Data from: Avoiding tipping points in fisheries management through Gaussian process dynamic programming

Model uncertainty and limited data are fundamental challenges to robust management of human intervention in a natural system. These challenges are acutely highlighted by concerns that many ecological systems may contain tipping points, such as Allee population sizes. Before a collapse, we do not know where the tipping points lie, if they exist at all. Hence, we know neither a complete model of the system dynamics nor do we have access to data in some large region of state space where such a tipping point might exist. We illustrate how a Bayesian non-parametric approach using a Gaussian process (GP) prior provides a flexible representation of this inherent uncertainty. We embed GPs in a stochastic dynamic programming framework in order to make robust management predictions with both model uncertainty and limited data. We use simulations to evaluate this approach as compared with the standard approach of using model selection to choose from a set of candidate models. We find that model selection erroneously favours models without tipping points, leading to harvest policies that guarantee extinction. The Gaussian process dynamic programming (GPDP) performs nearly as well as the true model and significantly outperforms standard approaches. We illustrate this using examples of simulated single-species dynamics, where the standard model selection approach should be most effective and find that it still fails to account for uncertainty appropriately and leads to population crashes, while management based on the GPDP does not, as it does not underestimate the uncertainty outside of the observed data.

模型不确定性与数据匮乏是实现自然系统人类干预稳健管理的根本性挑战。诸多生态系统可能存在临界点（如阿利种群规模（Allee population sizes））的相关担忧，恰恰凸显了这两类挑战的严峻性。在系统发生崩溃前，即便临界点确实存在，我们也无法确定其具体位置。因此，我们既无法完整构建系统动态的模型，也无法在临界点可能存在的大范围状态空间区域获取观测数据。

我们阐释了采用高斯过程（Gaussian Process, GP）先验的贝叶斯非参数方法，如何灵活表征这类内在不确定性。为在同时存在模型不确定性与数据有限的场景下生成稳健的管理预测，我们将高斯过程嵌入随机动态规划（stochastic dynamic programming）框架之中。我们通过仿真模拟，对比了该方法与基于模型选择（model selection）从候选模型集中选取最优模型的标准方法的表现。

研究发现，模型选择会错误地偏向不存在临界点的模型，进而制定出会导致种群灭绝的收获策略。高斯过程动态规划（Gaussian Process Dynamic Programming, GPDP）的表现几乎与真实模型一致，且显著优于标准方法。我们通过单物种种群动态的仿真案例验证了这一结论：即便在标准模型选择方法本该表现最优的场景中，该方法仍未能恰当考量观测数据以外的不确定性，最终引发种群崩溃；而基于GPDP的管理策略则未出现此类问题，因其不会低估观测数据覆盖范围以外区域的不确定性。