The robustness of an ecological network quantifies the resilience of the ecosystem it represents to species loss. It corresponds to the proportion of species that are disconnected from the rest of the network when extinctions occur sequentially. Classically, the robustness is calculated for a given network, from the simulation of a large number of extinction sequences. The link between network structure and robustness remains an open question. Setting a joint probabilistic model on the network and the extinction sequences allows analysis of this relation. Bipartite stochastic block models have proven their ability to model bipartite networks for example, plant-pollinator networks: species are divided into blocks and interaction probabilities are determined by the blocks of membership. Analytical expressions of the expectation and variance of robustness are obtained under this model, for different distributions of primary extinction sequences. The impact of the network structure on the robustness is analyzed through a set of properties and numerical illustrations. The analysis of a collection of bipartite ecological networks allows us to compare the empirical approach to our probabilistic approach, and illustrates the relevance of the latter when it comes to computing the robustness of a partially observed or incompletely sampled network.

中文翻译：

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通过概率模型研究双向生态交互网络的中尺度结构对其鲁棒性的影响

生态网络的稳健性量化了它所代表的生态系统对物种丧失的恢复力。它对应于灭绝顺序发生时与网络其余部分断开连接的物种比例。经典地，对于给定网络的鲁棒性是从大量灭绝序列的模拟中计算出来的。网络结构和鲁棒性之间的联系仍然是一个悬而未决的问题。在网络和灭绝序列上设置联合概率模型可以分析这种关系。二部随机块模型已经证明了它们模拟二部网络的能力，例如植物传粉者网络：物种被分成块，相互作用概率由成员块确定。在该模型下，对于初级灭绝序列的不同分布，得到了鲁棒性的期望和方差的解析表达式。通过一组属性和数值图解分析了网络结构对鲁棒性的影响。对一组二分生态网络的分析使我们能够将经验方法与我们的概率方法进行比较，并说明后者在计算部分观察或不完全采样网络的稳健性时的相关性。