Quantifying group specificity of animal vocalizations without specific sender information

Recordings of animal vocalization can lack information about sender and context. This is often the case in studies on marine mammals or in the increasing number of automated bioacoustics monitorings. Here, we develop a framework to estimate group specificity without specific sender information. We introduce and apply a bag-of-calls-and-coefficients approach (BOCCA) to study ensembles of cepstral coefficients calculated from vocalization signals recorded from a given animal group. Comparing distributions of such ensembles of coefficients by computing relative entropies reveals group specific differences. Applying the BOCCA to ensembles of calls recorded from group of long-finned pilot whales in northern Norway, we find that differences of vocalizations within social groups of pilot whales (Globicephala melas) are significantly lower than intergroup differences.

Figure 1

How to construct ensembles (bags-of-calls) for inter- and intragroup comparisons.

Figure 2

Examples for spectrograms, i.e., visualizations (color coding or gray scale) of the temporal evolution of the power spectral density) (left) and cepstrograms (right) for two vocalizations of long-finned pilot whales. Loosely speaking, a line in the cepstrogram (representing large values of $c(q,t)$ is shifted upwards, whenever two lines in the spectrogram approach each other. The color coding (gray scale) of the cepstrograms refers to $ln\left(c(q,t)/\text{max}\left[c\right(q,t\left)\right]\right)$ with $t=0,\cdots ,T$ and $T$ being the length of the call and $q=1,\cdots ,128$ being the index of each cepstral coefficient. Spectrograms are computed with a window length of $w=512$, allowing us to estimate $\frac{w}{2}$ spectral coefficients and $\frac{w}{4}=128$ cepstral coefficients for each time step.

Figure 3

Four examples for distributions of cepstral coefficients $c_i(q,t)$: (a), $p_{2,i}$ (b), $p_{7,i}$, (c) $p_{57,i}$, and (d) $p_{88,i}$ estimated for groups $i=\{B,D,F,G,H,I\}$.

Figure 4

Overlap in call usage. (a) Observations of calls within different groups of pilot whales. Note that call type numbering is arbitrary and does not reflect similarity in call structure, i.e., call $i$ and $i+1$ do not necessarily have to be similar in structure. Panels (b) and (c) show a similarity network and its adjacency matrix estimated by the OCU approach. Here the distance between edges in the network and the entries of the matrix represent the number of shared call types.

Figure 5

Symmetrized Kullback-Leibler indicate differences in distribution of cepstral coefficients. The blue (dark) solid lines represent intragroup comparisons, whereas the red (gray) dotted and orange (light gray) dashed lines represent intergroup comparisons. Each panel shows the result for the pairwise comparison of two groups as indicated in each panel's legend. The number of calls in ensembles created for pairwise group comparisons was chosen to be the same for inter- and intragroup comparisons.

Figure 6

Quantifying inter- and intragroup differences using BOCCA. (a) Numbers of calls in ensembles for pairwise group comparisons. Intergroup differences are larger than intragroup differences if the coefficients $v_{ij}$ (c) and $w_{ij}$ (b) are positive. Each comparison is done twice, calculating either intragroup difference of the group with more recordings or less recordings. Confidence Intervals [orange (light gray) shaded areas] are estimated by comparing randomly generated, not group-specific, ensembles and assuming that the resulting values follow Student's distribution. To test whether the similarity of groups B and J is due to recordings made during the common encounter of groups B and J, we repeat the analysis excluding all calls of group J that were recorded during the common encounter [plotted as green triangles in (b) and (c)]. The inverse of the weighted coefficients $s_{ij}=1/w_{ij}$ is expressed as the distance between edges in the network (d) and as entries of the network's adjacency matrix (e).

Figure 7

Comparing the results of OCU and BOCCA. (a) Ranking pairs of groups according to their similarity allows to compare the OCU ($y$ axis) and BOCCA ($x$ axis). Points on the diagonal represent pairs of groups which have the same similarity ranking according to both approaches. Two results (red squares and blue points) are obtained due to the asymmetry of BOCCA with respect to the group that is chosen to estimate the intragroup similarity. (b) The minimal number of swaps needed to transform the ranking according to the OCU approach into the BOCCA ranking is 9. We compare this to $r$, the number of swaps needed for sorting random vectors of 15 different integers. Estimating the distributions $p\left(r\right)$ using either ${10}^3, {10}^4$, and ${10}^5$ samples of random vectors, we find that the minimal number of swaps ($r_{\text{BOCCA-OCU}}=9$) is lower than than 94% of all calculated values of $r$.