IMT School for Advanced Studies, P.zza S. Francesco 19, 55100, Lucca, Italy.
Lorentz Institute for Theoretical Physics, University of Leiden, Niels Bohrweg 2, 2333, CA, Leiden, The Netherlands.
Sci Rep. 2020 Nov 16;10(1):19903. doi: 10.1038/s41598-020-76300-1.
Many real networks feature the property of nestedness, i.e. the neighbours of nodes with a few connections are hierarchically nested within the neighbours of nodes with more connections. Despite the abstract simplicity of this notion, various mathematical definitions of nestedness have been proposed, sometimes giving contrasting results. Moreover, there is an ongoing debate on the statistical significance of nestedness, since random networks where the number of connections (degree) of each node is fixed to its empirical value are typically as nested as real ones. By using only ergodic and unbiased null models, we propose a clarification that exploits the recent finding that random networks where the degrees are enforced as hard constraints (microcanonical ensembles) are thermodynamically different from random networks where the degrees are enforced as soft constraints (canonical ensembles). Indeed, alternative definitions of nestedness can be negatively correlated in the microcanonical one, while being positively correlated in the canonical one. This result disentangles distinct notions of nestedness captured by different metrics and highlights the importance of making a principled choice between hard and soft constraints in null models of ecological networks.
许多真实网络具有嵌套性，即节点连接数较少的节点的邻居在层次上嵌套在节点连接数较多的节点的邻居中。尽管这个概念抽象简单，但已经提出了各种嵌套性的数学定义，有时会给出相反的结果。此外，关于嵌套性的统计显著性存在争议，因为节点连接数（度）固定在其经验值的随机网络通常与真实网络一样嵌套。通过仅使用遍历且无偏的 null 模型，我们提出了一种澄清，利用了最近的发现，即度作为硬约束（微正则系综）的随机网络与度作为软约束（正则系综）的随机网络在热力学上是不同的。实际上，在微正则系综中，嵌套性的替代定义可能是负相关的，而在正则系综中则是正相关的。这个结果区分了不同度量捕捉的嵌套性概念，并强调了在生态网络的 null 模型中在硬约束和软约束之间做出有原则选择的重要性。
