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We propose a method to represent bipartite networks using graph embeddings tailored to tackle the challenges of studying ecological networks, such as the ones linking plants and pollinators, where many covariates need to be accounted for, in particular to control for sampling bias. We adapt the variational graph auto-encoder approach to the bipartite case, which enables us to generate embeddings in a latent space where the two sets of nodes are positioned based on their probability of connection. We translate the fairness framework commonly considered in sociology in order to address sampling bias in ecology. By incorporating the Hilbert-Schmidt independence criterion (HSIC) as an additional penalty term in the loss we optimize, we ensure that the structure of the latent space is independent of continuous variables, which are related to the sampling process. Finally, we show how our approach can change our understanding of ecological networks when applied to the Spipoll data set, a citizen science monitoring program of plant-pollinator interactions to which many observers contribute, making it prone to sampling bias.

The structure of a bipartite interaction network can be described by providing a clustering for each of the two types of nodes. Such clusterings are outputted by fitting a Latent Block Model (LBM) on an observed network that comes from a sampling of species interactions in the field. However, the sampling is limited and possibly uneven. This may jeopardize the fit of the LBM and then the description of the structure of the network by detecting structures which result from the sampling and not from actual underlying ecological phenomena. If the observed interaction network consists of a weighted bipartite network where the number of observed interactions between two species is available, the sampling efforts for all species can be estimated and used to correct the LBM fit. We propose to combine an observation model that accounts for sampling and an LBM for describing the structure of underlying possible ecological interactions. We develop an original inference procedure for this model, the efficiency of which is demonstrated on simulation studies. The pratical interest in ecology of our model is highlighted on a large dataset of plant-pollinator network.

Within food webs, species can be partitioned into groups according to various criteria. Two notions have received particular attention: trophic groups, which have been used for decades in the ecological literature, and more recently, modules. The relationship between these two group definitions remains unknown in empirical food webs because they have so far been studied separately. While recent developments in network theory have led to efficient methods for detecting modules in food webs, the determination of trophic groups (sets of species that are functionally similar) is based on subjective expert knowledge. Here, we develop a novel algorithm for trophic group detection. We apply this method to several well-resolved empirical food webs, and show that aggregation into trophic groups allows the simplification of food webs while preserving their information content. Furthermore, we reveal a 2-level hierarchical structure where modules partition food webs into large bottom-top trophic pathways whereas trophic groups further partition these pathways into sets of species with similar trophic connections. Bringing together trophic groups and modules provides new perspectives to the study of dynamical and functional consequences of food-web structure, bridging topological analysis and dynamical systems. Trophic groups have a clear ecological meaning in terms of trophic similarity, and are found to provide a trade-off between network complexity and information loss.