Towards Ecological Network Analysis with Gromov-Wasserstein Distances

Climate change is driving the widespread redistribution of species with cascading effects on predators and their prey. Formally comparing ecological interaction networks is a critical step towards understanding the impact of climate change on ecosystem functioning, yet current methods for ecological network analysis are unable to do so. We propose using the GromovWasserstein (GW) metric for quantifying dissimilarity between ecological networks. We demonstrates the corresponding optimal transport plans of this distance can be interpreted as species functional alignment between food webs. Our results show that GW transport plans align species from different mammal communities consistent with ecological understanding. Furthermore, we illustrate extensions of the GW distance to notions of averages and factorization over ecological networks. Ultimately, we propose the foundation for a novel interpretable topological data analysis framework to inform futureecological research and conservation management.