Dynamic Substrate for the Physical Encoding of Sensory Information in Bat Biosonar

Horseshoe bats have dynamic biosonar systems with interfaces for ultrasonic emission (reception) that change shape while diffracting the outgoing (incoming) sound waves. An information-theoretic analysis based on numerical and physical prototypes shows that these shape changes add sensory information (mutual information between distant shape conformations $<20\%$), increase the number of resolvable directions of sound incidence, and improve the accuracy of direction finding. These results demonstrate that horseshoe bats have a highly effective substrate for dynamic encoding of sensory information.

Figure 1

Different sample types used to obtain acoustic far-field (beam pattern) data on the emitter and receiver dynamics of greater horseshoe bat biosonar. (a) (NN) Digital noseleaf model used for computer animation of in vivo dynamics followed by numerical analysis. (b) (PN) Detailed physical replica of the noseleaf created through additive manufacturing (scaled $2\times$). (c) (BP) Portrait of a greater horseshoe bat. (d) (NP) Digital pinna model used to recreate dynamic behavior of 3D landmarks (shown as small spheres) obtained from stereo high-speed recordings. (e) (PP) Simplified deformable physical prototype modeled after the horseshoe bat pinna (scaled $2.5\times$).

Figure 2

Dynamic changes in noseleaf and pinna shapes result in a sequence of device characteristics (beam patterns) with low dependence as measured by mutual information. Bar height indicates normalized mutual information (in %) as a function of distance between the respective shape conformations (averaged over all conformation pairs with the respective separation value). Error bars indicate the maximum and minimum values for mutual information found across all pairs of conformation stages with the same distance. Distance is measured on an ordinal scale within a sample of representative conformations across the structures’ deformation cycle. NN, PN, NP, PP refer to the samples shown in Fig. 1.

Figure 3

Combining stages of a dynamic sensor increases the directional resolution in the presence of noise. Directional resolution is quantified by an upper bound on the number of resolvable directions that is a function of signal-to-noise ratio (additive white Gaussian noise [31]). The upper bound is expressed either directly as the maximum number of resolvable directions (right-hand axis) or as a directional resolution (in bits, i.e., ${\log }_2$ of the maximum number of resolvable directions, left-hand axis). Black: individual sensor conformation stages; dark gray: effect of averaging signals from an identical sensor conformation stage five times; light gray: effect of combining five different sensor conformation stages. NN, PN, NP, PP refer to the samples as shown in Fig. 1.

Figure 4

Combining dynamic sensor conformations increases directional accuracy. Estimation accuracy quantified by Cramér-Rao lower bound (CRLB). Top row: map of error ellipses (90% confidence intervals) for repeated individual sensor conformation stage (left-hand side) and combination of five different sensor conformation stages (right-hand side). Error ellipses are drawn on top of the averages over all beampatterns gains used in the respective scenario. Bottom row: distribution of accuracy (major axis of the error ellipses for the 90% confidence interval). Blue: individual sensor conformation stages, green: effect of averaging the same stage five times, red: effect of using five different sensor conformation stages. NN, PN, NP, PP refer to the samples as shown in Fig. 1.