Using a multivariate regression tree to analyze trade-offs between ecosystem services: Application to the main cropping area in France.

Analysis of trade-offs and synergies between ecosystem services (ES) and their underlying drivers is a main issue in ES research. The analysis is complex and requires innovative analytical approaches. To address this complexity, we used an original approach that combines a multivariate regression tree (MRT), data analysis, and spatial mapping. We applied this approach to the main cropping region in France (mainly the Paris basin of production) using an existing dataset (i.e. soil, climate, crop sequences and management) from the French National Ecosystem Assessment to determine relationships between agricultural production, two services to farmers - nitrogen provision to crops and water provision to crops - and three services to society - blue water provision, water quality regulation, and climate regulation. To support land managers and decision-makers, we also analyzed the extent to which manageable soil properties and agricultural practices (crop rotation and management) are major drivers of trade-offs or synergies. We demonstrated that water quality regulation, nitrogen provision to crops, and climate regulation have synergistic relationships in production situations in the northeastern region of the study area due to the types of crop rotation, frequency of cover crops in the crop rotation, the soil pH, and the soil available water capacity. We also identified that cover crops, while promoting these three ES, can drive a trade-off between two key water-related services: water provision to crops and blue water provision (i.e. between a service to farmers and one to society). By capturing non-linear relationships and threshold effects, our MRT-based approach overcomes the main limitations of classic statistical approaches. The approach is also spatially explicit and simple and intuitive to interpret, especially for non-scientists; our results thus provide researchers and ecosystem managers (e.g. agricultural policy makers) with key information to design ecosystem management strategies that promote a balanced bundle of ES.