Scaling of echolocation call parameters in bats

One of Neill Alexander’s many and diverse contributions to biology has been to relate scaling processes to form and function in animals (Alexander, 1981, 1996). Scaling is a powerful tool in understanding why animals function or behave in the ways they do. Many biological parameters are dependent on body size, including physiological, biomechanical and ecological processes (Peters, 1983; Calder, 1984; Schmidt-Nielsen, 1984). Scaling has been used, for example, to explain why body size is constrained within upper and lower limits in birds (Pennycuick, 1975; Rayner, 1996). In this paper, I will investigate how the scaling of echolocation call parameters influences form and function in bats. First, it is necessary to present some background information on when bats use echolocation and how echolocation call structure relates to function.

Echolocation is used to some extent by all bats in the suborder Microchiroptera (more than 750 species in the suborder) that have been studied to date. All microchiropterans probably use biosonar for orientation, but it is not always used for the detection and localisation of prey. The dominant frequencies of sound used in bat biosonar vary between approximately 11 kHz (Zbinden and Zingg, 1986; Fullard and Dawson, 1997) and 212 kHz (Fenton and Bell, 1981). Vision is of limited use during the night, and echolocation is effective for detecting obstacles, even in complete darkness (Griffin, 1958). Most microchiropterans (70 %; Hill and Smith, 1984) are at least partly insectivorous, and high–frequency echolocation is an ideal sensory system for detecting small, aerial insects at night. High frequencies must be used to obtain strong echoes from small targets (see below). Echolocation is not so effective for detecting prey objects hidden amongst objects that are not of interest to the bat, such as leaves. The problem for the bat is then to isolate the prey echo from the unwanted (clutter) echoes, and many insectivorous bats switch off echolocation when hunting for prey in clutter, such as above leaf litter on the ground. Prey may then detected by listening for prey-generated sounds (e.g. Fiedler, 1979), visually, if sufficient light is available (e.g. Bell, 1982), or by olfaction (G. Jones, unpublished observations). Many microchiropteran bats, especially those in the Family Phyllostomidae, eat nectar and fruit. Food may then be located by olfaction, with the final localisation of the fruit being achieved by echolocation (Thies et al., 1998). Fruits hanging in open spaces may be detected solely by echolocation (Kalko and Condon, 1998).

No bats in the suborder Megachiroptera echolocate, with the exception of species in the genus Rousettus. These bats echolocate by producing short clicks (1–2 ms) by tongue clicking (Herbert, 1985). Because their echolocation is specialised, and because their clicks are produced in a different way from the laryngeal-produced sonar pulses of microchiropterans, I will not consider them further.

I present analyses based largely on data collected by students and myself on time-expanded recordings of echolocation sequences from free-living bats in five continents. Search-phase (Griffin et al., 1960) calls from foraging or commuting bats are used. Supplementary data were taken from the literature. Review sources for echolocation call parameters are Jones (1994, 1996) and Waters et al. (1995). Additional data were taken from Schnitzler et al. (1994), Heller (1995), Kalko (1995a), Obrist (1995), Britton et al. (1997), O’Farrell and Miller (1997), Vaughan et al. (1997), Fenton et al. (1998), Kalko et al. (1998) and N. Vaughan, K. E. Barlow and M. R. Gannon (in preparation). In this review, my regression analyses are Type I linear regressions, and transformations to natural logarithms were performed on data for all scaling analyses.

I have adopted Schnitzler and Kalko’s (1998) categorization of echolocation calls into the frequency-modulated (FM), constant-frequency (CF) and quasi-constant-frequency (QCF) varieties, because the terminology is meaningful in a functional context. I also categorize bats into low-duty-cycle (<30 %) and high-duty-cycle (>30 %) types, with low-duty-cycle bats being intolerant of pulse–echo overlap, and high-duty-cycle taxa being tolerant (see Fig. 1 for a justification of this separation). The importance of duty cycle in shaping pulse design will become apparent. To allow my comparisons to be set in a phylogenetic context, I have separated bats into families in which sample sizes are sufficient. I therefore recognise the following groups: FM bats (split into Vespertilionidae, Phyllostomidae and ‘other families’, i.e. Natalidae and Mystacinidae); QCF bats (Vespertilionidae, Molossidae, Emballonuridae and ‘other families’, i.e. Mormoopidae, Noctilionidae and Craseonycteridae). All these groups comprise low-duty-cycle bat species. The high-duty-cycle groups are the Rhinolophidae, Hipposideridae and Pteronotus parnellii (Mormoopidae). Summary data on echolocation call parameters for these groups are given in Table 1.

Bat echolocation calls typically consist of FM (frequency-modulated) and CF (constant-frequency) components. FM sweeps cover a wide range of frequencies (typically an octave) in a short time (often less than 5 ms). Such calls show design features that are useful for localisation of objects because their echoes encode precise information about target range and angle (Schnitzler and Kalko, 1998). Rather than spreading energy relatively evenly over a call, some bats focus energy into a relatively narrow bandwidth over a longer duration (often less than approximately 3 kHz, over 5–20 ms). In these quasi-constant-frequency (QCF) components, detection of glints in echoes caused by sound reflecting off moving insect wings is enhanced, but localisation performance is diminished. Bats that use FM and QCF components in their calls typically operate at low duty cycles (<20 %, Fig. 1). They are intolerant of overlap between returning echoes and outgoing pulses (Kalko and Schnitzler, 1993), so are restricted to using relatively short pulses (Waters et al., 1995).

Some bats use long-duration CF calls with Doppler shift compensation; for example, species in the families Rhinolophidae and Hipposideridae in the Old World, and Pteronotus parnellii (Mormoopidae) in the New World. The bats lower the frequency of their calls to compensate for Doppler shifts induced by their own flight speeds (Schnitzler, 1968), so that the call always returns at a frequency to which their ears and auditory neurons are finely tuned (the acoustic fovea; Schuller and Pollak, 1979). Doppler shift compensation may be incomplete in hipposiderids (Habersetzer et al., 1984). Bats that use Doppler shift compensation may therefore separate pulse and echo in the frequency rather than in the time domain (Fenton et al., 1995), and this has consequences for the durations of the pulses that they can emit. The production of long pulses means that these bats operate at high duty cycles. Hipposiderids use duty cycles between 30 and 40 %, rhinolophids between 50 and 70 % and P. parnellii of approximately 50 % (Fig. 1). The differences in duty cycle among different categories of echolocating bats are demonstrated clearly when duty cycle is plotted against pulse duration. Pulse duration explains 80 % of the variation in duty cycle across all echolocating bat species.

Call structure reflects the foraging ecology of bats (e.g. Neuweiler, 1989). Hence, species that forage in open habitats often emit calls at low frequencies (that travel far), and calls can be of long duration since the objects of interest are distant and pulse–echo overlap is not problematic. Calls are often QCF in structure so that energy is focused into a narrow bandwidth to maximise ranging and so that detection is enhanced (Schnitzler and Kalko, 1998). Bats that forage along edge habitats often emit FM/QCF calls combining localisation accuracy from the FM components with detection performance from the QCF component. Bats that forage in clutter are of two general types. Both are sensitive to prey movement, although in different ways. Low-duty-cycle bats emit FM calls for orientation, and often switch off echolocation and rely on other sensory input for prey detection and localisation. Prey movement often generates sounds to which the bats respond (Marimuthu, 1997). High-duty-cycle CF bats can detect fluttering targets amongst echo clutter since echoes from moving insect wings contain abrupt changes in frequency and intensity whenever the wing position is normal to the sound beam (Neuweiler, 1989; Schnitzler and Kalko, 1998). Therefore, bats that use Doppler shift compensation can still detect prey in clutter by using echolocation.

From Table 1, it is clear that FM bats produce short calls and have the lowest duty cycles. Their calls are specialised for localisation, and they are generally broadband and lack any narrowband components. Some species may produce more than one call per predicted wingbeat, yet the duty cycle is usually less than 7 %. QCF species have longer pulses: their signals contain narrowband components, and their duty cycles are higher than those of FM species, improving their chances of detecting aerial prey. Duty cycle averages between 7 and 10 % in the QCF groupings studied. A higher duty cycle is not used because the bats often flap their wings without calling, leaving long intervals between pulses for the detection of distant targets. CF bats such as rhinolophids emit the longest pulses and have the highest duty cycles. Hipposiderids emit shorter pulses at higher frequencies for their body mass than do rhinolophids (Heller and von Helversen, 1989; Jones, 1996). Although some species presumably emit several pulses per wingbeat (Table 1), they do not attain the high duty cycles shown by rhinolophids. Hipposiderids often emit higher frequencies than do rhinolophids, and some species show only partial Doppler shift compensation (Habersetzer et al., 1984). Whether these factors contribute to hipposiderids operating at lower duty cycles than rhinolophids is not clear.

Echolocating bats often call at between 20 and 60 kHz (Fenton et al., 1998). This bandwidth reflects a compromise between the avoidance of high frequencies, which are severely affected by atmospheric attenuation (Lawrence and Simmons, 1982), and of low frequencies, which give only weak echoes from very small targets (Pye, 1993).

In many animal taxa, bigger species produce lower-frequency sounds (e.g. frogs, Ryan, 1985; birds, Ryan and Brenowitz, 1985). This is expected because structures associated with sound production, such as drum membranes and strings, produce lower-frequency sounds as linear size increases (Pye, 1979). I therefore predict that call frequency scales negatively with body size in echolocating bats. The maximal amplitude of echolocation call frequency scaled negatively with body mass in five families of bats (Rhinolophidae, Hipposideridae, Emballonuridae, Vespertilionidae and Molossidae) for which sample size was reasonable (Jones, 1996) and would almost certainly be found in a sixth (Phyllostomidae) given call frequency data from more species (Fig. 2). Exponents of the scaling relationship ranged between −0.36 and −0.49 for standard linear regression equations, and between −0.48 and −0.49 for the reduced major axis equations. There was no significant difference in slopes among families (Jones, 1996). Most rhinolophids and hipposiderids call at higher frequencies for their body mass than do species in other families, however. This is because they generally channel more energy into the second, rather than the first, harmonic in their calls.

I predict that pulse duration should scale positively with body mass in echolocating bats. Positive scaling should occur because bigger bats have higher wing loadings (because volume increases faster than surface, or wing, area with linear dimensions), so fly faster (Norberg, 1987). Their faster flight allows larger bats to probe for more distant targets. They can therefore increase their pulse duration because echoes return relatively late from distant targets, and pulse–echo overlap does not occur until long after the start of pulse emission. Smaller bats will try to detect closer targets and will use shorter pulses to avoid pulse–echo overlap. Pulse duration scales with body mass, but only in bats that emit QCF signals and in hipposiderids. Significant relationships for QCF bats are seen in the Vespertilionidae, the Molossidae and the Emballonuridae (Fig. 3). Bigger bats that emit FM signals do not emit longer signals, neither do larger rhinolophids.

Across bats in general, wingbeat frequency scales negatively with body mass (Jones, 1994; Norberg, 1998). Maximum wingbeat frequency scales negatively with body size in relation to the duration of the wing stroke, which in turn is inversely proportional to wing length (Pennycuick, 1972). Aerodynamic theory therefore predicts an exponent of −0.33 for the scaling of maximum wingbeat frequency. Minimum wingbeat frequency is predicted to scale in proportion to mass to the power −0.67 (Norberg, 1998). My updated analysis (Fig. 4) gives an exponent of −0.28 for the scaling of wingbeat frequency in echolocating bats, similar to the value of −0.27 cited by Norberg (1998).

Aerial hawking bats are predicted to emit one pulse per wingbeat when searching for prey. This is because calling is linked intimately with the wingbeat cycle. The echolocation calls of aerial hawking bats are intense. Laboratory measurements of flying bats give estimates of 103–106 dB peSPL re 2 ×10⁻⁵ N m⁻² at 10 cm for Pipistrellus pipistrellus for example (Waters and Jones, 1995). The only source level estimates (at 10 cm) for free-flying aerial-hawking bats are 100 dB peSPL for Myotis siligorensis, 110–115 dB SPL for Craseonycteris thonglongyai (Surlykke et al., 1993) and approximately 103 dB SPL for Myotis septentrionalis (Miller and Treat, 1993). These calls are intense, between the amplitudes of sound produced by thunder and a jet taking off nearby (Bradbury and Vehrencamp, 1998). It will cost a bat considerable energy to produce intense sound pulses when at rest (Speakman et al., 1989), but echolocation calls during flight are produced at no obvious extra cost to the cost of flight (Speakman and Racey, 1991). This is the consequence of the bat synchronising call production with the wingbeat (Suthers et al., 1972), using the downstroke muscles to power flight and to assist in the production of pressure for the production of intense echolocation pulses (Lancaster et al., 1995). The outcome of the predicted link between wingbeat cycle and vocalisation is that pulse repetition rate should scale with body mass in the same way that wingbeat frequency does. In fact, pulse repetition rate decreases much more rapidly as body mass increases in bats that hunt insects by aerial hawking (Fig. 4).

Most (75 %) echolocating bats produced 0.5–2 pulses per predicted wingbeat when searching for prey (Jones, 1994). When data are considered by echolocation category, there is a negative relationship between pulse repetition rate and mass in QCF vespertilionids and emballonurids, and in hipposiderids (Fig. 4). Larger QCF bats produce fewer than the predicted 1 pulse per wingbeat. Hence, the slopes for the scaling of pulse repetition rate are steeper than for wingbeat frequency in QCF vespertilionids (−0.42) and emballonurids (−0.79). This follows because mass increases as the cube, and surface area as the square, of linear dimensions. Large bats therefore have higher relative wing loadings than small bats. High wing loading confers fast, unmanoeuverable flight (Norberg and Rayner, 1987), and many large aerial insectivorous bats fly in open habitats. They often therefore echolocate distant targets and may sometimes not call during each wingbeat. They may not send out a sound pulse until the echo returns from an earlier call to a distant target.

This analysis of the scaling of pulse repetition rate with body mass is simplistic. Although it is informative about why small and medium-sized aerial insectivorous bats call at 1 pulse per wingbeat, does it tell us anything about bats that hunt by gleaning? What happens during prey-capture behaviour when bats attain pulse repetition rates of up to 200 Hz? And if the coupling of calling and flapping is an adaptation that allows the production of intense vocalisations during flight, and not at rest, why do some bats echolocate when perched?

Bats that hunt in clutter usually produce calls of low intensity (Waters and Jones, 1995), presumably to minimize the return of clutter echoes in complex habitats. Many gleaning bats produce more than one call per predicted wingbeat. Such species include Nycteris macrotis (Nycteridae), Macroderma gigas (Megadermatidae), Trachops cirrhosus (Phyllostomidae) and several species in the vespertilionid subfamily Kerivoulinae (Jones, 1994; Kingston et al., 1999) and in the family Hipposideridae (Jones, 1994). Kerivoula spp. produce batches of low-intensity pulses with gaps between them, and the repetition rate of pulse batches is much closer to the predicted wingbeat frequency than is the pulse repetition rate (Kingston et al., 1999). I therefore suggest that the bats are trading off call intensity against repetition rate. Instead of producing 1 pulse per wingbeat, some gleaning bats may produce a batch of low-intensity pulses during one exhalation. Gleaning bats can echolocate at high pulse repetition rates because the targets in which they are interested are often close. They can therefore avoid pulse–echo overlap by producing short calls with short pulse intervals.

A trade-off between call intensity and the number of pulses is also supported from investigations of the wingbeat cycle during terminal buzzes. Terminal buzzes are produced when an echolocating bat approaches a target, often an aerial prey item (Griffin et al., 1960). During the buzz, the pulse repetition rate is increased, and the pulse duration and pulse interval are shortened. The pulse repetition rate may reach 200 Hz during the terminal buzz (e.g. Jones and Rayner, 1988; Kalko, 1995b; Kalko and Schnitzler, 1989). Call intensity and auditory sensitivity both decrease as echolocating bats approach a target, seemingly so that perceived echo amplitude can be stabilized (Simmons and Kick, 1984; Hartley, 1992). Indeed, as a Daubenton’s bat, Myotis daubentonii, moves into a terminal buzz from the search phase, the bat produces batches of low-intensity calls per wingbeat rather than the one per wingbeat during the search phase (Britton, 1996).

Rhinolophid bats often echolocate while perched (e.g. Jones and Rayner, 1989; Neuweiler et al., 1987). If echolocation is costly when bats are stationary, this is unexpected. However, rhinolophids have a stiffened rib cage and specialised abdominal musculature that allows them to produce intense echolocation calls at relatively low cost when perched, thus allowing the detection of prey from perches and saving the high-energy costs associated with flight (J. R. Speakman, W. C. Lancaster, S. Ward, G. Jones and K. R. Cole, in preparation). It is not known whether other perch-feeding bats possess similar adaptations.

What is the relevance of the above scaling relationships? The most important consequences perhaps concern trade-offs between pulse duration and call frequency, constraints on prey detection and upper constraints on body size.

Low-duty-cycle bats are intolerant of pulse–echo overlap. They therefore emit shorter and shorter pulses as they approach targets. Larger bats fly faster and detect prey over longer ranges (Barclay and Brigham, 1991). High atmospheric attenuation at high frequencies means that high-frequency calls are only operational over a short range. Low-duty-cycle bats that use high frequencies must therefore emit short-duration calls if they are to avoid pulse–echo overlap. I therefore predict a negative relationship between pulse duration and peak frequency (see also Waters et al., 1995). The more detailed analysis reported here shows a linear relationship between logarithmically transformed values of pulse duration and frequency within QCF vespertilionids and emballonurids, and in hipposiderids. The relationship is almost significant in FM vespertilionids (P=0.051) (Fig. 5).

The significance of this relationship is that low-duty-cycle bats must use short pulses. However, short pulses reduce the chances of detecting insect wingbeats. The only mechanism that allows the use of long-duration calls at high frequency is to evolve Doppler shift compensation, so that pulse and echo can be separated in the frequency domain. Rhinolophid bats do this and therefore achieve the detection benefits of long pulses.

A frequency of 10 kHz has a wavelength of 3.4 cm in air, while 100 kHz has a wavelength of 3.4 mm. Theory predicts that spheres will reflect weak echoes if their circumference is smaller than the wavelength of the impinging sound (Pye, 1993). If insects reflect sound in a similar way to spheres, then bats must use relatively high frequencies to obtain strong echoes from them. Therefore, an understanding of the relationship between insect size and sound frequency is crucial to understanding the optimal call frequency used by echolocating bats. There is now evidence of a relationship between prey size and call frequency, as predicted by the Rayleigh effect, for insects (R. D. Houston, A. M. Boonman and G. Jones, in preparation). Reflectivity decreases sharply when the wave length exceeds the wing length of the insect being detected, and low-frequency ultrasound (20–30 kHz) reflects poorly from small insects (2.5–5.0 mm wing length). By using a model based on our knowledge of bat hearing, R.D. Houston, A. M. Boonman and G. Jones (in preparation) predict that small insects are unavailable to bats that use low frequencies and long-duration pulses. This is because low frequencies reflect weak echoes from small targets, and since low-frequency bats emit long pulses (see above), the emitted pulse would mask echoes from small insects. Moreover, because the bat’s middle ear muscles contract during pulse emission (Henson, 1965), the faint echoes from these small targets could not be detected by the bat, so very small insects are in theory unavailable to bats that use long-duration, low-frequency pulses.

Few species of microchiropteran bat weigh more than 50 g, and approximately 70 % of species weigh less than 20 g (Jones, 1996). Aerial-hawking bats range in mass from 2 g (Craseonycteris thonglongyai) to 160 g (Cheiromeles torquatus). It is tempting to believe that echolocation constrains maximal body size in bats because species in the Pteropodidae (Megachiroptera) are on average significantly heavier than all families of Microchiroptera, with species such as Pteropus giganteus weighing up to 1200 g. Megachiropterans do not use laryngeal sonar.

Because large bats emit low-frequency pulses, their calls have long wavelengths. They may therefore be unable to exploit very small prey. Echolocating bats may be restricted to being small because of these frequency constraints (Barclay and Brigham, 1991). Vision is not suited for the detection of targets at night, and most bat species use ultrasound for echolocation because it reflects strongly from small targets such as flying insects (see above). Body size in animals appears to set rigorous constraints on call frequency. The vocal apparatus of small animals can only produce high-pressure sound at high frequencies (Bradbury and Vehrencamp, 1998). In general, animals most effectively produce sounds with wavelengths equal to or smaller than their body size. This is not a problem for bats, which need to produce high-frequency sounds. If large bats cannot produce sounds of a sufficiently short wavelength to detect small insects, aerial-feeding bats may be limited in their maximum body size by echolocation constraints (Barclay and Brigham, 1991; Jones, 1996).

The intimate link between wingbeat and pulse emission may also limit body size in bats. Large bats may be unable to call at sufficiently high rates to build up a sufficiently detailed view of their surroundings. Prey detection rate may be limited by pulse repetition rate. If so, large aerial-feeding bats may be unable to detect insects at a fast enough rate to meet the high metabolic needs associated with being large (Jones, 1994). Heller (1995) analysed echolocation calls of the largest aerial insectivorous bat, Cheiromeles torquatus, and argued that it produced calls of higher frequency and at higher repetition rates than predicted for its body size. Heller (1995) therefore suggested that factors other than echolocation constraints explain size limitations on aerial insectivorous bats. However, Heller’s (1995) data show that the pulse repetition rate of Cheiromeles torquatus (6.3 Hz) is close to the wingbeat frequency (5.2 Hz) for a 160 g bat predicted by the relationship in Fig. 4. The bat is therefore producing close to the expected one pulse per wingbeat, as predicted if pulse repetition rate constrains body size. Thus, it seems that echolocation constrains body size in bats for reasons associated with the scaling of both call frequency and pulse repetition rate. Scaling analysis therefore gives insights into why echolocating bats are typically small.

I thank Kate Barlow, Tigga Kingston, Nikky Thomas and Nancy Vaughan for access to unpublished information and John Altringham for inviting me to prepare this paper. Rob Houston provided valuable comments on an earlier draft.