Spatial modelling of agro-ecologically significant grassland species using the INLA-SPDE approach

The use of spatially referenced data in agricultural systems modelling has grown in recent decades, however, the use of spatial modelling techniques in agricultural science is limited. In this paper, we test an effective and efficient technique for spatially modelling and analysing agricultural data using Bayesian hierarchical spatial models (BHSM). These models utilise analytical approximations and numerical integration called Integrated Nested Laplace Approximations (INLA). We critically analyse and compare the performance of the INLA and INLA-SPDE (Integrated Nested Laplace Approximation with Stochastic Partial Differential Equation) approaches against the more commonly used generalised linear model (glm), by modelling binary geostatistical species presence/absence data for several agro-ecologically significant Australian grassland species. The INLA-SPDE approach showed excellent predictive performance (ROCAUC 0.9271-0.9623) for all species. Further, the glm approach not accounting for spatial autocorrelation had inconsistent parameter estimates (switching between significantly positive and negative) when the dataset was subsetted and modelled at different scales. In contrast, the INLA-SPDE approach which accounted for spatial autocorrelation had stable parameter estimates. Using approaches which explicitly account for spatial autocorrelation, such as INLA-SPDE, improves model predictive performance and may provide a significant advantage for researchers by reducing the potential for Type I or false-positive errors in inferences about the significance of predictors.