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Accurate modelling of land-atmosphere carbon fluxes is essential for future climate projections. However, the exact responses of carbon cycle processes to climatic drivers often remain uncertain. Presently, knowledge derived from experiments complemented with a steadily evolving body of mechanistic theory provides the main basis for developing the respective models. The strongly increasing availability of measurements may complicate the traditional hypothesis driven path to developing mechanistic models, but it may facilitate new ways of identifying suitable model structures using machine learning as well. Here we explore the potential to derive model formulations automatically from data based on gene expression programming (GEP). GEP automatically (re)combines various mathematical operators to model formulations that are further evolved, eventually identifying the most suitable structures. In contrast to most other machine learning regression techniques, the GEP approach generates models that allow for prediction and possibly for interpretation. Our study is based on two cases: artificially generated data and real observations. Simulations based on artificial data show that GEP is successful in identifying prescribed functions with the prediction capacity of the models comparable to four state-of-the-art machine learning methods (Random Forests, Support Vector Machines, Artificial Neural Networks, and Kernel Ridge Regressions). The case of real observations explores different components of terrestrial respiration at an oak forest in south-east England. We find that GEP retrieved models are often better in prediction than established respiration models. Furthermore, the structure of the GEP models offers new insights to driver selection and interactions. We find previously unconsidered exponential dependencies of respiration on seasonal ecosystem carbon assimilation and water dynamics. However, we also noticed that the GEP models are only partly portable across respiration components; equifinality issues possibly preventing the identification of a "general" terrestrial respiration model. Overall, GEP is a promising tool to uncover new model structures for terrestrial ecology in the data rich era, complementing the traditional approach of model building

Reverse engineering model structures for soil and ecosystem respiration: the potential of gene expression programming