Click-based echolocation in bats: not so primitive after all

Abstract

Echolocating bats of the genus Rousettus produce click sonar signals, using their tongue (lingual echolocation). These signals are often considered rudimentary and are believed to enable only crude performance. However, the main argument supporting this belief, namely the click’s reported long duration, was recently shown to be an artifact. In fact, the sonar clicks of Rousettus bats are extremely short, ~50–100 μs, similar to dolphin vocalizations. Here, we present a comparison between the sonar systems of the ‘model species’ of laryngeal echolocation, the big brown bat (Eptesicus fuscus), and that of lingual echolocation, the Egyptian fruit bat (Rousettus aegyptiacus). We show experimentally that in tasks, such as accurate landing or detection of medium-sized objects, click-based echolocation enables performance similar to laryngeal echolocators. Further, we describe a sophisticated behavioral strategy for biosonar beam steering in clicking bats. Finally, theoretical analyses of the signal design—focusing on their autocorrelations and wideband ambiguity functions—predict that in some aspects, such as target ranging and Doppler-tolerance, click-based echolocation might outperform laryngeal echolocation. Therefore, we suggest that click-based echolocation in bats should be regarded as a viable echolocation strategy, which is in fact similar to the biosonar used by most echolocating animals, including whales and dolphins.

Appendix

Appendix A: Energy Flux Density

The term “Energy Flux Density”, which is useful for measuring the energy content of a transient sound wave, was defined in order to allow comparisons of sonar signal intensities between terrestrial and aquatic environments (Au 1993). To do so, the classical Energy Flux definition is modified to take into account both the signal duration and the acoustic impedance of the medium:

$$ E = {\frac{1}{\rho c}}\int\limits_{0}^{T} {P^{2} (t)} dt $$

where E is the energy flux density (in units of J/m²), P(t) is the time-varying sound pressure measured at 1-m from the source, T is the signal duration, ρ is the density of the medium (in units of kg/m³) and c is the sound velocity in the medium.

Appendix B: Wide band ambiguity function

The Ambiguity Function is a common tool in radar and sonar signal-design, used for quantitative estimations of the system’s sensitivity to Doppler shifts, and the effect of Doppler on range measurements. The wide-band ambiguity function (WBAF) considers the actual time-compression or expansion of the signal modeled by the Doppler effect, rather than the frequency-shift approximation which can be used for narrow-band signals (which is sufficient for most radar applications) (Levanon and Mozeson 2004).

The first modifications of the conventional ambiguity-function from radar theory to the case of wideband signals were done by Kelly and Wishner (1965) and Cahlander (1962)—the latter study applied the new wideband theory to analyzing bat signal design. Later, WBAF analysis of bat signals was used by several other researchers (Altes and Titlebaum 1970; Simmons and Stein 1980; Holderied et al. 2008)—all of them used the WBAF to analyze FM signals of laryngeal echolocators. Here, we applied for the first time the WBAF analysis to the case of click-based biosonar, and compared the results to a classic FM call, that of the big brown bat.

The WBAF describes the response of a matched filter to a pure returning echo (with no added noise or attenuation) for a set of target distances and relative speeds: See Fig. 2d. Each horizontal slice through the WBAF is a cross-correlation function calculated between the transmitted signal and a Doppler-distorted version, for a particular relative speed. For our calculations, we used the following version of the WBAF (Kelly and Wishner 1965):

$$ \chi (\tau ,\eta) = \eta^{{\frac{1}{2}}} \int {z(t)z^{*} (\eta (t - \tau ))dt} $$

where z(t) is the bat’s call waveform at time t, * stands for complex conjugation, τ is the time delay to the target (which is proportional to the target’s distance), and η is the Doppler scale factor:

$$ \eta = {\frac{1 + v/c}{1 - v/c}} $$

where v is the relative flight speed of the bat compared to the target, and c is the speed of sound (we used c = 343 m/s for the speed of sound in air).