Considering more complex covariate responses improves predictive performance in dynamic occupancy models

Saoirse Kelleher, Gurutzeta Guillera-Arroita, Marc Kéry, Jane Elith, Natalie Briscoe

Finding the right level of model complexity is a key challenge in most contexts, including ecology where data are often messy and underlying patterns complex. Dynamic occupancy models (DOMs) are increasingly used for modelling species distributions. DOMs have advantages over traditional species distribution models because their hierarchical structure allows them to explicitly model changes in occupancy over time while accounting for imperfect detection. The modelled processes (initial occupancy, colonisation, extinction, and detection) can be described as a function of covariates to account for heterogeneity in occupancy and detection dynamics. While this model structure is more complex than most alternative distribution models, in practice users of DOMs tend to fit simple linear responses to covariates with only infrequent use of non-linear responses or interactions. However, where data suffices and where ecologically justified, permitting more complex relationships between covariates and species occurrence may yield greater predictive power. Here, we assess how the complexity of covariate relationships affects the predictive performance of DOMs fit to Swiss breeding bird data. We find that models allowing quadratics and interactions tend to provide superior performance in predicting future occurrence, and that some covariates are only informative predictors when represented using non-linear relationships or interactions. Relying solely on linear relationships alone is not only inconsistent with ecological theory, but also potentially costly for predictive ability. To improve predictive power and the utility of these models for identifying important habitat and species at risk of declines, users of dynamic occupancy models should carefully consider not only their choice of candidate covariates, but also the functional forms of covariate relationships.