Neurons in the primary visual cortex (V1) are tuned to specific disparities between the two retinal images, which form the neural substrate for stereoscopic vision. We show that V1 neurons in tree shrews, but not in mice, display highly selective responses to narrow ranges of disparity in random-dot stereograms. Surprisingly, V1 neurons in both species show similarly strong tuning to gratings of varying interocular phase differences. This stimulus-dependent dissociation of disparity tuning can be explained by a network model that combines both feedforward and recurrent connections. The features of the model connections are supported by cortical organizations specific to each species. We validate this model by identifying putative inhibitory neurons and confirming their predicted disparity tuning in both species. Together, our studies establish a foundation for using tree shrews in studying binocular vision and raise an exciting possibility of how cortical columns could be uniquely important in computing stereoscopic depth.