Ecological and evolutionary dynamics were thought to operate on different time scales. Recent evidence showed that evolution could be rapid enough to interplay with ecological dynamics and form eco-evolutionary feedbacks. These feedbacks are hard to identify in nature, due to the complexity of the mechanisms and the difficulty of obtaining phenotypic, demographic, and environmental variables. We lack quantitative evidence on feedback effects in real systems, which prevents us from painting a complete view of feedback architectures. We develop a mathematical framework, neural ordinary differential equations (NODEs), to quantify feedbacks from time series data of the evolutionary, ecological, and environmental variables in the system. The framework combines ordinary differential equations and artificial neural networks, to identify, non-parametrically, drivers of evolutionary and ecological dynamics, and relies on the Geber method to recover the contribution of ecological change to evolution, and vice versa. We apply the technique to recover the coupling between the dynamics of three species in a prey-predator system. We find that main interactions, between the prey and top predator are conserved across replicates, while weaker interactions, between the intermediate predator and the other species, are not. We also apply the technique to recover eco-evolutionary feedbacks in two of Darwin’s finches species. We find that feedbacks involve a direct coupling between population dynamics and phenotypic change in only one of the species, while the other involves a coupling with resource levels. Our work demonstrates the potential of NODEs in uncovering drivers of dynamics in systems where prior mechanistic knowledge is lacking, and shows the importance of indirect effects in driving eco-evolutionary feedbacks in nature
