Knock-knock, who’s there: Sex-coding, competition and the energetics of tapping communication in the tok-tok beetle, Psammodes striatus (Coleoptera: Tenebrionidae)

I describe the abdomino-substratal tapping communication system of a Southern African tenebrionid beetle, Psammodes striatus (Fabricius, 1775) (Coleoptera: Tenebrionidae: Molurini), using computer simulation of tapping signals and computer-assisted acquisition of precise response timing data, augmented with data from natural beetle-beetle communication. Communication consists of trains of 5 - 7 Hz taps in groups or trains separated by 2-3 sec intervals. Male beetles spontaneously produce groups of tap-trains with 8 - 18 taps per train. If other beetles reply, an alternating duet commences. Solitary female beetles do not tap spontaneously but respond to male tapping with short, distinctive tap-trains containing 4 – 6 taps; they ignore female signals. In contrast, extensive communication occurs between male beetles, the nature of which changes significantly if the stimulus call is typical of male or of female beetles. Inter-male communication consists of long tap-trains, but males interacting with females produce shorter tap-trains and engage in phonotactic behavior that is absent in inter-male communication. Females respond highly preferentially to inter-male communication, rather than to the signals produced spontaneously by single males. Finally, I propose a simple model of the selective advantages of this unusual communication system, and calculate its approximate energetic leverage over random locomotion (∼13x).


INTRODUCTION 34
Communication via substrate vibrations is widespread among insects and is regarded primarily as a 35 mechanism for communication between potential mates (Greenfield 2002, Cocroft andRodriguez 2005;36 see also reviews by Hill 2001Hill , 2008. Among the coleoptera, vibrational communication or "tapping", 37 also known as "drumming", has been described in at least 24 species (summarized by Hill 2008). 38 Beetle taxa differ in the pulse repetition frequency of tapping, and in male vs. female participation in 39 tapping behavior. In the death watch beetle Xestobium rufovillosum, both males and females tap, 40 though males cannot be distinguished from females in terms of tapping characteristics (Birch and 41 Keenlyside 1991; White et al. 1993). Tschinkel and Doyen (1976) found that male tapping behavior in 42 the beetle Eusattus reticulatus increases in the presence of females, but that only males tap, and males 43 do not respond to the presence of other males. Similarly, Pearson and Allen (1996) reported that 44 females of another Eusattus species also do not tap, and Slobodchikoff and Spangler (1979) found that 45 only males of Eupsophulus castaneus tap. However, in the African tenebrionid beetle, Phryanocolus 46 somalicus, both males and females tap (Zachariassen 1977; Kristensen and Zachariassen 1980), but, as 47 with the death watch beetle, "the beetles cannot use the sound signals for determination of the sex of 48 other beetles". 49 I have quantified the energy cost of tapping communication in the South African molurine tenebrionid 50 Psammodes striatus, also known colloquially as the "toktokkie" or tok-tok beetle (Lighton 1987). Using 51 the energy cost data, together with data from an earlier study in which I measured the cost of 52 pedestrian locomotion in this species (Lighton 1985), I calculated that substrate-borne vibrational 53 communication was approximately tenfold more energetically efficient for mate-location than a random 54 walk (Lighton 1987). However, the description of the tapping communication in that paper was limited 55 to a broad description of the tap-trains produced by male beetles only. The purpose of this paper is to 56 refine that description, adding data on male vs. female tapping behavior, and on male-male tapping 57 interactions. A simple model is proposed to explain the selective benefit of male-male communication in 58 this species, and the energy allocation advantages of tapping communication over mate-location by 59 locomotion are explored. 60

METHODS AND MATERIALS 61
Animals 62 Males and females of Psammodes striatus were collected during October in the austral spring from 63 Sandy Bay (Cape Peninsula, South Africa). All beetles were labeled on one elytron with a small circle of 64 white correcting fluid (Tipp-Ex; Tipp-Ex Company, Frankfurt, Germany) on which a code number was 65 written. The beetles were kept on fine sand and small stones in glass vivaria in an air-conditioned 66 laboratory at the University of Cape Town (22 ± 1 ºC, with a natural day/night lighting cycle) and were 67 separated by sex. Oats and lettuce were supplied ad libitum. Beetles maintained in this way remained in 68 apparent good health and were de-labeled and released at the site of capture after the study was 69 concluded. 70

Tap-monitoring and analysis techniques 71
A brief description of tapping behavior is necessary to place the monitoring methodology in context. 72 Close observation in the field and the laboratory established that the beetles tapped in "trains" of ~4-20 73 taps, depending on sex and circumstance. Tap-trains were separated by a short pause. Furthermore,  74 tap-trains occurred in "groups". Each group consisted of a variable number of tap-trains, separated in 75 time from each other by no more than 5-10 seconds, as opposed to the much longer and more variable 76 pauses between groups of trains. The beetles communicate with each other by alternating tap-trains 77 (beetle A -beetle B -beetle A, etc.) in duets. If no inter-beetle communication is taking place, male 78 beetles will occasionally produce spontaneous groups of tap-trains. 79 The train of taps was chosen as the basic unit for monitoring purposes. Because inter-tap pauses within 80 tap-trains were nearly constant (see Results), a train of taps could be accurately described by its 81 duration and the number of taps comprising it. Further, by measuring the time elapsed between trains, 82 each train could be placed in temporal relation with its neighbors. 83 The beetle being monitored was kept in a glass-walled terrarium (300 x 220 x 220 mm i.d.) with a 50 mm 84 deep layer of fine sand covering its base. An electret microphone was buried in the top layer of this 85 sand. A 300 x 220 mm sheet of 3mm thick medium density fiberboard (Masonite), on which the beetle 86 had complete freedom of movement, was placed on the sand in contact with the body of the 87 microphone. The terrarium was placed on a heavy granite-topped balance table to isolate it from  88 acoustic interference. The output of the microphone was fed into a variable-gain amplifier, then into a 89 Schmitt trigger and an adjustable monostable multivibrator. The gain of the amplifier was adjusted so 90 that the weakest tap produced by the beetle under study would trip the Schmitt trigger. This sensitivity 91 did not change significantly over the entire surface of the board. The monostable was designed to give a 92 10 msec output pulse, preventing the counting of multiple pulses from each impact. The resulting pulse 93 was fed into an Acorn BBC computer running monitoring software written by the author. 94 If a tap was detected that was not followed by a further tap within 400 ms (about twice the normal 95 inter-tap period within a tap-train) it was ignored. Such single signals were always caused by electrical 96 transients or mechanical disturbances. If the tap formed part of a train, the time of the first tap was 97 stored, and further taps were counted until 400 ms had elapsed without the detection of a further tap. 98 The time from the first tap (less 400 ms), and the time elapsed from the end of the penultimate tap-train 99 to the first tap of the last train were stored in the computer, together with the number of taps in the last 100 train. All times were measured with a resolution of 10 msec. These data were regularly transferred to 101 disc together with date, time and observational notes, allowing a complete reconstruction of tapping 102 activity during the monitoring period. 103 Stimulation was applied to the beetles as computer-synthesized "taps" which consisted of 4 msec bursts 104 of 666 Hz squarewaves. These were fed via a 0.5W power amplifier into a 50 mm permanent-magnet 105 speaker placed cone down on the Masonite floor of the monitoring container. The amplifier gain was 106 adjusted so that a soft but audible tap was produced. The number of taps produced together with their 107 period, length and spacing were controlled by the computer. An inter-tap period of 170 ms was adopted 108 throughout the experimentation, as this was close to the mean inter-tap period of both male and female 109 beetles, and initial experiments showed negligible response effects with moderate changes in tap 110 period. Marked changes in response occurred when the number of taps per train was altered, so this 111 parameter was chosen as the sole variable in the presented stimulus for this study. 112 Observation of interacting beetles revealed a stereotyped alternation of response between tappers (see 113 Results). A 'conversation' was initiated by unstimulated tapping by one beetle, to which another beetle 114 replied with a train of taps. The first beetle would then reply with a second train of taps, and so on. The 115 computer mimicked this behavior. Initially, it synthesized a single train of taps every minute. If the 116 beetle responded, the stimulus was re-presented 1.50 s after the completion of the beetle's "reply". This 117 value was chosen as a compromise between the typical delays shown by male and female beetles (see 118 Results), to ensure inter-comparability of results between runs. The beetle then replied again, followed 119 by the computer, and so on. As such 'conversations' could continue almost indefinitely (>3 h), a 120 standardized monitoring format was adopted in which the beetle was first stimulated for 20 minutes 121 (the "stimulated state"), following which stimulation stopped (the "poststimulated state"). The 122 poststimulus period ended ten minutes after stimulation stopped, or -if the beetle continued producing 123 trains of taps after this period -until at least 5 seconds had elapsed between trains. The computer could 124 produce a fixed number of stimulus taps per train, or change the number of stimulus taps at random 125 within specified limits. Stimulus taps per train were varied at random between 2 and 18 inclusive (with a 126 constant number of taps within each monitoring period) for data discussed in this paper. 127 Statistics 128 All means are accompanied by their standard deviations and N. The significance criterion employed for 129 all tests was p < 0.05. All statistical software was written by the author and validated against example 130 data sets from Sokal and Rohlf (1973) and Bailey (1959). For comparisons between small (n < 100) data 131 sets with similar variances, Student's t test was used. Variances were tested for significant difference 132 with the F test. Where variances differed significantly but sample sizes were below 100, the approximate 133 t test was used (Bailey 1959). Frequency distributions of data are displayed as probability distributions 134 rather than standard histograms. "Probability" is used in the sense of the maximum likelihood estimator 135 (i.e. P[n] = [number of occurrences of n]/[total number of occurrences]). The area under the distribution 136 is equal to unity. This method eliminates differences in sample size. Linear regression was performed by 137 the least-squares method. Where noted in the text, slopes were linearized by appropriate axis 138 transformations. As an index of variability, the coefficient of variation (CV; standard deviation / mean 139 expressed as a percentage) was used. 140

141
The communication behavior of Psammodes striatus is highly stereotyped. The beetle, whether male or 142 female, taps or drums on the substrate by elevating its body and then directing it downwards so that the 143 abdominal tergites forcibly contact the substrate. Male beetles, but not females, possess a small patch 144 of plumose setae at the point of contact, the function of which is unknown. Initial exploration of the 145 system uncovered little variation between individuals except on the basis of body mass, which 146 significantly altered tapping frequency (author's unpublished data). Thus, the beetles used in this study 147 were selected from a larger sample of beetles on the basis of near-identical body masses. This reduced 148 the feasible sample size to three male and two female beetles, mean masses 2.7 ± 0.1 and 3.0 ± 0.1 g 149 respectively. To compare the stimulated communication results to actual male-female interactions, 150 these data were supplemented by two additional pairs of freely communicating male and female 151 beetles in the same body mass range. 152

Unstimulated tapping behavior 153
See Table 1 for a summary of the data for male beetles. Fig. 1 shows the probability distribution of taps 154 per train for female and male beetles. 155 Female beetles did not engage in unstimulated tapping. Tapping by female beetles was fairly 156 rare even when introduced into vivaria with males and constantly stimulated by the males' calls. After 157 insemination, females responded less often, if at all, to males' calls (author's unpublished data). Most 158 duetting interactions were between males, rather than between males and females. No inter-female 159 communication was ever observed even when several females were kept together for long periods. 160

Stimulated tapping behavior 161
A total of 105572 stimulated taps, comprising 4352 trains and 546 groups, delivered by three male and 162 two female beetles during 48 monitoring periods of 30 minutes each, were analyzed. Each beetle was 163 allocated 9-10 monitoring periods. Results are shown in Tables 2 and 3. 164 Stimulated females tapped with a very narrow frequency distribution ( Fig. 1 "Female", Table 3). 165 The number of response taps per train did not vary as a function of the number of stimulus taps per 166 train (linear regression, P > 0.3). The female tap-train appears to be a binary or yes/no response; either 167 given or withheld, depending on the acceptability of the stimulus. Other female call parameters were, 168 however, affected, as shown later. 169 (unstimulated). Female tapping was in response to male tapping signals (stimulated), as they did not tap 173 without stimulation. Energy cost in this and subsequent figures is based on 1.725 mJ tap -1 for a beetle 174 weighing ~3 grams (Lighton 1987). 175 176 Males, in contrast to females, showed a wider taps/train distribution and a significantly higher 177 number of taps/train, with the male mode approximately two-fold higher than the female mode ( Fig. 1  178 "Male", Table 3). The wider distribution is explained by a significant increase in the number of reply 179 taps/train in response to increasing stimulus taps/train (Fig. 2). 180 Males were, however, significantly more likely to engage in protracted duets (number of  185 response tap-trains) if stimulated by tap/train numbers characteristic of female beetles (Fig. 3). As 186 energy expenditure increases linearly with increasing numbers of taps (assuming a constant tap impact 187 and inter-tap period, which is valid; Lighton 1987), this graph also acts as an indication of how much 188 energy is expended by the male beetle as a function of stimulus tap-number. 189 The males thus showed a distinct response to stimulus tap-trains containing fewer than 8 taps. 193 In addition to tapping persistently in response to such female-characteristic tap-trains, they engaged in 194 phonotactic behavior, which consisted of regular rotational re-orientations of their principal body axis 195 combined with intermittent locomotion, probably serving to alter the amplitude (for linear changes in 196 position) or phase relationships (for rotational changes) of the stimulus signal in a manner informative 197 to a male beetle attempting to locate the source of the stimulus. These behaviors did not occur if the 198 stimulus taps exceeded 8 taps per train. The induction of phonotactic behavior is shown by the sharply 199 increased CV (28 vs. 18%; Table 3)   Consequently, as shown in Table 3, the data for male tapping parameters were split into 207 responses to stimuli characteristic of females (< 8 taps/train) and those unambiguously characteristic of 208 males (> 9 taps/train). Fig. 5 shows the probability distributions for all combinations (female, stimulated; 209 male, unstimulated; male, stimulated at < 8 or > 8 taps/train; and male in the poststimulus state, after 210 being stimulated at < 8 or > 8 taps/train). 211 The intensity of female response to a tapping stimulus, as assayed by the number of total 218 response tap-trains per monitoring period, was a strong, indeed exponential, function of the number of 219 taps per stimulus train. Females did not respond at all to stimulus tap-trains containing fewer than 6 220 taps, and responded with six-fold greater intensity to tap-trains near the top of the male range (N = 16 -221 18 taps/train) than to those near the bottom of the male range (6 -8 taps/train). Fig. 6 shows the 222 pattern. 223 In addition, females replied to stimulus tap-trains significantly more rapidly as the numbers of 227 stimulus taps/train increased (Fig. 7). The pause before responding to a stimulus was always much 228 longer for males than for females and varied according to stimulus conditions, as shown in Fig. 8. 229 analysis, as they were unlikely to be statistically meaningful. However, they do suggest that the females, 239 though they do not spontaneously initiate tapping, may attempt to reestablish contact with another 240 beetle with which they were communicating and which has recently stopped tapping. 241 "Natural" male-female tapping behavior 242 Two male-female duets which took place in a partitioned monitoring tank, allowing only acoustic 243 contact between the beetles, were monitored. These interchanges, which lasted 11 and 18 minutes, 244 consisted respectively of 1651 and 2973 taps (224 and 372 trains). Data from these interchanges were 245 combined, as no significant differences in taps/train, response time, etc. were found between the two. 246 Plotting a small portion of one interchange as taps per train with a time-directed X axis reveals the 247 essential distinctions between male and female signals quite well (Fig. 9). In particular, note how the 248 female trains contain fewer taps and follow very closely on the male signals. 249

Male-female communication 256
In P. striatus, the female operates as a transponder rather than as an initiator. In any dual 257 signaling system, biological or not, the ultimate object of which is direction-finding and co-location, it is 258 logical for one partner to stay in place and respond to "ping" signals, while the other dynamically 259 initiates those responses and then employs them to locate the transponder. Consequently, the 260 transponder replies quickly while the initiator waits until the probability of a reply has declined to near-261 zero before sending another "ping." This is seen clearly in the male post-stimulus distribution in Fig. 5,  262 and probably explains the lack of spontaneous tapping by females. For the female to act as a 263 transponder, responding only when stimulated and with a distinctive, low-redundancy, low-energy, 264 minimal-delay signal to the high tap-numbers characteristic of male tapping, may allow her to allocate 265 more of her energy budget for essentials such as producing viable eggs. This may carry a selective 266 advantage in a xeric environment where energy must be conserved, whether because of energy or 267 water limitation (Louw and Seely, 1982;Edney, 1971). The narrowly defined nature of the female's 268 response may also be important in species recognition. Such precise timing is a property of this form of 269 communication which is predictable on theoretical grounds (the spectral information content of a tap, 270 as opposed to an airborne signal such as a stridulation, is negligible). Thus, male beetles produce a 271 variable, broad-band signal which is significantly affected by the presence, absence, nature and even the 272 recent history of suitable acoustic stimuli, while the female responds with an unambiguous 273 transponder/locator signal -if she responds at all. 274

Male-male communication 275
The tap-happy male behavior seems intuitively counteradaptive. On energetic grounds alone, 276 profligate communication behavior should be selected against. Indeed, when the beetles are kept in 277 captivity, tapping among males is an almost round-the-clock activity. These interactions are not 278 dissimilar to the "rival's songs' discussed in Dumortier (1963), which, however, are aggressive and 279 territorial. No aggressive encounters were seen to take place between males in this species, though 280 when two tapping males meet, one will usually try to mount the other. This behavior is identical to that 281 used by males when mounting females and is likely triggered by the size and shape of the other beetle, 282 as this species shows negligible sexual dimorphism and, judging from its tiny eyes and small number of 283 ommatidia, its vision appears to be rudimentary. Observation suggested that these beetles are only 284 aware of each other at very close range (2-4 cm) unless tapping was involved (author's unpublished 285 observations). 286 The phenomenon of specific interactions between males in communicating insects has received 287 attention (see especially Spooner 1968;Alexander 1968Alexander , 1975 Fig. 4). This is energetically expedient. Engaging in phonotactic behavior to 299 locate other males would be genetically unproductive and wasteful of energy. In addition, inter-male 300 phonotaxis would lead to aggregation of the males, reducing the area covered by their signals, and thus 301 -assuming a random distribution of females -reducing the probability that an individual male would 302 attract a reply from a passing female. Such a phenomenon may in fact occur in the tenebrionid beetle 303 Eupsophulus castaneus (Slobodchikoff and Spangler 1979). It is perhaps significant that in that species, 304 the females do not tap (ibid). Thus Eupsophulus females cannot be phonotactically located by the males, 305 which aggregate when calling. 306 If the tap-number probability distributions are used to calculate the probability that a signal 307 from one distribution is a member of another, this effect is clearly seen. Thus the probability of a signal 308 characteristic of a female call occurring in an unstimulated male call can be estimated at 0.1058, 309 whereas the corresponding probability for an inter-male call is only 0.0289 -in other words, inter-male 310 calling increases the sex-coding of a tapping signal by almost 4-fold, even if one ignores the two-fold 311 difference in speed of response to stimuli (1.03 second for females vs. >= 2.09 seconds for males) which 312 presumably adds some information to the process of sex recognition. In a sense, the males' behavior is 313 more to the females' than the males' advantage if the female does indeed act on this information. 314 These phenomena lead one to hypothesize that the female will respond preferentially to large 315 tap per train numbers, as they in turn imply not only greater fitness but the likely presence of more than 316 one male, with a correspondingly increased probability of fertilization and, perhaps more importantly, of 317 inter-male competition. The number of female response trains does indeed increase exponentially with 318 increasing numbers of taps per stimulus train (Fig. 6). One might infer that such energetic signaling 319 would handicap the male beetle by making him more conspicuous to potential predators. If so, the 320 selective advantage of elevated female responsiveness apparently outweighs that handicap (for a 321 general discussion, see Grafen 1990 and references therein). 322 The "communication circle": a speculative model to be sensitive (Autrum 1963). Absolute communication distances in these beetles are uncertain; let us 328 call the radius of the circle of communication r, and set its value equal to unity. The area of the 329 communication circle is then π radius units. 330 Obviously, two beetles cannot communicate if they are more than one radius unit apart. For 331 communication to take place, their circles must interpenetrate and the total area their combined signals 332 will cover must be smaller, and with it the probability of a female occurring in that combined area 333 (though this may be partly offset if the distribution of these beetles is "patchy", leading to an increased 334 probability that a female will be present if two males are already present). If males are closer together, 335 the probability that communication between them will occur begins to rise. At the same time, their 336 shared area increases relative to the single-male state. It can be shown that 337 where As is the shared area, and s the beetle separation, in radius units. The proportional shared 339 area reaches 0.33 when the beetles can potentially communicate, and rises to 1.00 when the two 340 beetles are a negligible distance apart. It is immediately obvious that males communicating at the limits 341 of their ranges have areas of "exclusive communication' equal to 0.67 of their circles of communication, 342 in which they can receive replies from a female beetle without the other male's knowledge. Moreover, 343 the female will be stimulated by tap-numbers characteristic of inter-male communication, considerably 344 increasing her responsiveness (Fig. 6). 345 It is therefore not to the males' advantage to locate each other or otherwise attempt to aggregate once 346 inter-male communication has started. Though this means that a male can participate if another male 347 begins to communicate with a female that they can both hear, it also means that he may use a 348 considerable amount of energy in the process of "homing", and that he may encounter competition 349 from the male closer to the female. Consequently the standardized shared area of the circles can be 350 regarded as an index of potential competition, if the simplifying assumption is made that all interactions 351 are between beetles with identical radii of influence. The potential competition index is zero if the males 352 are physically far removed from each other (> 2 radii). However, its value becomes non-zero between 2 353 and 1 radii, even before the beetles can became directly aware of each other. This seeming paradox 354 means that both beetles may now be within the signaling range of a third beetle replying to one or both 355 of them, and are therefore potentially able to act as competitors even though they are not aware of 356 each other. The value of this index reaches 0.33 when the beetles can become aware of each other 357 directly, and climbs to unity when the beetles are a negligible distance apart and neither can 358 communicate with a third beetle without the other's knowledge. 359 At two or more radii apart, individual males have a consistent advantage owing to the absence 360 of competition and increased area of exclusive communication, but the advantage is low owing to a) the 361 relative infrequency with which they tap when not stimulated, and b) the female's low responsiveness 362 to the small tap-numbers characteristic of unsolicited male tapping. Then, as one intuitively expects, 363 individual male advantage is sharply reduced as the males draw together. Any interchange initiated by 364 one male with a female may be heard by the other male (for example, the female may be between 365 them), while the effective tap-number remains in its unstimulated condition. The situation changes 366 abruptly when the males can communicate. As soon as they start to do so, their tapping density rises 367 from ca. 8 taps per minute to ca. 100 and their tap-number from ~9 to ~15, significantly increasing the 368 probability of female replies. Even corrected for the distance-dependent probability of this interchange 369 starting, the advantage now swings abruptly in the direction of the individual male. Thus, the individual 370 male -thanks to inter-male communication -now has not only a much greater absolute chance of 371 eliciting a response from a female, but also a distinct probability that this response will be imperceptible 372 to the other male, and hence to his benefit alone. It could thus be argued that individual selection is a 373 strong component in the maintenance of this behavior by natural selection. Even when competition is 374 almost certain to occur (i.e. close to the other male), the mean benefit gained by inter-male tapping can 375 in individual terms be reduced by only 50% if either male has an equal chance of displacing the other 376 and mating with the female. This reduction is still a huge improvement over the unstimulated condition, 377 and is therefore still to the advantage of the individual. 378 The advantage to females of male-male communication If the situation is now viewed from the female's perspective, it is to her advantage to 380 preferentially reply in the presence of more than one male. This is particularly true if the probability of 381 inter-male competition is high (which can be increased if her sensitivity to signals is equal to that of the 382 males', but her signal can be heard over a larger radius, perhaps as a result of slightly heavier mean 383 body mass in females [author's unpublished observations]). This results in a correspondingly greater 384 probability that the more robust and determined male will mate with her (see especially Reinhold et al. 385 1998). This may contribute little if anything to her short-term advantage, but will help to ensure that her 386 genetic complement is paired to that of a beetle that has demonstrated a competitive edge over 387 another, and therefore maximizes the probability that her offspring will successfully transfer her genetic 388 complement to the next generation. In ultimate terms this is probably the driving force behind inter-389 male communication. Paradoxically the advantage gained by individual males, though perhaps 390 significant, has only been gained within the framework of the female's pattern of response -which may 391 work to her benefit only if inter-male competition is an important factor in inter-male communication. 392

Energy savings 393
The metabolic energy cost per tap is 1.725 mJ for a beetle weighing ~3 g (Lighton 1987). The 394 position of the tap in the tap-train has no significant effect on its cost as determined by kinematic 395 analysis, which also revealed an efficiency, or power output as a percentage of metabolic input, of 23%, 396 a typical value for muscle efficiency across a broad range of taxa (Mogensen et al. 2006 and references 397 therein). For male beetles with a mean unstimulated tap-train of 9.63 taps train -1 and a mean number of 398 tap-trains per group of 4.74 trains group -1 (see Table 1), sending a tapping message thus costs 78.7 mJ. If 399 we assume a modest tapping communication range of 0.5 m and a circular reception area for substrate-400 borne vibrations, the 78.7 mJ energetic investment allows an area of 0.785 m 2 to be searched for other 401 beetles. This is equivalent to a search cost of ~100 mJ m -2 . Pedestrian locomotion, in contrast, can be 402 reasonably assumed to allow direct detection of beetles no more than ~5 cm to either side, creating a 403 "swathe of contact" ~10 cm wide. The minimum cost of transport in this species is known (~100 mJ m -1 404 for a 3 g beetle; calculated from Lighton 1985). Each meter walked thus covers a search area of 0.1 m 2 , 405 yielding a search cost of 100 / 0.1 or 1000 mJ m -2 . From this, we estimate that the energy required for a 406 beetle to search an area for a prospective mate via tapping communication is approximately 12.7-fold 407 less than encountering another beetle via the flaneur method (walking). This does not consider the 408 ~50% probability that a beetle thus encountered is of the same sex, or the possibility that a female 409 beetle is unreceptive. It is, however, complicated by the existence of male-male interactions that will 410 add energy expenditure -from which it is reasonable if marginally Panglossian (Gould and Lewontin, 411 1979) to infer that such interactions confer benefits that outweigh their cost, as discussed above 412 ("communication circle"