A Response duration (N = 37 playback experiments) and B approach distance (N = 37 playback experiments) by males to playbacks of second-order (red) and third-order (blue) allies. Black dots represent the mean, with 95% confidence intervals shown. Triangles represent playbacks for which the association indices (i.e. social bond strengths) between the male played back and the subject male(s) were between 0.1 and 0.2, i.e. relatively weak bonds for dyads within the same second-order alliance (red triangles), and relatively strong bonds for third-order alliance dyads (blue triangles) (see Fig. 1B). Asterisks denote statistical significance (***p < 0.0001; **p = 0.002; linear mixed-effect models). Source data are provided as a Source data file.