Inferring species absence from zero-sighting records using analytical Bayesian models with population growth

The eradication of invasive species and surveillance to detect new incursions are important for protecting native biodiversity and agricultural productivity, and are being applied across increasingly large areas due to improvements in eradication tools and funding commitments. For an effective and cost-efficient assessment of eradication success or population absence, quantitative frameworks play a critical role, with many current methods relying on Bayesian stochastic models to simulate the monitoring and detection processes. While flexible, Bayesian simulation models of monitoring systems can be computationally expensive, particularly when applied over large areas or when trying to capture rare events. In addition, it can be difficult to gain insight into system behaviour from large simulation models. Here, we develop analytical solutions for the posterior distributions of these simulation models and derive expressions for statistics of interest, such as the probability of pest absence and population size, given no detections. Solutions are fast and simple to apply and explicitly expose the nonlinear interactions between system drivers—prior assumptions, population growth and detection processes. Using an example application, we demonstrate that solutions are equivalent to published simulation results, with the potential to simplify and extend current analysis. We also show that model results without population growth, results with deterministic growth and results with stochastic growth can be quite different, with the potential to affect management decisions. Analytical solutions for the posterior distributions of these Bayesian models offer a powerful and efficient means of assessing population absence following eradication or surveillance programmes, which complements current simulation-based methods.