FIGURE 1. Weak pairwise cross-correlations and the failure of the independent approximation.

a, A segment of the simultaneous responses of 40 retinal ganglion cells in the salamander to a natural movie clip. Each dot represents the time of an action potential. b, Discretization of population spike trains into a binary pattern is shown for the green boxed area in a. Every string (bottom panel) describes the activity pattern of the cells at a given time point. For clarity, 10 out of 40 cells are shown. c, Example cross-correlogram between two neurons with strong correlations; the average firing rate of one cell is plotted relative to the time at which the other cell spikes. Inset shows the same cross-correlogram on an expanded time scale; x-axis, time (ms); y-axis, spike rate (s^-1). d, Histogram of correlation coefficients for all pairs of 40 cells from a. e, Probability distribution of synchronous spiking events in the 40 cell population in response to a long natural movie (red) approximates an exponential (dashed red). The distribution of synchronous events for the same 40 cells after shuffling each cell's spike train to eliminate all correlations (blue), compared to the Poisson distribution (dashed light blue). f, The rate of occurrence of each pattern predicted if all cells are independent is plotted against the measured rate. Each dot stands for one of the 2¹⁰ = 1,024 possible binary activity patterns for 10 cells. Black line shows equality. Two examples of extreme mis-estimation of the actual pattern rate by the independent model are highlighted (see the text).