关系$C_i\sim A_i^η$，其中$η\approx 1.02$。这被称为异速生长标度幂律关系，因为根据本文提出的算法，$A_i$可以被视为新陈代谢，而$C_i$可以被视为从顶点$i$开始的子网络的身体质量。最后，这些幂律指数之间的一个简单的关系，$η=(α-1)/(β-1)$，数学推导和经验食物网测试。
英文摘要：
Food webs can be regarded as energy transporting networks in which the weight of each edge denotes the energy flux between two species. By investigating 21 empirical weighted food webs as energy flow networks, we found several ubiquitous scaling behaviors. Two random variables $A_i$ and $C_i$ defined for each vertex $i$, representing the total flux (also called vertex intensity) and total indirect effect or energy store of $i$, were found to follow power law distributions with the exponents $α\approx 1.32$ and $β\approx 1.33$, respectively. Another scaling behavior is the power law relationship, $C_i\sim A_i^η$, where $η\approx 1.02$. This is known as the allometric scaling power law relationship because $A_i$ can be treated as metabolism and $C_i$ as the body mass of the sub-network rooted from the vertex $i$, according to the algorithm presented in this paper. Finally, a simple relationship among these power law exponents, $η=(α-1)/(β-1)$, was mathematically derived and tested by the empirical food webs.
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