A computer model of the auditory periphery was used to address the question of what constitutes the physiological substrate of absolute auditory threshold. The model was first evaluated to show that it is consistent with experimental findings that auditory-nerve fiber spikes can be predicted to occur when the running integral of stimulus pressure reaches some critical value [P. Heil and H. Neubauer, J. Neurosci. 15, 7404-7415 (2001)]. It was then modified to examine two ways in which the accumulation and clearance of receptor presynaptic calcium might explain this effect. Both methods gave results that matched the animal data. It was also shown how the rate of clearance of presynaptic calcium could be used to explain the origin of differences between low and high spontaneous-rate fiber types. When spiking activity is aggregated across a number of similar high spontaneous-rate fibers and used as the input to a model of a cochlear nucleus coincidence neuron, its response can be used to judge whether or not a stimulus is present. A simulated psychophysical experiment then demonstrated that this simple decision procedure can reproduce measurements of absolute auditory threshold for tones in quiet where the threshold is a joint function of both time and level.