(A) All neurons were assumed to be completely eye-centered, that is tuning shifted by 20° under eccentric fixation protocol. These tuning curves were injected with different levels of noise by Matlab function ‘awgn’. The smaller the signal to noise ratio (SNR, from left to right), the noisier the tuning curve was. For example, the top panels exhibit one trial of the responses sampled at a resolution of 1°. We repeated this sampling for five times and computed the mean firing rate at each azimuth at a resolution of 12° as the tuning curve (bottom panels), a process of which was similar to the real neural recording experiment. Error bars are standard error of mean. (B) Under each noise level, a population of 100 cells was created, and DI was computed in the exact same way as for the real neurons. It is clear that when noise is getting larger in the tuning curves, the DI values tend to be more broadly distributed, generating some seemingly head-centered units. However, the number of these units is small, and importantly these units are statistically defined as ‘unclassified’ based on the bootstrap test procedure. (C) The strength of directional tuning was quantified using a direction discrimination index (DDI, Takahashi et al., 2007) given by: . DDI not only computes the peak to trough modulation (Rmax-Rmin), but also the response variability (SSE: sum squared error around the mean response; N: total number of trials; M: total number of stimulus directions). DDI ranges within [0 1], corresponding to weak and strong SNR, respectively. (D) DI is not significantly dependent on DDI (R = 0.11, p=0.3, Spearman rank correlation) for hypothetical neurons tested under SRN = 5.