The pupil dilates and reconstricts following task events. It is popular to model this task-evoked pupil response as a linear transformation of event-locked impulses, whose amplitudes are used as estimates of arousal. We show that this model is incorrect and propose an alternative model based on the physiological finding that a common neural input drives saccades and pupil size. The estimates of arousal from our model agreed with key predictions: Arousal scaled with task difficulty and behavioral performance but was invariant to small differences in trial duration. Moreover, the model offers a unified explanation for a wide range of phenomena: entrainment of pupil size and saccades to task timing, modulation of pupil response amplitude and noise with task difficulty, reaction time–dependent modulation of pupil response timing and amplitude, a constrictory pupil response time-locked to saccades, and task-dependent distortion of this saccade-locked pupil response.
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