Against a backdrop of rising uncertainty driven by a warming climate, environmental policy has become increasingly reliant on precautionary buffers to safeguard public health, prevent irreversible environmental damages and limit the likelihood of exceeding critical thresholds. These probabilistic constraints are usually implemented under a separability assumption even though outcomes are often dependent. Examples include ambient air pollution and water quality standards, phytosanitary trade measures, and reference points in fisheries management. In this paper, we characterize how stochastic dependence among environmental variables influences environmental policy when the governing regulatory systems use probabilistic precautionary buffers. Our approach builds on Sklar's theorem and the copula representation of multivariate distributions and uses stochastic dependence orderings to compare policy design for different dependence structures including correlated, independent and separable risks. Dependence typically renders policy based on separability suboptimal and we characterize how policy should be adjusted in the presence of correlated risks. We illustrate the theory using fisheries management in the Gulf of Maine, one of the fastest-warming ocean ecosystems on the planet. In its multispecies fishery, even a mild positive correlation between stocks can result in a substantial reduction in effort limits if overfishing is to be avoided.

在气候变暖导致不确定性上升的背景下，环境政策越来越依赖预防性缓冲措施来维护公共健康，防止不可逆转的环境破坏并限制超过关键阈值的可能性。这些概率约束通常是在可分离性假设下实现的，即使结果通常是相关的。例子包括环境空气污染和水质标准，植物检疫贸易措施以及渔业管理参考点。在本文中，我们描述了当监管体系使用概率性预防性缓冲区时，环境变量之间的随机依赖性如何影响环境政策。我们的方法基于Sklar' s定理和多变量分布的copula表示，并使用随机依赖性排序比较不同依赖性结构（包括相关，独立和可分离风险）的策略设计。依赖关系通常会使策略基于可分离性欠佳，并且我们描述了在存在相关风险时应如何调整策略。我们用缅因州海湾的渔业管理来说明这一理论，该海湾是地球上变暖最快的海洋生态系统之一。如果要避免过度捕捞，即使是种群之间的温和正相关也可能导致努力极限的显着降低。依赖关系通常会使策略基于可分离性欠佳，并且我们描述了在存在相关风险时应如何调整策略。我们用缅因州海湾的渔业管理来说明这一理论，该海湾是地球上变暖最快的海洋生态系统之一。如果要避免过度捕捞，即使是种群之间的温和正相关也可能导致努力极限的显着降低。依赖关系通常会使策略基于可分离性欠佳，并且我们描述了在存在相关风险时应如何调整策略。我们用缅因州海湾的渔业管理来说明这一理论，该海湾是地球上变暖最快的海洋生态系统之一。如果要避免过度捕捞，即使是种群之间的温和正相关也可能导致努力极限的显着降低。