Abstract To circumvent reporting spurious correlations, species distribution models often explicitly account for spatial autocorrelation, for example by including spatially structured random effects. The validity of statistical inference derived from such models has been tested by simulations using null environmental predictors that do not have any causal dependency with the response. Such null environmental predictors can be obtained by permutations of the original predictors or by simulating spatial structures resembling the original predictors. In such approaches, it is important that the permuted or simulated predictors reflect the nature of spatial variation present in the original predictors. Here we present a novel approach for generating realistic null predictors by a shift‐&‐rotate (S&R) approach: we extract environmental variables after randomly translating and rotating the sampling area within a window of defined environmental layers. In this way, the null environmental variables have fully realistic spatial variation and covariation, but no relationship to the response variable. We implement the S&R approach to three main R‐functions and demonstrate with a simulation study how they can be used to untangle causal versus non‐causal relationships within species distribution modelling. These methods allow us to quantify the predictive power attributed within the models due to non‐causal correlations generated by the realistic structure of the environmental covariates. In our case study, we identify when a model incorrectly estimates parameter values, yet still has high predictive power due to the structured nature of the predictor variables. The use of null models is imperative in ecological modelling for testing the accuracy of statistical inference in complex ecological systems and the choice of these null models is far from trivial. Here we provide R functions for generating spatially realistic null models to use in species distribution modelling as well as other spatially explicit fields such as landscape genetics.
Read full abstract