OccuGAMs : Non‐linear occupancy and abundance modelling with imperfect detection

Abstract Hierarchical occupancy and abundance models (HOAMs) have become a leading approach for inferring wildlife population dynamics because they explicitly account for imperfect detection. HOAMs are suitable for sampling approaches that produce detection histories from repeated visits to the same sites, including direct observations (e.g. bird point counts), indirect observations (e.g. tracks, dung) and remote and passive sensors (e.g. camera traps, acoustic recorders). Wildlife often exhibits non‐linear temporal trends or threshold‐like responses to environmental conditions. However, traditional HOAMs address non‐linearity crudely using global polynomial functions, despite well‐documented limitations. Generalised additive models (GAMs) provide a more flexible approach to non‐linearity, allowing smooth data‐driven estimation through basis functions and penalised splines. Yet, GAMs have remained sparsely adopted in hierarchical occupancy modelling, in part due to the need for custom code in Bayesian modelling languages. We demonstrate the applicability of GAMs within the occupancy and abundance modelling framework (hereafter ‘OccuGAMs’) by comparing traditional HOAMs with polynomials to OccuGAMs. In simulations, OccuGAMs recovered non‐linear relationships more accurately and more often, scoring better on energy and variogram metrics and produced more stable responses at smaller sample sizes. Polynomials performed well in some scenarios but were less generalisable, making OccuGAMs the more robust overall choice, especially when there is no a priori guidance about the functional form. Limitations of OccuGAMs include interpretability of model parameters and sensitivity to the choice and number of basis functions, which can be assessed with diagnostic tools. To promote wider accessibility, we provide code for OccuGAM implementation in JAGS and Stan as well as in the R packages flocker and mvgam .