Baffling Cricket Harp

frequency falls below a critical value known as the cutoff frequency, f*. The cutoff frequency depends upon the flare of the horn, which is described by the equation:

Ax and A0 are the cross-sectional areas of the horn at distance x from the throat and at the throat, respectively, and fi is a constant known as the flaring constant. The cutoff frequency, f*, is estimated reasonably well by the equation:

To transmit low frequencies well, therefore, the horn should have a small flaring constant. A well-designed horn is flared so that the cutoff frequency is about an octave below the lowest frequency to be transmitted. Performance is also improved by making the cutoff as sharp as possible. Ordinary horns do badly in this respect, because acoustical performance degrades appreciably even at frequencies much higher than the cutoff. In the jargon of acoustical engineering, the "skirts" of the frequency response curve are wide. Configuring the horn as a Klipsch horn, though, helps make the cutoff frequency "sharper"—that is, the horn maintains high performance even at frequencies very close to f*.

The Singing Burrows of Mole Crickets Most of these design principles for horns were known to musical instrument makers centuries before acoustical engineers came along to tell them they got it right. I don't mean to be flip—acoustical physics has put the design principles for musical instruments on a solid theoretical footing, and this is unequivocally a Good Thing. But the original designers of musical instruments did not bring this type of knowledge to their work. Their knowledge of design was based on a collection of cultural norms, passed down from master to apprentice, continually modified and improved upon in the process.

If this description sounds like an analogy to natural selection, it is a deliberate one. Enormous rewards flowed to those who introduced new and successful innovations to instrument design and fabrication: Antonio Stradivari died a rich man. Similarly high rewards (not monetary, of course, but reproductive) might accrue to animals that refine the ability to communicate with sound, either by transmitting it well or by receiving it well. Indeed, natural selection has refined the acoustical devices used by insects to a remarkable degree. Insect ears, for example, are on a par with vertebrate eyes as organs of remarkable quality in design and function. But there is one outstanding example of refinement in an acoustical structure crafted by an insect.

These acoustic devices are constructed by a group of relatively large crickets, members of the insect family Gryllidae, known collectively as the mole crickets, so called because of their habit of constructing extensive networks of underground tunnels. These tunnels may be so dense in pastures and fields that the crickets become significant agricultural pests. But it is their song, not their economic importance, that concerns us here.

Although mole crickets themselves are rather large (up to six centimeters length), they do not have especially large harps. The tones in mole cricket songs range from about 1.5 kHz up to about 3.6 kHz, which means their harps radiate sound at comparatively long wavelengths. As we have seen, this should make mole crickets poor emitters of sound: they should, like most crickets, emit only a soft chirp. Yet, mole crickets actually produce one of the loudest sounds made by animals. Mole cricket songs can be heard by humans as far away as 600 m. The song of one, a European mole cricket, Gryllotalpa vinae, sets the ground around it visibly vibrating to a radius of 20 centimeters or so.

Mole crickets accomplish this remarkable feat by building singing burrows, which happen to incorporate many of the features that make horns such marvelous acoustic devices. The singing burrows con structed by an American mole cricket, Scapteriscus acletus, nicely illustrate these design features (Fig. 10.7). One of the cricket's tunnels is expanded to a capacious bulb. The singing burrow itself extends from the bulb first horizontally and then turns upward, expanding in cross-section as it goes. At the opening to the surface it is quite wide. The tunnel extending from the bulb is called the horn, which in fact flares like an exponential horn. Separating the bulb from the horn is a narrow constriction. When the male cricket sings, it positions itself at this constriction, facing inward, so that the wings are placed right at the constriction. This configuration should look familiar to you—it is a Klipsch horn. It would appear that these insects have hit upon the same solutions for boosting acoustic performance that musical instrument makers have.

Before getting carried away by the similarity, though, we need to ask some critical questions. As intriguing as its shape might be, the burrow might only be shaped like a Klipsch horn. Does it really work like a Klipsch horn? Here is where the physical foundation laid down by acoustical engineers comes in handy, because we can use it to predict how the burrow, given its shape, should perform. If its expected performance as a horn matches what we know about the song produced by the cricket, then it may indeed be working as a Klipsch horn. Three questions immediately come to mind. First, will the burrow's cutoff frequency fall comfortably below the frequency of the sound it needs to amplify? Second, will the air enclosed in a burrow resonate at a frequency that corresponds to the resonant frequency of the cricket's harp? Third, could the bulb in the tunnel act like the bulb of a Klipsch horn?

We have already seen (equation 10.5) that the cutoff frequency of an exponential horn is determined by its rate of flare. The measured flaring constant for the Scapteriscus burrow is about 49.5 m-1, and equation 10.5 tells us the burrow's cutoff frequency should be about 1.3 kHz. The harp membrane of the Scapteriscus wing resonates at frequencies ranging between 2.5 kHz to 3.0 kHz. The resonant frequency of the harp, therefore, is about an octave higher than the burrow's

Figure 10.7 The singing burrow of Scapteriscus acletus. a: In side view, the horn and bulb are seen to be arranged in the configuration of a Klipsch horn. b: Top view. Shaded lines inside the horn are contour lines added by the artist. c: Cutaway showing the location and orientation of a singing cricket. [From Nickerson, Snyder, and Oliver (1979)]

Figure 10.7 The singing burrow of Scapteriscus acletus. a: In side view, the horn and bulb are seen to be arranged in the configuration of a Klipsch horn. b: Top view. Shaded lines inside the horn are contour lines added by the artist. c: Cutaway showing the location and orientation of a singing cricket. [From Nickerson, Snyder, and Oliver (1979)]

cutoff frequency. You will recall this to be the "rule of thumb" that instrument makers use for flaring the horns they make. So far, so good.

The horn should also have a resonant frequency that comes close to the resonant frequency of the harp. Acoustical theory helps in answering this question too. Unfortunately, the formula is rather complicated, only approximate, and loaded with seemingly arbitrary terms. Its single virtue is that it works well. The horn's resonant frequency, f0, should be:

where L is the horn's effective length (which is its actual length plus 0.6 times the radius of the horn's opening), and h is the length of horn required for its diameter to increase by roughly 2.72 times (actually, by the base of the natural logarithm, e). All these quantities are easily estimated from plaster casts of the burrows. For the Scapteriscus burrow, the value of h is about 40 mm. Lengths range from 65 mm to 85 mm and average radii of the mouth range from 20 mm to 25 mm. Plugging these values into equation 10.6 gives

Table 10.1 Estimated and actual volumes of the capacitative bulbs in singing burrows of three species of mole cricket.

Dominant Estimated Measured frequency of bulb volume bulb volume

Scapteriscus acletus 2.75 4,100 to 6,500 7,000

Gryllotalpa vinae 3.40 12,700 to 19,700 10,250 to 15,500

Gryllotalpa gryllotalpa 1.60 15,600 to 21,000 12,500 to 16,000

an estimated resonant frequency of the burrow of 2.6 to 2.8 kHz. This nicely overlaps the harp's resonant frequency of 2.5 kHz to 3.0 kHz: again, the features of the burrow are consistent with the idea that the burrow is acting as an exponential horn.

The bulb also is about the size one would expect for a Klipsch horn. Here, the formulas acoustical engineers give us are even more approximate, but the best one (from Klipsch himself) indicates the volume V of the bulb of a Klipsch horn should be:

where A is the cross-sectional area of the narrow opening between the bulb and horn and R is the distance along the horn required for its cross-sectional area to double (R is related to the flaring constant, f [equation 10.4]). For the Scapteriscus burrow, A ranges from 110 to 150 mm2, and R ranges from 13 to 15 mm. The formula yields a range of bulb volumes from about 4,150 mm3 to as large as 6,530 mm3. The actual volume of the turnaround gallery is about 7,000 mm3: pretty good correspondence, given that the measurement of volume itself is somewhat inexact. In fact, this correspondence holds for the singing burrows constructed by other mole crickets as well (Table 10.1).

So the shape of the mole cricket burrow is consistent with its acting as a Klipsch horn. But does the burrow actually amplify the sound coming from the cricket's harp, as a Klipsch horn should? Again, the evidence suggests strongly that it does. Amplification by the burrow can be estimated by measuring the intensity of sound emanating from a sound generator— essentially a simulated cricket harp—placed inside the burrow. Comparing this sound with that of the simulated harp standing alone gives a direct estimate of amplification. Indeed, the Scapteriscus burrow amplifies sound, not only at the harp's resonant frequency but over frequencies ranging from 2.5 kHz to 3.0 kHz. The amplification is very large and is greatest—250 times— at the resonant frequency of the Scapteriscus harp (2.7 kHz). This strongly suggests the burrow is tuned to resonate at the harp's natural frequency. Further evidence comes from alterations made to the burrow's structure. Caving in the bulb, for example, should reduce amplification, because doing so compromises the diversion of capacitative work to the bulb that is characteristic of the Klipsch horn. In fact, caving in the bulb drops sound emission from the burrow by 6 to 12 decibels.

So the evidence seems to confirm that the singing burrow, at least that of Scapteriscus, amplifies the sound emerging from the harp. The benefits a mole cricket may accrue from this are manifold, but one obvious advantage lies in the more efficient conversion of muscle work into sound, the raison d'être for horns in the first place. Conversion of muscle work to sound has been estimated for two species of European mole cricket, Gryllotalpa vinae and Gryllotalpa gryllotalpa, which also construct singing burrows (which we will examine in detail momentarily). For comparison, this estimate has also been made for a field cricket that

Table 10.2 Muscle power used to generate sound compared with emitted sound intensity for three species of European cricket.

Muscle power Mean sound Efficiency Song frequency

Gryllotalpavinae 3.5 1.2 34 3.6

Gryllotalpa gryllotalpa 1.0 0.025 1.5 1.6

Gryllus campestris 1.2 0.06 5 4.4

does not build a singing burrow, Gryllus campestris. The numbers are compiled in Table 10.2.

The results are mixed, in an instructive way. First of all, Gryllotalpa vinae in its burrow is clearly a superstar: a whopping 34 percent of its muscle power is converted to sound. This is impressive performance, better than anything we humans are capable of: commercial loudspeaker systems commonly operate at conversion efficiencies of about 2 percent. Scapteriscus burrows probably would yield conversion efficiencies similar to the burrows of Gryllotalpa vinae. Not all "singing burrows" are good acoustic amplifiers, however. Conversion efficiency for Gryllotalpa gryllotalpa is only about 1.5 percent. This performance is poorer than that of a garden-variety field cricket, Gryllus campestris, which uses no external acoustical contrivances and still manages a conversion efficiency up around 5 percent.

This variation in performance may reflect imperfections of burrow construction, or it may simply reflect different approaches to attracting mates that each work well in their own ways. For example, the singing burrow of Gryllotalpa gryllotalpa opens to the surface through numerous small openings rather than through a single flaring horn as characterizes Scapteriscus burrows. The perforated opening of the Gryllotalpa gryllotalpa burrow may muffle the emission of sound, rather as a pillow placed over a loudspeaker would (Fig. 10.8). The relatively low-frequency song (1.6 kHz), even though it emerges with less power, should nevertheless travel further, because lower-frequency sounds generally do. Gryllus campestris may have a relatively higher conversion efficiency because it "tunes" its harp to resonate at a higher frequency, which should improve the baffling provided by the wings and hence the efficiency of sound production. These crickets' high-frequency song may also reflect off surfaces the cricket sits on more effectively than would the lower-frequency songs of mole crickets. Whatever the explanation, exceptions to the theory remind us of two maxims that biologists forget at their peril: (1) perfection isn't everything and (2) there are many ways to crack a nut.

Broadcast Beacons and Guidance Beacons

Mole crickets' singing burrows fall into two functional types, and the shapes of the burrows likewise fall into two categories, as illustrated in Figure 10.9. The first, exemplified by the Scapteriscus burrow, opens to the surface through a single flared horn, with the long axis parallel to the axis of the burrow. In the second type, common to the various burrows constructed by Gryllotalpa, the opening is more oblong and is oriented with its long axis perpendicular to the burrow's axis. In some species, like Gryllotalpa major, the horn opens through a single oblong opening, while in others, like Gryllotalpa vinae, the horn has two openings whose centers are arrayed perpendicular to the burrow's long axis. In some, like Gryllotalpa gryllotalpa, the openings are screened by overlying soil.

The two types of burrows emit sound in different ways. The single opening of the Scapteriscus burrow broadcasts sound as a point source, so that sound radiates from the opening as a fairly uniform hemispheri-

bulb horn multiple horn openings bulb

Tunel Gryllus Campestris

Figure 10.8 Cross-section (above) and top view (below) of the singing burrow of Gryllotalpa gryllotalpa. Doublet horns lead to several small openings at the surface. [After Bennet-Clark (1970)]

escape tunnel cal wave. The Gryllotalpa burrows, on the other hand, broadcast as a so-called line source, in which the sound radiates as a semicircular disk oriented at right angles to the line.4

These two types of "sound beams" each solve the problem of getting the male's message to potential mates, but in different ways. In both, the male must project sound at sufficient power so that a female can hear it when she intercepts the sound wave. Female crickets, for their part, are surprisingly hard of hearing. For a male cricket's song to get the attention of a female, it has to be loud, about 60 decibels or higher— about the intensity of loud chatter at a cocktail party. The male cricket sings louder than this: at one meter from the hole, the song is about 90 decibels—about the sound intensity of an automobile horn blaring one meter from your ear.

The hemispherical bubble of sound emerging from a Scapteriscus burrow radiates to about 30 meters before it becomes too soft to attract the female's atten

4. The fact that the Gryllotalpa vinae burrow has a double opening does not matter acoustically, since two point sources emit sound as a line source does if they are positioned closely enough.

tion. What would happen, though, if the same power was used to drive sound from a line source like the Gryllotalpa burrow? Flattening the sound bubble will project sound further in one dimension, just as squashing a spherical wad of pie crust dough makes it wider (precisely, 42 times wider than the hemispherical bubble, or out to 42 m), although it would have a narrower breadth. This might pay off for a male cricket in three ways.

First, flattening the sound envelope also broadens it, increasing the probability that a female flying about at random will encounter the 60 dB edge of the sound bubble. A few simple calculations show that the "sweep area" of a disk-shaped "sound net" is about 50 percent larger than that of a hemispherical sound bubble emitted at the same intensity. Flattening the sound bubble may also enable a male cricket to distinguish itself more clearly from other males. Gryllotalpa males often sing in leks, large assemblages of males concentrated in a limited area, all competing at once for the attention of females. Leks derive their name from the remarkable communal displays of galliform birds, such as prairie chickens. Several dozen males may line up to display for a single female. The female comes to the lek and sits back and enjoys the show until she chooses



Figure 10.9 Various shapes of the singing burrows of four species of mole crickets.

the male with which she wishes to mate.5 In the visually spectacular display of prairie chicken leks, it is simple to distinguish one male from another. However, distinguishing one male from another in an acoustical lek, like a mole cricket lek, is more difficult. First, one male must ensure that his sound envelope does not overlap another's. Hemispherical sound envelopes present obvious difficulties here, since intense calls will tend to merge into a mega-envelope of sound. This may work fine for attracting females to the lek, but overlapping may not be much help in guiding her to the burrow of any particular male. Flattening

5. The word lek probably has a Swedish origin, from the word for "playground" or "sporting ground."

the sound envelope may reduce the chance that one male's sound envelopes will merge imperceptibly into another's. A flattened sound envelope also acts more effectively as a guidance beacon for the female.

Singing Burrows as "Organs of Extreme Perfection" The singing burrows of mole crickets are certainly wonderful structures. Now, wonder is a good nursemaid of science, because it is the fount of curiosity. It makes a poor partner, though. Science works best when it asks critical questions, and it is our nature as human beings that we do not ask probing questions of that which holds us in thrall. So, when confronted with a truly wonderful structure like the mole cricket burrow, it is important to splash cold water on your face and ask: how does the singing burrow come to be such an apparently well-designed acoustic structure?

An easy answer to this question would invoke the perfecting power of natural selection. Natural selection, so the story goes, rewards "good" adaptations and penalizes "bad" ones. If singing a loud, pure song is important to a male cricket's reproductive success, we could expect natural selection to force the gradual perfection of the singing burrow into the wonderful structure it is. This may very well be so, but it is not a wholly satisfactory explanation. All it really does is transfer our sense of wonder from the singing burrow itself to the supposed power of natural selection. This mode of reasoning has led biologists and others to ascribe almost magical powers to natural selection and to the genes it works on. As many others have pointed out, this is a problem that has plagued evolutionary biology ever since Darwin.

Darwin himself fretted about the implications for his theory of natural selection of what he called "organs of extreme perfection," of which the vertebrate eye is the exemplar. In a nutshell, the problem with organs of extreme perfection is this: how can one credibly assert the spontaneous origin of a complex and perfectly formed structure like the eye? To do so, one must posit a constellation of simultaneous develop-

mental events, all of which are required to make the structure work properly: the retina must be arranged just so;the cornea must be shaped to refract the light just so, the diameter of the eyeball must correspond just so to the focal length of the cornea and lens; and so forth. If any one of these numerous requirements is not met, you do not have a properly functioning structure. It strains credulity to propose that all these things could be made to happen all at once and properly in the helter-skelter milieu of natural selection.

Evolutionary biologists have since come to grips with the problem of organs of extreme perfection, although the problem survives in some fringe elements of biology, like creation science. For one thing, most biologists now have no problem in believing that even a poorly functioning eye is an improvement over an eye that functions even worse, or over no eye at all. So approaching perfection through the gradual improvement in function implied by natural selection does not now seem as high a barrier as it seemed to Darwin and his contemporaries. We also know that the development of eyes is not as complicated as it was once thought—the arthropod homeotic gene eyeless has related genes scattered throughout the animal kingdom. These closely related genes nevertheless promote the development of a wide variety of eye types, including eyes as seemingly disparate as the compound eyes of insects and the camera eyes of vertebrates and some molluscs.

Nevertheless, this "solution" to the matter of organs of extreme perfection still doesn't banish wonder from biology: a feeling of awe still pops up in the view of genes as wondrous arbiters of evolutionary destiny. I grant that this feeling may be natural when we are considering structures, like eyes, that must arise through a process of organic development. But is it so credible when we are talking about external organs of extreme perfection, like the singing burrow of mole crickets? If natural selection explains the construction of such "amplifiers," how do these genes work their wonder? Does the cricket carry around in its DNA a blueprint, a plan, of the perfect acoustic bur row, which it uses to construct the actual burrow? The principle of Goldberg's lever means that we cannot dismiss the possibility out of hand, but it is still hard to believe.

Feedback Tuning of the Singing Burrow Some insight into this question may be gleaned by observing how Scapteriscus constructs its burrow. The cricket begins by excavating the bulb, initially to give itself room to maneuver while it is tunneling. The cricket then pushes its way, head first, out to the surface, opening up the burrow to the outside. Then it goes through a repeating series of three behaviors:

• The cricket pushes dirt out the opening, using its mouth parts and spreading movements of its forelimbs. This action itself will help to flare the mouth of the tunnel as it expands.

• The cricket backs into its tunnel, turns around at the bulb, and emits a short chirp.

• Following the chirp, the cricket moves deeper into the burrow and begins to push soil backwards, moving it out of the burrow. The reworking takes place mostly at the bottom of the tunnel, but the cricket also scoops dirt from the top and sides. Both the bulb and horn of the singing burrow are worked during this stage.

The cricket repeats this sequence several times for about an hour, at which time he settles down and begins to sing for several hours.

During burrow building, the characteristics of the song change dramatically (Fig. 10.10). At the beginning of the job, the harp resonates at about 2.7 kHz, but there is considerable sound energy in both the second and third harmonics (5.5 kHz and 8.2 kHz, respectively). The energy in these secondary frequencies is wasted energy for the cricket, because they are relatively high-frequency sounds and so will not radiate very far. Nor is the female programmed to hear sounds at these frequencies. Furthermore, they represent en a.

Relative intensity -10

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