  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 e.g. 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.
