For insects that communicate using airborne sound, physical constraints on sound production and transmission lead to a relationship between body size and signal frequency. The efficiency with which sound is radiated depends on the size of the sound-producing structure. The lower the frequency, the larger the structure needed for efficient sound radiation (Michelsen and Nocke, 1974; Bennet-Clark, 1998a). This constraint places a lower limit, but not an upper limit, on the frequency of sounds used in communication. Once a sound has been radiated into the air, absorption of sound energy and scattering by objects in the sound path are both frequency-dependent, favouring lower frequency sounds for long-distance communication (Bradbury and Vehrencamp, 1998). As a compromise between these two constraints, animals often produce sounds whose frequencies are near the lower limit of efficient sound radiation (Bennet-Clark, 1998a).

The link between size and signal frequency has important evolutionary consequences. Because the size of the sound-producing structure is often closely related to overall body size, comparative studies usually reveal a negative relationship between body size and sound frequency among insects and other animals which use sound for long-distance communication (Ryan and Brenowitz, 1985; Bennet-Clark, 1998a; Gerhardt and Huber, 2002). Within species, ecological sources of selection on body size can influence the evolution of communication systems through their correlated effect on signal frequency (Ryan and Wilczynski, 1991). Social sources of selection may target frequency directly as a result of its reliable association with body size (Morton, 1977; Gerhardt and Huber, 2002).

In contrast to species which communicate using airborne sound, the relationship of body size to signal frequency has not been systematically investigated for species which communicate using substrate vibrations. Use of the vibratory channel is far more prevalent in insects than the use of airborne sound (Michelsen et al, 1982; Markl, 1983; Claridge, 1985b; Gogala, 1985a; Henry, 1994; Stewart, 1997; Virant-Doberlet and Cokl, 2004), which probably occurs in hundreds of thousands of species (Cocroft and Rodriguez, 2005). One of the most striking differences between the signals of species communicating with vibrations and those communicating with sound is that the vibratory signals, on the whole, have much lower carrier frequencies (Cocroft and Rodriguez, 2005). It is unclear whether body size plays as important a role in the evolution of vibratory signals as it does in the evolution of airborne signals. There is recent evidence for the importance of frequency differences for mate recognition in species using pure tone signals for vibratory communication (Rodriguez et al., 2004). If divergence in signal frequency is decoupled from divergence in body size in such species, then vibratory signal frequency may be an evolutionarily labile trait, and one that could contribute to the rapid evolution of reproductive isolation among diverging populations.

Plant stems and leaves are among the most widely used substrates for insect communication. Plant borne vibratory signals are transmitted in the form of bending waves (Michelsen et al., 1982; Gogala, 1985a; Barth, 1997). As with sound waves, absorption of energy during propagation of bending waves is frequency-dependent, with greater losses at higher frequencies (Greenfield,

2002). Therefore, as with airborne sound, frequency-dependent attenuation should favour lower frequency signals for longer range communication. A second, less predictable influence on vibration transmission arises from the frequency filtering properties of plant stems and leaves. Although such filtering can favour lower frequency signals, it does not always do so, and there are too few studies of the vibration transmitting properties of plant tissue to permit broad generalisations (Michelsen et al., 1982; Cokl and Virant-Doberlet, 2003; Cocroft and Rodriguez, 2005).

The question is whether the mechanics of vibratory signal production impose a relationship between body size and signal frequency as with airborne sounds. Although use of substrate vibrations releases animals from some constraints on signal frequency, such as the acoustic short-circuit which makes radiation of low frequency sounds by small dipole sources inefficient (Gerhardt and Huber, 2002), the potential for other size-related constraints on signal frequency has not been explored. Little is known about the coupling of a vibratory signal between an insect and a plant stem (Michelsen et al., 1982). The details of vibratory signal production are also unknown in most cases, apart from observations of which body parts are involved (Virant-Doberlet and Cokl, 2004). Our lack of knowledge of the details of vibratory signal production and transmission prevent us from making specific predictions about the relationship of body size to frequency.

Here we take an empirical approach to the question of size-frequency relationships in vibratory signals. Comparing the spectral features of vibratory signals across different individuals and species, or using data drawn from different studies, presents two challenges. First, the distribution of energy across the different frequencies in a signal will be influenced by the properties of the substrate on which a signal is recorded (Michelsen et al., 1982). For signals using a narrow band of frequencies, the influence of substrate may be small or absent (Sattman and Cocroft,

2003). For signals containing a wider range of frequencies, differences in substrate filtering properties may introduce a significant amount of variation into a comparative dataset. Second, different investigators may use transducers which measure different components of a vibratory signal, and this will be reflected in the amplitude spectrum of the signal. For example, in a signal with a range of frequencies, acceleration amplitude will increase by 6 dB/octave relative to velocity amplitude. In this study we use methods which minimise substrate- and transducer-induced variation in signal amplitude spectra; or, for comparisons in which these sources of variation cannot be eliminated, we discuss their implications for interpretation of the results.

We investigated the relationship between body size and frequency at three levels: within a population; between closely related species; and across a wide range of species in different insect orders. For our investigations of size-frequency relationships within populations, we recorded a sample of individuals on a common substrate. For comparisons among closely related species, we use our own library of recordings of the signals of membracid treehoppers, and for the broader comparison we have drawn information from the literature.

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