Ecological examples of nonstationarity, nonlinearity, and statistical interactions in dynamic structural equation models

This is a Preprint and has not been peer reviewed. This is version 1 of this Preprint. You must log in to post a comment. There are no comments or no comments have been made public for this article. This is a Preprint and has not been peer reviewed. This is version 1 of this Preprint. Add a Comment You must log in to post a comment. Comments There are no comments or no comments have been made public for this article. Ecologists are adapting structural causal modelling for spatial, phylogenetic, and time-series analysis. However, ecological extensions of path analysis and structural equation models (SEM) typically assume that interactions (“path coefficients”) are stationary, linear, and additive, while ecological and evolutionary dynamics are often nonstationary, nonlinear, and include statistical interactions. Here, we combine moderated SEM (estimating path coefficients as model variables) with dynamic SEM (estimating both simultaneous and lagged interactions among variables), develop a new “path-lag-slope” notation to specify this combination, and demonstrate it using a simulation experiment and three ecological case studies. The simulation experiment confirms that an autocorrelated “random-slope” model can estimate the nonstationary impact of one variable on another, but that the random slope is shrunk towards a constant value as data become less informative. The first case study then demonstrates nonstationarity by estimating an autoregressive slope linking a regional climate index to local ocean temperature near Vancouver Island. The second demonstrates nonlinearity by approximating Lotka-Volterra dynamics for two predator-prey systems, which closely match estimates of interactions and carrying capacity from traditional ordinary-differential equation methods. The third demonstrates statistical interactions by using monthly plankton samples (1962-1994) to show that resource-consumer-predator interactions in Lake Washington have a dome-shaped response to temperature. We envision several uses in causal analysis: (1) testing whether path coefficients are nonstationary; (2) estimating nonlinear responses given missing data; and (3) linking ecological parameters to hypothesized drivers in applied modelling. https://doi.org/10.32942/X24S96 Aquaculture and Fisheries Life Sciences, Marine Biology, Population Biology, Terrestrial and Aquatic Ecology dynamic structural equation model, random slopes, moderated structural equation model, nonstationary, Lotka-Volterra model Published: 2026-01-13 14:58 Last Updated: 2026-01-13 14:58 CC-By Attribution-NonCommercial-NoDerivatives 4.0 International Conflict of interest statement: None Data and Code Availability Statement: Data for sea surface temperature at Departure Bay are available online: https://open.canada.ca/data/en/dataset/719955f2-bf8e-44f7-bc26-6bd623e82884/resource/17c30115-25de-4bad-9286-51d3ef467793, and we use the copy from July 23, 2025 and downloaded Nov. 3, 2025. Data for the Pacific Decadal Oscillation were downloaded from JISAO (http://research.jisao.washington.edu/pdo/PDO.latest.txt) on Nov. 6, 2018, as analyzed previously by Thorson et al. (2020). Data for Lake Washington are from the MARSS package release 3.11.9 (Holmes et al., 2012), as collected by Dr. W. T. Edmondson, funded by the Andrew Mellon Foundation, and curated by Dr. Daniel Schindler. All analysis is conducted using R-package dsem release 2.0.0 (https://github.com/James-Thorson-NOAA/dsem@dev). Code and data to reproduce all figures is available in a GitHub repo (https://github.com/James-Thorson/DSEM-varying-paths), publicly available upon acceptance and distributed as a ZIP file during peer review. Language: English