Wasserstein Motifs: Non-deterministic Alignment of Ecological Networks

We study the problem of ecological network (food web) alignment, where we seek to identify structural equivalences among species and uncover backbones of interactions that represent shared functional substructures. These fundamental properties reveal the functional relationships that sustain ecosystems, enabling more accurate predictions of biodiversity responses to environmental change. Existing methods are computationally expensive, not scalable, and hard to interpret ecologically. We provide a first rigorous formalization of food web alignment based on network motifs, and show existing methods popularized in the ecological community are equivalent to minimizing a Fused Gromov-Wasserstein-like cost functional, termed Wasserstein Motifs. Moreover, we propose an interpretable and provably correct algorithm that efficiently computes non-deterministic alignments between food webs by leveraging their representation as feature measure networks. As a byproduct, we introduce a novel approach for identifying non-deterministic backbones of interactions in food webs. Experiments on a continental-scale dataset of 129 Sub-Saharan African mammal food webs demonstrate significant gains in accuracy, scalability, and interpretability over state-of-the-art methods. Our results establish a principled bridge between ecological network science and optimal transport, opening avenues for the analysis of complex ecological structured data.