Dynamic structural equation models synthesize ecosystem dynamics constrained by ecological mechanisms

Abstract Ecological analyses typically involve many interacting variables. Ecologists often specify lagged interactions in community dynamics (i.e. vector‐autoregressive models) or simultaneous interactions (e.g. structural equation models), but there is less familiarity with dynamic structural equation models (DSEM) that can include any simultaneous or lagged effect in multivariate time‐series analysis. We propose a novel approach to parameter estimation for DSEM, which involves constructing a Gaussian Markov random field (GMRF) representing simultaneous and lagged path coefficients, and then fitting this as a generalized linear mixed model to missing and/or non‐normal data. We provide a new R‐package dsem, which extends the ‘arrow interface’ from path analysis to represent user‐specified lags when constructing the GMRF. We also outline how the resulting nonseparable precision matrix can generalize existing separable models, for example, for time‐series and species interactions in a vector‐autoregressive model. We first demonstrate dsem by simulating a two‐species vector‐autoregressive model based on wolf–moose interactions on Isle Royale. We show that DSEM has improved precision when data are missing relative to a conventional dynamic linear model. We then demonstrate DSEM via two contrasting case studies. The first identifies a trophic cascade where decreased sunflower starfish has increased urchin and decreased kelp densities, while sea otters have a simultaneous positive effect on kelp in the California Current from 1999 to 2018. The second estimates how declining sea ice has decreased cold‐water habitats, driving a decreased density for fall copepod predation and inhibiting early‐life survival for Alaska pollock from 1963 to 2023. We conclude that DSEM can be fitted efficiently as a GLMM involving missing data, while allowing users to specify both simultaneous and lagged effects in a time‐series structural model. DSEM then allows conceptual models (developed with stakeholder input or from ecological expertise) to be fitted to incomplete time series and provides a simple interface for granular control over the number of estimated time‐series parameters. Finally, computational methods are sufficiently simple that DSEM can be embedded as component within larger (e.g. integrated population) models. We therefore recommend greater exploration and performance testing for DSEM relative to familiar time‐series forecasting methods.