Statistical significance of secondary peaks in the auto-correlation function

Wässle and colleagues first observed that the local structure of cell mosaics was approximately hexagonal1, as the histogram of the angular difference of all neighbors to a reference cell within some distance showed a mode at 60deg. Their analysis was based on the location of the cell bodies (not the receptive fields). However, the same conclusion holds true if one uses the actual centers of the receptive field themselves, obtained by simultaneously mapping them by means of electrode arrays2. Supplementary Fig 1 shows a (smoothed) auto-correlation of a sample mosaic of receptive field centers shown on the left. These data are from one of the reconstructed mosaics in Gauthier et al (2009). The center peak at the origin was removed to ease visualization. It can be seen the structure of the secondary peaks is clearly hexagonal. Further, one can also detect the presence of additional peaks beyond the secondary peaks, indicating the spatial scale over which the RGC mosaic is hexagonal extends farther than its immediate neighborhood. The spatial scale over which such hexagonal structure is present is now a matter of additional research.