Reply to Pachai et al.

Peripheral vision is fundamentally limited by the spacing between objects. When asked to report a target's identity, observers make erroneous reports that sometimes match the identity of a nearby distractor and sometimes match a combination of target and distractor features. The classification of these errors has previously been used to support competing 'substitution' [1] or 'averaging' [2] models of the phenomenon known as 'visual crowding'. We recently proposed a single model in which both classes of error occur because observers make their reports by sampling from a biologically-plausible population of weighted responses within a region of space around the target [3]. It is critical to note that there is no probabilistic substitution or averaging process in our model; instead, we argue that neither substitution nor averaging occur, but that these are misclassifications of the distribution of reports that emerge when a population response distribution is sampled. This is a fundamentally different way of thinking about crowding, and on this basis we claim to have provided a mechanism unifying categorically distinct perceptual errors. Our goal was not to model all crowding phenomena, such as the release from crowding when target and flanks differ in color or depth [4]. Pachai et al.[5] have suggested that our model is not unifying because it inaccurately predicts perceptual performance for a particular stimulus. Although we agree that our model does not predict their data, this specific demonstration overlooks the critical aspect of the model: perceptual reports are drawn from a weighted population code. We show that Pachai et al.'s [5] own data actually provide evidence for the population code we have described [3], and we suggest a biologically-plausible analysis of their stimuli that provides a computational basis for their 'grouping' account of crowding.