Spatial confounding in Bayesian species distribution modeling

Abstract

1) Species distribution models (SDMs) are currently the main tools to derive species niche estimates and spatially explicit predictions for species geographical distribution. However, unobserved environmental conditions and ecological processes may confound the model estimates if they have direct impact on the species and, at the same time, they are correlated with the observed environmental covariates. This, so‐called spatial confounding, is a general property of spatial models and it has not been studied in the context of SDMs before. 2) We examine how the estimation accuracy of SDMs depends on the type of spatial confounding. We construct two simulation studies where we alter spatial structures of the observed and unobserved covariates and the level of dependence between them. We fit generalized linear models with and without spatial random effects applying Bayesian inference and recording the bias induced to model estimates by spatial confounding. After this we examine spatial confounding also with real vegetation data from northern Norway. 3) Our results show that model estimates for coarse scale covariates, such as climate covariates, are likely to be biased if a species distribution depends also on an unobserved covariate operating on a finer spatial scale. Pushing higher probability for a relatively weak and smoothly varying spatial random effect compared to the observed covariates improved the model's estimation accuracy. The improvement was independent of the actual spatial structure of the unobserved covariate. 4) Our study addresses the major factors of spatial confounding in SDMs and provides a list of recommendations for pre‐inference assessment of spatial confounding and for inference‐based methods to decrease the chance of biased model estimates.

Spatiotemporal joint species distribution modelling: A basis function approach

“…Finally, this simulation did not assess the performance of any of the methods on spatially structured covariates. In such cases, the issue of spatial confounding (Mäkinen et al, 2022) may present itself as a potential issue, affecting inferential properties such as coverage probabilities and Type I errors of the regression coefficients , due to collinearity between the spatially structured covariate and spatially structured basis functions/latent variables. This issue would have affected all methods tested in this simulation (except the spatially independent stacked SDM), although its severity would be specific to the precise model setup; see also our discussion in Appendix D.…”

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

“…a temporal trend or habitat change as in our two case studies), confounding is minimized due to the added temporal component of multi-season data. We have found that recent guidelines for minimizing spatial confounding and understanding its effects in spatially explicit SDMs are applicable to SVC SDMs (Mäkinen et al, 2022), although further research is needed to understand when such confounding may occur and how to best mitigate it.…”

Integrated species distribution models to account for sampling biases and improve range‐wide occurrence predictions

“…A more extreme option would have been to leave spatial latent effects out also from the model fitting and explain variation in species' log intensity solely with environmental variables. However, such non‐spatial model would have returned overly optimistic uncertainties to model estimates and not necessarily improved estimates' accuracy (Mäkinen et al., 2022). Moreover, the model structure chosen here corresponds to state‐of‐the‐art SDMs, introduced e.g.…”

“…citizen science, data integration, INLA, range prediction, sampling bias, spatial latent effect, Trochilidae relevant covariates (Hawkins et al, 2007;Kim, 2021;Mäkinen et al, 2022). In earlier integrated SDMs which have focused on relatively narrow spatial extents, the risk of such spatial confounding was relatively small (Gelfand & Shirota, 2019;Simmonds et al, 2020), but a recent study showed that spatial confounding impacted the covariate effect estimates already on a country wide extent (Renner et al, 2019).…”

“…The potential of spatial latent effects in cases where there is no spatially explicit covariate data of sampling intensity has been demonstrated previously (Ahmad Suhaimi et al., 2021; Gelfand & Shirota, 2019; Renner et al., 2019; Simmonds et al., 2020), but the approach has as yet not been validated for the full extent of species geographical ranges (Isaac et al., 2020). Indeed, previous work suggested that spatial latent effects might create inaccurate and counter‐intuitive covariate coefficient estimates due to inherent collinearity with relevant covariates (Hawkins et al., 2007; Kim, 2021; Mäkinen et al., 2022). In earlier integrated SDMs which have focused on relatively narrow spatial extents, the risk of such spatial confounding was relatively small (Gelfand & Shirota, 2019; Simmonds et al., 2020), but a recent study showed that spatial confounding impacted the covariate effect estimates already on a country wide extent (Renner et al., 2019).…”