With an eye on uncertainty: Modelling pupillary responses to environmental volatility

Living creatures must accurately infer the nature of their environments. They do this despite being confronted by stochastic and context sensitive contingencies—and so must constantly update their beliefs regarding their uncertainty about what might come next. In this work, we examine how we deal with uncertainty that evolves over time. This prospective uncertainty (or imprecision) is referred to as volatility and has previously been linked to noradrenergic signals that originate in the locus coeruleus. Using pupillary dilatation as a measure of central noradrenergic signalling, we tested the hypothesis that changes in pupil diameter reflect inferences humans make about environmental volatility. To do so, we collected pupillometry data from participants presented with a stream of numbers. We generated these numbers from a process with varying degrees of volatility. By measuring pupillary dilatation in response to these stimuli—and simulating the inferences made by an ideal Bayesian observer of the same stimuli—we demonstrate that humans update their beliefs about environmental contingencies in a Bayes optimal way. We show this by comparing general linear (convolution) models that formalised competing hypotheses about the causes of pupillary changes. We found greater evidence for models that included Bayes optimal estimates of volatility than those without. We additionally explore the interaction between different causes of pupil dilation and suggest a quantitative approach to characterising a person’s prior beliefs about volatility.Author summary: Humans are constantly confronted with surprising events. To navigate such a world, we must understand the chances of an unexpected event occurring at any given point in time. We do this by creating a model of the world around us, in which we allow for these unexpected events to occur by holding beliefs about how volatile our environment is. In this work we explore the way in which we update our beliefs, demonstrating that this updating relies on the number of unexpected events in relation to the expected number. We do this by examining the pupil diameter, since—in controlled environments—changes in pupil diameter reflect our response to unexpected observations. Finally, we show that our methodology is appropriate for assessing the individual participant’s prior expectations about the amount of uncertainty in their environment.