Temperature Carryover Effect Revealed for Marine Fishes Using Spatio-Temporal Distributed Lag Models

Understanding the impact of changing temperature on population densities is necessary to predict the likely impact of climate anomalies (e.g., marine heatwaves) or forecast distribution shifts under future climate scenarios. Population densities are often analyzed using spatio-temporal models (STMs), which typically predict densities based on local habitat conditions while also estimating latent spatial and spatio-temporal variation. Recent research extends STMs by also estimating density responses to habitat conditions at nearby locations using a "spatially distributed lag" (SDL) that averages habitat conditions in the vicinity of samples. Here, we extend the SDL by incorporating insights from diffusion-enhanced STMs to simultaneously estimate spatially distributed and time-lagged responses to nearby and past habitat conditions (a "spatio-temporal distributed lag" STDL). We then use summer bottom trawl survey data from the eastern Bering Sea (1982-2024) to measure whether spatial and/or temporal lags are parsimonious when predicting population density from temperature anomalies for six ecologically important fishes. Results show that time-lagged responses are parsimonious, positive, and substantial (correlation of 0.20-0.83 per year) for five species, and that density responses to temperature anomalies also diffuse outward over time for four species at 30-53 km per year. A self- and cross-test simulation experiment shows that model selection can identify the appropriate model and that parameter estimates are approximately unbiased. We therefore conclude that temperature carryover effects arise in marine fishes and implement the method in the R package sdmTMB so that future studies can estimate nonlocal and time-lagged responses when measuring density responses to habitat.