Accurate model representation of land- atmosphere carbon fluxes is essential for climate projections. However, the exact responses of carbon cycle processes to climatic drivers often remain uncertain. Presently, knowledge derived from experiments, complemented by a steadily evolving body of mechanistic theory, provides the main basis for developing such models. The strongly increasing availability of measurements may facilitate new ways of identifying suitable model structures using machine learning. Here, we explore the potential of gene expression programming (GEP) to derive relevant model formulations based solely on the signals present in data by automatically applying various mathematical transformations to potential predictors and repeatedly evolving the resulting model structures. In contrast to most other machine learning regression techniques, the GEP approach generates "readable" 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). Based on real observations we explore the responses of the different components of terrestrial respiration at an oak forest in south-eastern England. We find that the GEP-retrieved models are often better in prediction than some established respiration models. Based on their structures, we find previously unconsidered exponential dependencies of respiration on seasonal ecosystem carbon assimilation and water dynamics. We noticed that the GEP models are only partly portable across respiration components, the identification of a "general" terrestrial respiration model possibly prevented by equifinality issues. Overall, GEP is a promising tool for uncovering new model structures for terrestrial ecology in the data-rich era, complementing more traditional modelling approaches.