Wasserstein Motifs: Optimal Transport for Ecological Network Alignment

Status: Ongoing (since May 2024) · Advisors: César A. Uribe, Lydia Beaudrot · Affiliations: Rice University & Michigan State University

We study ecological network (food web) alignment: identifying structural equivalences among species and uncovering backbones of interactions that represent shared functional substructures. Existing approaches are computationally expensive, hard to scale, and difficult to interpret ecologically.

We give a first rigorous formalization of food web alignment based on network motifs, and show that methods popularized in the ecological community are equivalent to minimizing a Fused Gromov–Wasserstein-like cost functional — what we term Wasserstein Motifs. We propose an interpretable, provably correct algorithm that efficiently computes non-deterministic alignments by treating food webs as feature measure networks, and as a byproduct, a new way to identify non-deterministic interaction backbones. On a continental-scale dataset of 129 Sub-Saharan African mammal food webs, the method delivers large gains in accuracy, a 158× speedup, and improved interpretability over the state of the art. An extended journal manuscript is in preparation.

Materials

• Conference paper — Identifying Common Backbones of Interactions Underlying Food Webs via Non-Deterministic Alignments, ICASSP 2026: IEEE Xplore (DOI) · author copy with appendix (PDF)
• Extended manuscript — Wasserstein Motifs: Non-deterministic Alignment of Ecological Networks, LMRL Workshop @ ICLR 2026 (oral, non-archival): OpenReview
• Slides — INFORMS Optimization Society Conference 2026 (oral presentation)
• Poster (PDF) — ICASSP 2026 / Texas Colloquium on Distributed Learning