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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‐packagedsem, 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 demonstratedsemby 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.

Trait associations are widely analysed using phylogenetic comparative methods (PCM) to account for correlations among related species. Similarly, traits are measured for some but not all species, and missing continuous traits (e.g. growth rate) can be imputed using ‘phylogenetic trait imputation’ (PTI), based on evolutionary relatedness and trait covariance. However, PTI has not been available for categorical traits, and estimating covariance among traits without ecological constraints risks inferring implausible evolutionary mechanisms.

Here, we extend previous PCM and PTI methods by (1) specifying covariance among traits as a structural equation model (SEM), and (2) incorporating associations among both continuous and categorical traits. Fitting a SEM replaces the covariance among traits with a set of linear path coefficients specifying potential evolutionary mechanisms. Estimated parameters then represent regression slopes (i.e. the average change in trait Y given an exogenous change in trait X) that can be used to calculate both direct effects (X impacts Y) and indirect effects (X impacts Z and Z impacts Y).

We demonstrate phylogenetic structural‐equation mixed‐trait imputation using 33 variables representing life history, reproductive, morphological, and behavioural traits for all >32,000 described fishes worldwide. SEM coefficients suggest that one degree Celsius increase in habitat is associated with an average 3.5% increase in natural mortality (including a 1.4% indirect impact that acts via temperature effects on the growth coefficient), and an average 3.0% decrease in fecundity (via indirect impacts on maximum age and length). Cross‐validation indicates that the model explains 54%–89% of variance for withheld measurements of continuous traits and has an area under the receiver‐operator‐characteristics curve of 0.86–0.99 for categorical traits.

We use imputed traits to classify all fishes into life‐history types, and confirm a phylogenetic signal in three dominant life‐history strategies in fishes. PTI using phylogenetic SEMs ensures that estimated parameters are interpretable as regression slopes, such that the inferred evolutionary relationships can be compared with long‐term evolutionary and rearing experiments.