Figure 8

Network-structure curves and SRI distributions by season. Black curves show the number of Girvan-Newman clusters in the thresholded network (left y-axis). Gray bars show the fraction of dyads with the given SRI value (right y-axis). Red dots show the points at which the network-structure curves display slope changes at the significance level of 0.05 or below with the window size w = 0.2 (see Methods; exact P-values for this and other window sizes are shown in Additional file 8: Figure S7). While the majority of ties are weaker than 0.2 in both real and randomized data, the distribution has a long tail in real data but not in randomized data. Randomized network shows no ties above a threshold of 0.5, and a nearly level network structure curve up to this threshold with no significant slope changes. In contrast, observed networks for each season show peaked curves with significant changes in slope. Q _max remains above 0.6 for real data while for randomized data it peaks and falls sharply (see Additional file 9: Figure S8).