Abstract
Introduction: Pupil size is commonly used to estimate arousal by assuming pupil size is a linear transformation of task events. However, this assumption has not been tested. Methods / Results: Both pupil size and saccade rate entrain to task timing, but only pupil size is amplitude-modulated by arousal. We propose that a noisy common input drives both saccades and pupil size. We formalize this hypothesis in a linear-nonlinear model in which pupil size is the output of a low-pass filter acting on the noisy common input and a saccade is generated each time this same input crosses a threshold. Unlike previous work, we do not assume that the input to the pupil is simply the timing of task events, but rather that it has more complex dynamics. Ten observers performed an orientation discrimination task that varied in difficulty in alternate runs (75 trials/run; 4 s/trial). We estimated the dynamics of the common input as well as its amplitude. The amplitude was associated with arousal, i.e., significantly modulated by task difficulty, accuracy, and reaction time. Our model predicted task-evoked pupil responses equally well for easy and difficult trials, with 81% variance explained overall. In a second experiment, we ran 2 and 4 s trials in separate blocks. Our model’s single free parameter generalized between the two timings whereas previous (linear) models failed to (reduction in R^2 between in- and out-of-sample fits: 2.5x larger for linear model vs. our model). Discussion: Saccades and pupil size share a common input, consistent with recent reports that electrical stimulation of superior colliculus neurons above or below the threshold of saccade generation evokes a pupil response (Joshi et al., 2016; Wang & Munoz, 2020). Our model formalizes this observation. We offer a novel algorithm, based on this model, yielding arousal estimates that are accurate and generalizable.