ELECTROCOMMUNICATION IN GYMNOTOID WAVE FISH: SIGNIFICANCE OF A TEMPORAL FEATURE IN THE ELECTRIC ORGAN DISCHARGE

Abstract

1. In the single electric organ discharge (EOD) of Eigenmannia and Sternopygus the duration of the head-positive EOD half-wave (P) was found to be shorter than the duration of the head-negative half-wave (N). There were individually different P/N ratios in both species. High P/N ratios were found in Sternopygus discharging at high repetition rates, and small P/N ratios were correlated with low EOD frequencies. Furthermore, the data presented in Figure 1 suggest a correlation between the P/N ratio and the sex in Sternopygus. Fig. 1.  P/N ratios of five Sternopygus (open circles) and eleven Eigenmannia (filled squares) are plotted against the EOD frequency (F). The EOD wave shapes in both species are shown to the left. There is a sinusoidal head-positive half-wave with the duration P and a trapeziform head-negative half-wave with the duration N. The P/N ratio is 0.6 in the lower EOD and 0.9 in the upper EOD. Both signals have the same duration (EOD wave length) T. Figure options Download full-size image Download as PowerPoint slide 2. In beats composed of EODs and sine waves with frequencies slightly different from that of the EOD (1 F stimuli) or from the second harmonic of the EOD (2 F stimuli) successive beat half-waves increase their amplitudes from the beat minimum to the beat maximum, and they decrease their amplitudes from the beat maximum to the minimum. With respect to corresponding zero crossings of the EODs, zero crossings of beat half-waves come earlier in one section of the beat cycle (= phase lead), and they are delayed in the other section of the beat cycle (phase lag) (Fig. 2, A, C). In beats composed of EODs and sine waves with frequencies close to the first subharmonic of the EOD (1/2 F stimuli) successive beat half-waves alternate high with low amplitudes and phase lead with phase lag (phase alternation) (Fig. 2D). Fig. 2.  Comparison of pure EODs with amplitude and phase patterns in beat waves caused by the superposition of EODs and different stimuli. EODs (solid lines) and stimuli (dotted lines) are presented in the upper traces. Beat waves are shown in the middle, and sections of phase modulation of positive beat half-waves and of negative beat half-waves are illustrated below the beat waves. The length of one beat cycle is indicated by the length of the two complementary sections of phase modulation. The temporal displacement between zero crossings of EODs and beat waves is given by vertical lines: solid lines indicate zero crossings of the EODs from positive to negative polarity, and dashed lines indicate EOD zero crossings from negative to positive polarity. Time runs from left to right. EODs are added to sine waves (A) and EOD-mimicking stimuli (B) at frequencies below the EOD frequency as well as to sine waves below the second harmonic (C) and the first subharmonic (D) of the EOD. Interactions of EODs and EOD-mimicking signals above and below the first subharmonic of the EOD are shown in (F) and (E). Figure options Download full-size image Download as PowerPoint slide 3. In beats composed of EODs and EOD-mimicking signals (the P/N ratios are smaller than 1) with frequencies close to the first subharmonic of the EOD, the duration of the head-positive stimulus half-wave (P stim) is proportional to the duration of the section of phase alternation within the head-positive and the head-negative beat cycle. The duration of the section of phase lag in the positive beat cycle and of phase lead in the negative beat cycle is proportional to T eod (EOD interval) minus P stim (Fig. 3). The quotient P stim / T eod - P stim is called the phase quotient of the beat. If the phase quotient is 1, sections of phase lead, phase lag and phase alternation have the same duration, and every second beat half-wave increases from the beat minimum to the beat maximum, and decreases from the beat maximum to the beat minimum. The more the phase quotient is smaller than 1, sections of phase lead and phase lag increase at the expense of sections of phase alternation, and the relative number of beat half-waves with nearly constant amplitudes increases at the expense of the amplitude modulated beat half-waves. The more the phase quotient is greater than 1, the more the sections of phase alternation increase, and the more successive beat half-waves alternate high with low amplitudes (Fig. 4, lower part). Fig. 3.  Sections of phase modulation in a 1/2 F beat cycle are illustrated by means of stimulus phase shifts in certain phases of the EOD. Three stimuli of nearly twice the EOD wave length are shown above and below an EOD trace, respectively. Vertical lines in the upper part of the figure indicate EOD zero crossings from negative to positive polarity. Vertical lines in the lower part indicate EOD zero crossings from positive to negative polarity. The origin of negative phase sections is illustrated in the lower part, and the origin of positive phase sections is shown in the upper part of the figure: during a stimulus phase shift from the position at the upper right to the position in the upper middle or vice versa, EOD zero crossings coincide only with phases of the negative stimulus half-wave. Resulting beat waves would be delayed (lag). The phase shift is proportional to the difference between the EOD interval (T eod) and the positive stimulus half-wave (P stim). During a stimulus phase shift from the upper middle to the upper left or vice versa, every second EOD zero crossing coincides with a phase of the negative stimulus half-wave, and all others coincide with phases of the positive stimulus half-wave. Resulting beat waves would alternate, the phase lag with the phase lead (alt). The phase shift is proportional to P stim. The two complementary phase sections are proportional to T eod. (from negative to positive polarity) Figure options Download full-size image Download as PowerPoint slide Fig. 4.  Upper part: JAR values in two Eigenmannia as a function of phase quotients in 1/2 F beats. Solid line: responses to seven beats/s and a positive phase shift of the stimuli (F eod = 441 Hz, (P/N) eod = 0.78). Dashed line: responses to two beats/s and negative phase shift of the stimuli (F eod = 428 Hz, (P/N) eod = 0.64). Lower part: three 1/2 F beat cycles with different phase quotients (1/4 in the left, 1 in the middle and 4/1 in the right beat). Sections of phase modulation in positive and negative beat half-waves are shown to the right of each beat. Below the beats, corresponding constituent signals are presented: EODs (solid lines) and 1/2 F stimuli (dotted lines). There is a positive phase shift of the stimuli. Time runs from bottom to top. Figure options Download full-size image Download as PowerPoint slide 4. The Jamming Avoidance Response (JAR) in Eigenmannia was found to be a maximum function of the phase quotient of beats composed of EODs and EOD-mimicking signals close to the first subharmonic of the EOD. The response was graded on both sides of a best phase quotient of about 1 (P stim was about half the EOD interval). There was no systematic response when the phase quotient was very small or when P stim was about T eod, i.e., when the stimulus matched the temporal feature of subharmonic sine and square waves (Fig. 4, upper part). 5. The temporal displacement between the head-positive and the head-negative beat maximum was found to depend not only on the direction of the relative phase shift between the EODs and the stimuli but also on the position of the positive and the negative maxima in the EOD and in the stimulus. Therefore, reliable information about whether the simulus frequency is above or below that of the EOD, will not be provided to Eigenmannia by the temporal sequence of positive and negative beat maxima alone (Fig. 5). Fig. 5.  Temporal sequence of beat maxima as a function of the stimulus phase shift and the position of maxima in the interval of EOD and stimuli. An EOD trace is presented in the middle of the figure. The time between the positive and the negative maximum in the EOD is longer than the corresponding time in the stimulus shown above the EOD, and it is shorter than the corresponding time in the stimuli shown below the EOD. Vertical solid lines indicate positive and negative EOD maxima. Vertical dashed lines indicate negative stimulus maxima. The EOD-mimicking stimuli are drawn incomplete and might be close to once or twice of the EOD wave length. Sine waves are shown at the bottom of the figure. All stimuli are in antiphase to the EOD in the middle of the figure (position, yielding a beat minimum). To the left and to the right positive stimulus maxima coincide with positive EOD maxima (position, yielding positive beat maxima). Numbers indicate the temporal sequence of maxima in the beat cycle, e.g., at a positive shift of the stimulus, shown above the EOD trace, the coincidence of the negative maxima of EOD and stimulus (negative beat maximum) is earlier (1.) than the coincidence of the positive maxima of EOD and stimulus (positive beat maximum) (2.). Arrows indicate the direction of stimulus phase shifts. At a negative shift (neg. shift), the stimulus frequency is below, and at a positive shift (pos. shift), the stimulus frequency is above that of the EOD or the first subharmonic of the EOD. Figure options Download full-size image Download as PowerPoint slide