Generalized graphical mixed models connect ecological theory with widely used statistical models

Ecological dynamics are analyzed across multiple sites, times, and variables. Here, we introduce the family of generalized graphical mixed models (GGMMs) and show that it extends structural equation, generalized additive, and generalized linear mixed models. GGMMs represent ecological systems using a mathematical graph, where each analytic unit (node for each site-time-variable) has a direct effect on other units via specified linear interactions (edges). This graph is composed by combining elementary ecological relationships like ecological interactions, evolutionary trade-offs, time-lags, and spatial diffusion. GGMMs are then expressed using simultaneous equations, efficiently estimated using Gaussian Markov random fields, and used for prediction, inference, and causal analysis. We demonstrate GGMMs using three contrasting case studies: tracking cohorts in age-structured models; phylogenetic path analysis; and diffusion-enhanced spatio-temporal models. We conclude that GGMMs connect ecological theory with statistical models that are applied for inference, prediction, and causal analysis throughout ecology. DOI https://doi.org/10.32942/X2963M Subjects Applied Statistics, Aquaculture and Fisheries Life Sciences, Biodiversity, Environmental Sciences, Multivariate Analysis

mathematical graph, generalized linear mixed model, Generalized additive model, Structural Equation Model, diffusion, Species Interactions, phylogenetic path analysis Dates Published: 2025-06-06 15:20 Last Updated: 2025-06-06 15:20 License CC-BY Attribution-NonCommercial-ShareAlike 4.0 International Additional Metadata Conflict of interest statement: None Data and Code Availability Statement: All code and data required to replicate analyses and figures are available on GitHub online (https://github.com/James-Thorson/GGMM/) [To be made publicly accessible upon acceptance]. The mammal phylogeny was downloaded from VertLife (https://vertlife.org/phylosubsets/) and was developed by Upham et al. (2019). The mammal traits were accessed from PanTHERIA (Jones et al., 2009), available online from ESA archives (https://esapubs.org/archive/ecol/E090/184/metadata.htm). The proportional abundance-at-age data for rex sole in the Gulf of Alaska is publicly available (https://github.com/noaa-afsc/goa_rex/blob/main/runs/2025_cie_review/2021_accepted_model_inputs/GOA_Rex_8_2021.dat) from the 2024 stock assessment (McGilliard, 2024) and distributed for a Center for Independent Experts 2025 review of the rex sole assessment. Language: English