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Many models in ecology, evolutionary biology, and, more generally, biological systems, have underlying graphical structures. These include probabilistic models such as Gaussian graphical models, staged tree models, structural equation models, and latent tree models, as well as deterministic models, such as linear compartment models. Drawing on current trends and strengths in algebraic statistics, this workshop will put such models front and center by introducing existing techniques and known challenges.. Motivated by evolutionary biology, microbiomes, epidemiology, and ecosystem modeling, the workshop will be multidisciplinary, bringing together researchers from multiple fields to study these combinatorial models and their applications.