Soils are natural ecosystems that provide ecosystem services, whose provision depends on multiple soil properties, climate conditions and human management. Dependence among soil ecosystem services (SESs) must therefore be considered to reliably assess risks of improving SES, as a function of weather conditions or soil properties. The present study described dependence among regulating and provisioning SESs predicted by a biophysical soil and crop model, based on a dataset of soils in France. We applied vine copula modeling as a statistical method that can model joint distribution functions of three SESs and enabled us to estimate probabilities of exceeding a level of one SES as a function of another SES. Trade-offs may need to be made between them to manage soil and water resources and achieve a given yield. By highlighting the degree of dependence among multiple SESs, copula models thus provide information that may improve understanding or management of ESs.

土壤是提供生态系统服务的自然生态系统，其提供取决于多种土壤特性、气候条件和人类管理。因此，必须考虑土壤生态系统服务（SES）之间的依赖性，以可靠地评估改善 SES 的风险，将其作为天气条件或土壤特性的函数。本研究描述了基于法国土壤数据集的生物物理土壤和作物模型预测的调节和供应 SES 之间的依赖性。我们应用 vine copula 建模作为一种统计方法，可以对三个 SES 的联合分布函数进行建模，并使我们能够估计超过一个 SES 水平作为另一个 SES 函数的概率。可能需要在它们之间进行权衡，以管理土壤和水资源并实现给定的产量。通过强调多个 SES 之间的依赖程度，Copula 模型提供了可以提高对 ES 的理解或管理的信息。