  The behavior of ecological systems mainly relies on the interactions between
the species it involves. We consider the problem of inferring the species
interaction network from abundance data. To be relevant, any network inference
methodology needs to handle count data and to account for possible
environmental effects. It also needs to distinguish between direct interactions
and indirect associations and graphical models provide a convenient framework
for this purpose. We introduce a generic statistical model for network
inference based on abundance data. The model includes fixed effects to account
for environmental covariates and sampling efforts, and correlated random
effects to encode species interactions. The inferred network is obtained by
averaging over all possible tree-shaped (and therefore sparse) networks, in a
computationally efficient manner. An output of the procedure is the probability
for each edge to be part of the underlying network. A simulation study shows
that the proposed methodology compares well with state-of-the-art approaches,
even when the underlying graph strongly differs from a tree. The analysis of
two datasets highlights the influence of covariates on the inferred network.
Accounting for covariates is critical to avoid spurious edges. The proposed
approach could be extended to perform network comparison or to look for missing
species.
