The hippocampus has been proposed to encode environments using a representation that contains predictive information about likely future states, called the successor representation. However, it is not clear how such a representation could be learned in the hippocampal circuit. Here, we propose a plasticity rule that can learn this predictive map of the environment using a spiking neural network. We connect this biologically plausible plasticity rule to reinforcement learning, mathematically and numerically showing that it implements the TD-lambda algorithm. By spanning these different levels, we show how our framework naturally encompasses behavioral activity and replays, smoothly moving from rate to temporal coding, and allows learning over behavioral timescales with a plasticity rule acting on a timescale of milliseconds. We discuss how biological parameters such as dwelling times at states, neuronal firing rates and neuromodulation relate to the delay discounting parameter of the TD algorithm, and how they influence the learned representation. We also find that, in agreement with psychological studies and contrary to reinforcement learning theory, the discount factor decreases hyperbolically with time. Finally, our framework suggests a role for replays, in both aiding learning in novel environments and finding shortcut trajectories that were not experienced during behavior, in agreement with experimental data
