To ensure survival, animals must update the internal representations of their environment in a trial-and-error fashion. Psychological studies of associative learning and neurophysiological analyses of dopaminergic neurons have suggested that this updating process involves the temporal-difference (TD) method in the basal ganglia network. However, the way in which the component variables of the TD method are implemented at the neuronal level is unclear. To investigate the underlying neural mechanisms, we trained domestic chicks to associate color cues with food rewards. We recorded neuronal activities from the medial striatum or tegmentum in a freely behaving condition and examined how reward omission changed neuronal firing. To compare neuronal activities with the signals assumed in the TD method, we simulated the behavioral task in the form of a finite sequence composed of discrete steps of time. The three signals assumed in the simulated task were the prediction signal, the target signal for updating, and the TD-error signal. In both the medial striatum and tegmentum, the majority of recorded neurons were categorized into three types according to their fitness for three models, though these neurons tended to form a continuum spectrum without distinct differences in the firing rate. Specifically, two types of striatal neurons successfully mimicked the target signal and the prediction signal. A linear summation of these two types of striatum neurons was a good fit for the activity of one type of tegmental neurons mimicking the TD-error signal. The present study thus demonstrates that the striatum and tegmentum can convey the signals critically required for the TD method. Based on the theoretical and neurophysiological studies, together with tract-tracing data, we propose a novel model to explain how the convergence of signals represented in the striatum could lead to the computation of TD error in tegmental dopaminergic neurons.