Inference about spatial or temporal processes, such as understanding how various predictors may explain spatio-temporal variation in a system of interest, is often complicated by spatial and/or temporal scale mismatches. Mismatches can occur either in the scales at which response and predictor data have been gathered, or in the scales at which ecological and environmental processes take place. Indeed, what we observe at a given place and time may integrate the influence of environmental variables further afield or in the past, as the seabird productivity example below illustrates.

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Variables such as seabird breeding productivity, measured at the level of a seabird colony (blue dot on the map), may be predicted by conditions over unknown distances at sea (represented by concentric rings), and with unknown time lags. The yellow to red colours illustrate increasing levels of sea surface temperatures.

This project built on the signal (also known as “scalar-on-function”) regression framework for identifying the spatial or temporal extent of the "zone of influence" of predictors the response. In addition, we explored how this simple framework could be extended to ask questions about more complex lagged processes, including those involving multiple predictors, multi-level, non-linear or spatio-temporal lagged effects, and different types of lagged predictor interactions.

This work significantly extends the range of research questions that researchers may ask about the spatial or temporal zone of influence of multiple predictors on their systems. We also provide guidance for fitting these specific models with mainstream statistical software. This provides extra flexibility to combine lagged predictors with other fixed or random effects components and likelihoods, as required by each case study.

To demonstrate our findings, a series of vignettes has been developed, providing, for each model type:

• A verbal description of the model,
• A mathematical description,
• A generic implementation (in R, using the well-established “mgcv” package),
• An illustration with case study exploring how seabird breeding productivity may be explained by the influence of environmental variables (such as prey availability proxies), integrated over a priori unknown areas of sea and temporal windows,
• Guidance for model validation, graphical representation and inference from the model.
• Simulation examples.

Contextual information, theory and vignettes can be found in the “Slides” and “Vignettes” menu of the delivery workshop webpage under the section “Project 2: Estimating Effect Size Variation Across A Zone Of Influence”.

Investigators: Thomas Cornulier (BioSS), Dave L. Miller (BioSS, UKCEH), Kate Searle (UKCEH), Charlotte Regan (UKCEH), Maria Bogdanova (UKCEH)