Guidelines for the use of spatially-varying coefficients in species distribution models


Species distribution models (SDMs) are increasingly applied across macroscales using detection-nondetection data sources. However, assumptions of stationarity in species-environment relationships or population trends are frequently violated at broad spatial scales. Bayesian spatially-varying coefficient (SVC) models can readily account for nonstationarity, yet their use is relatively scarce, due, in part, to a gap in understanding both the data requirements needed to fit SVC SDMs, as well as the inferential benefits of applying a more complex modeling framework. Using simulations, we present guidelines and recommendations for fitting single-season and multi-season SVC SDMs. We display the inferential benefits of SVC SDMs using an empirical case study assessing spatially-varying trends of 51 forest birds in the eastern US from 2000-2019. We provide user-friendly software to fit SVC SDMs in the spOccupancy R package. While all datasets are unique, we recommend a minimum sample size of approximately 500 spatial locations when fitting single-season SVC SDMs, while for multi-season SVC SDMs, approximately 100 sites is adequate for even moderate amounts of temporal replication (e.g., 5 years). Within our case study, we found 88% (45 of 51) of species had strong support for spatially-varying occurrence trends. Further, SVC SDMs revealed spatial patterns in occurrence trends that were not evident in simpler models that assumed a constant trend or separate trends across ecoregions. We suggest five guidelines: (1) only fit single-season SVC SDMs with more than approximately 500 sites; (2) consider using informative priors on spatial parameters to improve spatial process estimates; (3) use data from multiple seasons if available; (4) use model selection to compare SVC SDMs with simpler alternatives; and (5) develop simulations to assess the reliability of inferences. These guidelines provide a comprehensive foundation for using SVC SDMs to evaluate the presence and impact of nonstationary environmental factors that drive species distributions at macroscales.