Figure 3. Significant SS is observed in the groups of 10 neurons exhibiting HOIs.

(A) (Left) Comparison of the observed SS probabilities of sub-groups of neurons with predictions of the pairwise model. Abscissa, the size of sub-groups. Ordinate, the percentage deviation of observed from predicted average SS probabilities of sub-groups of neurons, where the normalization divides the difference by SS probability predicted from a pairwise model. The comparison was performed for all possible sub-groups of neurons in the 1000 groups of 10 neurons. Whiskers represent 1.5 times the distance from 25th to 75th percentile. Dots are outliers. (Right) Comparison of the observed SS probabilities of the sub-groups with predictions of the SS model. Note the difference in the scales of the ordinates in the Left and Right panels. (B) Distribution of percentage entropy margins for HOIs for the SS groups (red, 16%), i.e. groups for which the SS model showed significantly better fit than the pairwise model, and the rest of the groups (gray, 84%). The right inset shows distribution of the parameter of the SS groups. The distribution was heavily biased toward positive , indicating prevalent excess SS. (C) Group size dependency of the number of SS groups. Solid lines with different colors indicate different numbers of groups selected from each slice: 5, 10, 50 groups per slice, for a total of 100, 200, and 1000 groups of size from 20 slices, respectively. The dashed black line is the result of selecting non-overlapping groups from each slice (see Methods). Thus, the fraction of SS groups and its group size dependency were robust to the degree of overlap between sampled groups in each slice. (D) Scatter plots of entropy margins for HOIs versus entropy margins for SS. The same color indicates groups selected from the same slice culture. Filled circles indicate SS groups. Dashed lines represent different proportions of HOI entropy margin explained by the SS term, . We excluded 13 outliers from the plots. (E) Cumulative distribution function of the proportion of SS, , in the groups exhibiting HOIs (> 3%).