1. 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.
2. 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.
3. 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.
4. 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.

中文翻译：

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使用具有人口增长的分析贝叶斯模型从零视记录中推断物种缺失

1. 根除入侵物种和监测新入侵物种对于保护本地生物多样性和农业生产力非常重要，并且由于根除工具和资金承诺的改进，正被应用于越来越大的地区。对于根除成功或人口缺失的有效且具有成本效益的评估，定量框架起着至关重要的作用，许多当前的方法依赖于贝叶斯随机模型来模拟监测和检测过程。
2. 虽然灵活，但监控系统的贝叶斯模拟模型的计算成本可能很高，尤其是在大面积应用或试图捕获罕见事件时。此外，很难从大型仿真模型中深入了解系统行为。在这里，我们为这些模拟模型的后验分布开发了分析解决方案，并推导出了感兴趣的统计数据的表达式，例如在没有检测到的情况下害虫不存在的概率和种群规模。
3. 解决方案应用起来既快速又简单，并明确暴露了系统驱动因素之间的非线性相互作用——先验假设、人口增长和检测过程。使用示例应用程序，我们证明解决方案等效于已发布的仿真结果，具有简化和扩展当前分析的潜力。我们还表明，没有人口增长的模型结果、确定性增长的结果和随机增长的结果可能大不相同，有可能影响管理决策。
4. 这些贝叶斯模型的后验分布的分析解决方案提供了一种强大而有效的方法来评估根除或监测计划后的人口缺失，它补充了当前基于模拟的方法。