Detecting sounds in quiet is the simplest task performed by the auditory system, but the neural mechanisms underlying perceptual detection thresholds for sounds in quiet are still not understood. Heil and Neubauer [Heil, P., Neubauer, H., 2003. A unifying basis of auditory thresholds based on temporal summation. Proc. Natl. Acad. Sci. USA 100, 6151-6156] have provided evidence for a simple probabilistic model according to which the stimulus, at any point in time, has a certain probability of exceeding threshold and being detected. Consequently, as stimulus duration increases, the cumulative probability of detection events increases, performance improves, and threshold amplitude decreases. The origin of these processes was traced to the first synapse in the auditory system, between the inner hair cell and the afferent auditory-nerve fiber (ANF). Here we provide further support for this probabilistic "continuous-look" model. It is derived from analyses of the distributions of the latencies of the first spikes of cat ANFs with very low spontaneous discharge rates to tones of different amplitudes. The first spikes in these fibers can be considered detection events. We show that, as predicted, the distributions can be explained by the joint probability of the occurrence of three independent sub-events, where the probability of each of those occurring is proportional to the low-pass filtered stimulus amplitude. The "temporal integration" functions of individual ANFs, derived from their first-spike latencies, are remarkably similar in shape to "temporal integration" functions, which relate threshold sound pressure level at the perceptual level to stimulus duration. This further supports a close link between the mechanisms determining the timing of the first (and other) evoked spikes at the level of the auditory nerve and detection thresholds at the perceptual level. The possible origin and some functional consequences of the expansive power-law non-linearity are discussed.