Compensation can be defined as a process by which a system is able to regain its normal state in response to losing a part of its structure. From genes to individuals to communities, compensatory processes ensure functionality, stability and resilience. While there is a rich literature on compensation in natural and semi-natural communities, as well as for crop monocultures, quantification of compensation in the context of diversified agro-ecosystems, such as binary crop mixtures, has remained underdeveloped. We elaborate a method of quantifying compensation which is consistent across systems of only one component (monocultures) and two component-systems (mixtures). Using plant communities and their response to loss of plant density as an example, we apply this concept to a published data set on experimentally grown monocultures and mixtures of beans and oats. Against loss of plant density, oat and bean monocultures compensated 46 % and 33 % of grain yield, respectively. Compensation in the mixture was small (9%) when compensating loss of bean density, but larger (42 %) when bean density was fixed, compensating against loss of oat density. Remarkably, in the case of fixed bean density, the mixtures did not show a higher degree of compensation than the oats monoculture (i.e. where bean density is fixed at zero seeds). Further, we generalize this approach by characterizing four variables, the Contributor (which suffers the loss that needs to be compensated; e.g. plant density), the Reductor (which leads to a reduction in the Contributor; e.g. a mortality factor reducing plant density), the Outcome (which is the variable of interest that directly depends on the Contributor; e.g. grain mass per unit area), and the Compensator (which represents the variable responsible for the compensation, e.g. the grain mass per remaining plant) and summarize this as the ‘CROC’ model of compensation. We provide a framework for quantitative research on compensation in intercropping and other contexts, and its relationship to resilience and stability. The analysis of compensation in mixtures can help to develop the potential of diversification for improving multifunctional performance of agro-ecosystems, especially in response to biotic and abiotic stresses.

补偿可以定义为系统在失去部分结构时能够恢复其正常状态的过程。从基因到个人再到社区，补偿过程确保了功能、稳定性和弹性。虽然有大量关于自然和半自然社区补偿以及作物单一栽培的文献，但在多样化农业生态系统（如二元作物混合物）背景下的补偿量化仍然不发达。我们详细阐述了一种量化补偿的方法，该方法在只有一种成分（单一栽培）和两种成分系统（混合物）的系统中是一致的。以植物群落及其对植物密度损失的反应为例，我们将此概念应用于已发布的关于实验种植的单一栽培以及豆类和燕麦混合物的数据集。针对植物密度的损失，燕麦和豆类单一栽培分别补偿了谷物产量的 46% 和 33%。当补偿豆密度损失时，混合物中的补偿很小 (9%)，但当豆密度固定时，补偿更大 (42%)，补偿燕麦密度的损失。值得注意的是，在豆密度固定的情况下，混合物没有表现出比燕麦单一栽培（即豆密度固定在零种子）更高的补偿程度。此外，我们通过表征四个变量来概括这种方法，贡献者（遭受需要补偿的损失；例如植物密度），减少者（导致贡献者减少；例如死亡率因子降低植物密度），结果（这是直接取决于贡献者的感兴趣变量；例如每单位面积的谷物质量）和补偿器（代表负责补偿的变量，例如每株剩余植物的谷物质量）并将其总结为'CROC' 补偿模式。我们为间作和其他情况下的补偿及其与恢复力和稳定性的关系的定量研究提供了一个框架。对混合物补偿的分析有助于开发多样化的潜力，以提高农业生态系统的多功能性能，特别是在应对生物和非生物胁迫方面。和补偿器（代表负责补偿的变量，例如每个剩余植物的谷物质量）并将其总结为“CROC”补偿模型。我们为间作和其他情况下的补偿及其与恢复力和稳定性的关系的定量研究提供了一个框架。对混合物补偿的分析有助于开发多样化的潜力，以提高农业生态系统的多功能性能，特别是在应对生物和非生物胁迫方面。和补偿器（代表负责补偿的变量，例如每个剩余植物的谷物质量）并将其总结为“CROC”补偿模型。我们为间作和其他情况下的补偿及其与恢复力和稳定性的关系的定量研究提供了一个框架。对混合物补偿的分析有助于开发多样化的潜力，以提高农业生态系统的多功能性能，特别是在应对生物和非生物胁迫方面。