Acoustic Effects Accurately Predict an Extreme Case of Biological Morphology

The biosonar system of bats utilizes physical baffle shapes around the sites of ultrasound emission for diffraction-based beam forming. Among these shapes, some extreme cases have evolved that include a long noseleaf protrusion (sella) in a species of horseshoe bat. We have evaluated the acoustic cost function associated with sella length with a computational physics approach and found that the extreme length can be predicted accurately from a fiducial point on this function. This suggests that some extreme cases of biological morphology can be explained from their physical function alone.

Figure 1

Bourret’s horseshoe bat (Rhinolophus paradoxolophus) has an extraordinarily long noseleaf sella: (a) a typical horseshoe-bat noseleaf (sella length 2.7 mm) in the Big-eared horseshoe bat (Rhinolophus macrotis), (b) Bourret’s horseshoe bat (sella length 9.1 mm). In each image, the sella is marked by an arrow. The two species shown are closely related and both belong to the taxonomic “philippinensis group”. Measured by maximum forearm length, the Big-eared horseshoe bat is only about 16% smaller than Bourret’s horseshoe bat [6].

Figure 2

Scaling of the sella allows controlled experimentation while retaining natural shape complexity: The examples of scaled digital noseleaf representations shown are derived from a single specimen of Bourret’s horseshoe bat. The scaling factor of each derived shape relative to the original sella is indicated below the shape. The natural length of the sella shown [the same as in Fig. 1b] was 9.1 mm; the sellas of the other two noseleaves studied were 7.8 and 8.2 mm long.

Figure 3

Sella scale affected the beam pattern of the three harmonics in different ways as evident by directivity examples obtained at different sella scales (columns) for the three harmonics of the biosonar pulse (rows): Beam gain (individually normalized for each beam pattern) is coded linearly by color ($s$ scale bar). Gain contours are spaced in increments of 0.2 and grid lines in increments of 15° for latitude and longitude. The white meridian marks the azimuth of the maximum beam gain for the first and second harmonic. The white horizontal bars indicate the 90%-of-maximum beam gain points between at which beamwidth was measured.

Figure 4

The natural length of the sella is a fiducial point in the relationship between sella scale and beamwidth: (a) average beamwidth at an amplitude threshold of 90% of maximum beam gain, with averaging over specimen and frequency (2nd harmonic: 6 frequencies from 50 to 55 kHz); error bars depict the standard deviation, (b) average residual of a two-segment piecewise linear fit to beamwidth as a function of sella scale, the residual is minimized if the border between the segments is placed at the natural sella length, (c) average number of lobes along the beam pattern cross section in the 3rd harmonic (6 frequencies from 77 to 82 kHz) defined by the meridian through the global beam gain maximum; error bars depict the standard deviation, (d) average residual of a two-segment piecewise linear fit to average lobe number as a function of sella scale.