Supplementary Figure 15: Self consistency of sound amplitude ratios validates distance estimation approach

Six panels (a – f) represent sound amplitude ratios on calibrated microphones in all bird pairs: 1-2, 1-3, 1-4, 2-3, 2-4, and 3-4. Each dot represents two notes (produced by two different birds) separated by a small time interval (<0.6 s between note onsets). During these quasi-synchronous notes we considered the positions of animals as fixed. The horizontal axis reports the square root of the ratio S^*_i/S_j of microphone amplitudes, where the amplitude S^*_i on the vocalizing animal’s back-attached microphone is marked by an asterisk. The vertical axis displays the corresponding ratio when the other animal is vocalizing. The coefficient b_ij is the regression coefficient estimated by minimizing the sum of squares of residuals ɛ_k, k = 1,…,N (see panel a), where N indicates the number of quasi-synchronous notes. Coefficients b_ij are close to 1, indicating validity of our calibration approach, but significant spread of points reveals low accuracy of one-shot measurements. For distance estimation we assumed that both backpacks had equal distances to the beaks of carrying birds and that these distances were much smaller than the distances between animals.