Dispersive and non-dispersive waves through plants: implications for arthropod vibratory communication

Abstract

Vibratory communication in arthropods is a widespread phenomenon. Arthropods living on plants have been reported to use only dispersive bending waves in the context of prey-predator, competition, social and sexual interactions. Differences in signal structure have also been postulated to work as species recognition mechanisms and speciation agents. Using two identical laser Doppler vibrometers and a wavelet analysis, we quantified the wave propagation modes in rush stems (Juncus effusus) over the whole range of frequencies used by arthropods. A non-dimensionalized analysis shows that mechanical waves propagate not only as dispersive bending waves, but also as non-dispersive waves. Our analysis implies that an arthropod can communicate through non-dispersive bending waves by either producing signals of high frequencies or by choosing large stems, two widely different options tapping into the physiological and the behavioural repertoires, respectively. Non-dispersive waves, unreported so far in insect vibratory communication in plants, present serious advantages over dispersive bending waves in terms of signal integrity and may well be much more widely used than anticipated, in particular for species recognition.

Figure 1

Scalograms (two-dimensional plots of continuous wavelet transform) and oscillograms of signals recorded by the two distant lasers focusing on a rush stem. (a) The first laser recorded a typical transient signal generated by the falling ball. The scalogram indicates a wide-band spectrum. The second laser recorded the signal after its propagation through the plant at 45 cm from the impact point. Because of dispersion phenomenon, the signal recorded (b) after propagation shows high frequencies arriving first, leading lower frequencies (see arrows). This phenomenon is, however, true only for frequencies lower than 5 kHz. Y-axis of oscillograms refers to signal velocity but not to wave velocity. Note the change of range between the oscillograms. For convenience, wavelet scale a has been converted into frequency scale (kHz). Horizontal grey level bar indicates the range for the absolutes values of regression coefficients.

Figure 2

Dispersion of substrate-borne waves in a rush stem. (a) Relation between the square root of the frequency f (kHz) and velocity c (m s⁻¹) for five stems: velocity first increases with the square root of frequency and then remains stationary whatever the frequency. The vertical dashed line is at f=5 kHz (i.e. √f=2.23 kHz). (b) Non-dimensionalized analysis investigating the combined effects of frequency and stem radius on wave velocity. Observations are compared with Bernouilli–Euler (dashed line) and Timoshenko (continuous line) beam theories.