In our density surface models , we observe that the spatial smooth term s(x, y) often explains a large proportion of the deviance. However, our goal is to model species density primarily as a function of environmental covariates rather than location. Including s(x, y) risks overfitting to spatial structure that may be better explained by environmental variables, especially when these covariates are spatially correlated with x and/or y.
When we exclude s(x, y), we see high residual spatial autocorrelation (Moran’s I > 6), which suggests that the model is missing important spatial structure. Including s(x, y) reduces autocorrelation, but undermines our ability to interpret environmental drivers.
Is there a principled way to account for spatial autocorrelation in DSMs without including the spatial smooth term s(x, y)? Are there recent methodological advances that allow for capturing spatial dependence while still attributing variation to environmental covariates?