Shapley values reveal the drivers of soil organic carbon stock prediction

Insights into the controlling factors of soil organic carbon (SOC) stock variation are necessary both for our scientific understanding of the terrestrial carbon balance and to support policies that intend to promote carbon storage in soils to mitigate climate change. In recent years, complex statistical and algorithmic tools from the field of machine learning have become popular for modelling and mapping SOC stocks over large areas. In this paper, we report on the development of a statistical method for interpreting complex models, which we implemented for the study of SOC stock variation. We fitted a random forest machine learning model with 2206 measurements of SOC stocks for the 0-50 cm depth interval from mainland France and used a set of environmental covariates as explanatory variables. We introduce Shapley values, a method from coalitional game theory, and use them to understand how environmental factors influence SOC stock prediction: what is the functional form of the association in the model between SOC stocks and environmental covariates, and how does the covariate importance vary locally from one location to another and between carbon-landscape zones? Results were validated both in light of the existing and well-described soil processes mediating soil carbon storage and with regards to previous studies in the same area. We found that vegetation and topography were overall the most important drivers of SOC stock variation in mainland France but that the set of most important covariates varied greatly among locations and carbon-landscape zones. In two spatial locations with equivalent SOC stocks, there was nearly an opposite pattern in the individual covariate contribution that yielded the prediction - in one case climate variables contributed positively, whereas in the second case climate variables contributed negatively - and this effect was mitigated by land use. We demonstrate that Shapley values are a methodological development that yield useful insights into the importance of factors controlling SOC stock variation in space. This may provide valuable information to understand whether complex empirical models are predicting a property of interest for the right reasons and to formulate hypotheses on the mechanisms driving the carbon sequestration potential of a soil.