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.