Analysis of the jamming avoidance response in the electric fish Gymnotus carapo

The electric fish Gymnotus carapo emits brief (4 ms) electric pulses separated by much longer intervals of high regularity (coefficient of variation 0.01–0.02). Two main changes in the firing patterns of electric organ discharge were observed when two fish were placed together. (1) All fish pairs showed an increase in the frequency difference between the two fish, in comparison with the value observed in isolated fish, prior to the interaction. This change increased the number of beats per second between both discharge trains, i.e., the number of times per second that the higher rate discharge sweeps the lower rate one when displayed on an oscilloscope. (2) When the sweeping velocity fell below 2–3 sweeps/s, transient frequency increases were also observed in the electric organ discharge of the higher rate fish when they were about to discharge simultaneously. The contribution to jamming avoidance of these two changes was analyzed by comparing recordings of behavioral interactions with simulations produced by a computational model. The jamming effect of the firing of a conspecific located in the same tank was evaluated by counting the number of coincidences between both trains (occurrence of discharges of the two fish within 2 ms of one another). The number of coincidences was evaluated as a function of the sweeping velocity in both simulations (with and without transient frequency increases) and real fish. As the sweeping velocity increased, single coincidences increased slightly in simulations without transient frequency increases, whereas the successive coincidences (coincidences repeated in successive discharges) decreased abruptly. The simulation including transient frequency increases eliminated the successive coincidences and decreased the single ones. Only when the sweeping velocity was less than 2–3 sweeps/s, did transient frequency increases improve the coincidence-avoiding performance of the simulation. The number of coincidences observed in natural behavioral interactions for the different sweeping velocities coincided with the distributions obtained with the simulations. As successive coincidences are known to be more detrimental for electrolocation than single ones, the increase in the sweeping velocity may be considered a jamming avoidance strategy in Gymnotus carapo, in addition to the already described transient frequency increases. Received: 2 June 1998 / Accepted in revised form: 18 November 1998     

‘Ancestral’ neural mechanisms of electrolocation suggest a substrate for the evolution of the jamming avoidance response

Summary The genusSternopygus, believed to reflect ancestral traits of gymnotiform electric fish, is closely related to the more modern genusEigenmannia (Mago-Leccia 1978; Fink and Fink 1981).Sternopygus is the only known genus of electric fish that does not perform a jamming avoidance response (JAR) to minimize the potentially detrimental effects of signal interference between discharging neighbors (Bullock et al. 1972, 1975), and its ability to electrolocate objects is rather immune to jamming (Matsubara and Heiligenberg 1978).By studying the responses of midbrain neurons to stimulus regimes effective in eliciting the JAR inEigenmannia, we found thatSternopygus has neurons capable of discriminating the sign of the difference frequency between interfering electric organ discharges (EODs). These sign-selective neurons, which are believed to be important elements in the control of the JAR inEigenmannia, may, therefore, fulfill a more general function in the detection of moving objects and conspecifics but could potentially be assembled for the evolution of a JAR inSternopygus. The relative immunity to jamming in this genus may result, in part, from a stronger reliance upon the ampullary electrosensory system which operates in the DC and low-frequency range, outside the EOD spectrum of these fish.Abbreviations AM amplitude modulation - Df frequency difference - EOD electric organ discharge - JAR jamming avoidance response     

Motor control of the jamming avoidance response of Apteronotus leptorhynchus: evolutionary changes of a behavior and its neuronal substrates

The two closely related gymnotiform fishes, Apteronotus and Eigenmannia, share many similar communication and electrolocation behaviors that require modulation of the frequency of their electric organ discharges. The premotor linkages between their electrosensory system and their medullary pacemaker nucleus, which controls the repetition rate of their electric organ discharges, appear to function differently, however. In the context of the jamming avoidance response, Eigenmannia can raise or lower its electric organ discharge frequency from its resting level. A normally quiescent input from the diencephalic prepacemaker nucleus can be recruited to raise the electric organ discharge frequency above the resting level. Another normally active input, from the sublemniscal prepacemaker nucleus, can be inhibited to lower the electric organ discharge frequency below the resting level (Metzner 1993). In contrast, during a jamming avoidance response, Apteronotus cannot lower its electric organ discharge frequency below the resting level. The sublemniscal prepacemaker is normally completely inhibited and release of this inhibition allows the electric organ discharge frequency to rise during the jamming avoidance response. Further inhibition of this nucleus cannot lower the electric organ discharge frequency below the resting level. Lesions of the diencephalic prepacemaker do not affect performance of the jamming avoidance response. Thus, in Apteronotus, the sublemniscal prepacemaker alone controls the change of the electric organ discharge frequency during the jamming avoidance response.     

Modeling the variability of firing rate of retinal ganglion cells.

Impulse trains simulating the maintained discharges of retinal ganglion cells were generated by digital realizations of the integrate-and-fire model. If the mean rate were set by a "bias" level added to "noise," the variability of firing would be related to the mean firing rate as an inverse square root law; the maintained discharges of retinal ganglion cells deviate systematically from such a relationship. A more realistic relationship can be obtained if the integrate-and-fire mechanism is "leaky"; with this refinement, the integrate-and-fire model captures the essential features of the data. However, the model shows that the distribution of intervals is insensitive to that of the underlying variability. The leakage time constant, threshold, and distribution of the noise are confounded, rendering the model unspecifiable. Another aspect of variability is presented by the variance of responses to repeated discrete stimuli. The variance of response rate increases with the mean response amplitude; the nature of that relationship depends on the duration of the periods in which the response is sampled. These results have defied explanation. But if it is assumed that variability depends on mean rate in the way observed for maintained discharges, the variability of responses to abrupt changes in lighting can be predicted from the observed mean responses. The parameters that provide the best fits for the variability of responses also provide a reasonable fit to the variability of maintained discharges.     

The African wave-type electric fish,Gymnarchus niloticus,lacks corollary discharge mechanisms for electrosensory gating

Gymnarchus niloticus, a wave-type African electric fish, performs its jamming avoidance response by relying solely upon afferent signals and does not use corollary discharges from the pacemaker nucleus in the medulla which generates the rhythmicity of electric organ discharges. This is in sharp contrast to the mode of sensory processing found in closely related African pulse-type electric fishes where afferent signals are gated by corollary discharges from the pacemaker for the distinction of exafferent and reafferent stimuli. Does Gymnarchus still possess a corollary discharge mechanism for other behavioral tasks but does not use it for the jamming avoidance response? In this study, I recorded from and labeled medullary neuronal structures that either generate or convey the pacemaker signal for electric organ discharges to examine whether this information is also sent directly to any sensory areas. The pacemaker nucleus was identified as the site of generation of the pacemaking signal. The pacemaker neurons project exclusively to the lateral relay nucleus which, in turn projects exclusively to the medial relay nucleus. Neurons in the medial relay nucleus send unbranched axons to the spinal electromotoneurons. These neurons are entirely devoted to drive the electric organ discharges, and no axon collaterals from these neurons were found to project to any sensory areas. This indicates that Gymnarchus does not possess the neuronal hardware for a corollary discharge mechanism.     

An internal current source yields immunity of electrosensory information processing to unusually strong jamming in electric fish

Summary The electric organ of a fish represents an internal current source, and the largely isopotential nature of the body interior warrants that the current associated with the fish's electric organ discharges (EODs) recruits all electroreceptors on the fish's body surface evenly. Currents associated with the EODs of a neighbor, however, will not penetrate all portions of the fish's body surface equally and will barely affect regions where the neighbor's current flows tangentially to the skin surface. The computational mechanisms of the jamming avoidance response (JAR) in Eigenmannia exploit the uneven effects of a neighbor's EOD current to calculate the correct frequency difference between the two interfering EOD signals even if the amplitude of a neighbor's signal surpasses that of the fish's own signal by orders of magnitude. The particular geometry of the fish's own EOD current thus yields some immunity against the potentially confusing effects of unusually strong interfering EOD currents of neighbors.Abbreviations DF frequency difference - ELL electrosensory lateral line lobe - EOD electric organ discharge - JAR jamming avoidance response     

Correlation between discharges of human motor units during prolonged muscle contraction

Motor unit (MU) potentials were recorded from the human rectus femoris and biceps brachii muscles during prolonged isometric contraction. Interspike intervals and intervals between adjacent discharges of 2 MUs (cross-intervals of MU pairs) were measured. Synchronization was expressed by the following criteria: the cross-interval histogram; comparison of the number of coincidences between discharges of 2 MUs observed experimentally with the mean probable number of coincidences; the frequency of appearance of N successive coincidences of spikes from different MU pairs; comparison of the mean duration of interspike intervals preceding a synchronized discharge with the mean duration of the remaining interspike intervals for the same MU. For some MU pairs the number of coinciding spikes was greater than the expected number of random coincidences. Synchronized spikes could form a train of consecutive coincidences. The mean duration of interspike intervals preceding a synchronized discharge was somewhat less than the mean duration of the remaining interspike intervals for MUs forming a synchronously firing pair.Institute of Problems of Information Transmission, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 4, No. 1, pp. 68–74, January–February, 1972.     

‘Recognition units’ at the top of a neuronal hierarchy?

The electric fish, Eigenmannia, is able to discriminate the sign of the frequency difference, Df, between a neighbor's electric organ discharges (EODs) and its own. The fish lowers its EOD frequency for positive Dfs and raises its frequency for negative Dfs to minimize jamming of its electrolocation ability by a neighbor's EODs of similar frequency. This jamming avoidance response (JAR) is controlled by a group of 'sign-selective' neurons in the prepacemaker nucleus (PPN) that is located at the boundary of the midbrain and the diencephalon (Fig. 1). Extracellular recordings from a total of 35 neurons revealed a great similarity between behavioral and neuronal response properties: 1. All neurons fired vigorously for negative Dfs and were almost silent for positive Dfs, regardless of the orientation of the jamming stimulus, and thus discriminated the sign of Df unambiguously (Fig. 2). 2. In accordance with behavioral observations, individual neurons failed to discriminate the sign of Df when the jamming stimulus had the same field geometry as the signal mimicking the animal's own EOD (Fig. 3). 3. Df magnitudes which evoke strongest JARs, usually 4 to 8 Hz, also induced most vigorous responses in sign-selective neurons (Fig. 5). 4. Behavioral and neuronal thresholds for the detection of small jamming signals were similar. Threshold for sign selectivity was reached when the amplitude ratio of the jamming signal to the EOD mimic, measured near the head surface, was 0.001. This value corresponds to a maximal temporal disparity (a necessary cue for performing a correct JAR) of 1 to 2 microseconds for signals received by the two sides of the body in a transverse jamming field (Fig. 7). 5. The effects of two jamming fields, offered orthogonally to each other, may interact nonlinearly at the behavioral as well as at the neuronal level. A positive Df presented in one field may suppress behavioral and neuronal responses to modulations of the sign of Df in the other field (Fig. 8c).     

The jamming avoidance response ofEigenmannia: properties of a diencephalic link between sensory processing and motor output

Summary Brain regions participating in the control ofEigenmannia's electric organ discharge frequency were localized by electrical microstimulation and anatomically identified by means of horseradish peroxidase deposition. A diencephalic region was found which, when stimulated, caused electric organ discharge (EOD) frequency increases of similar magnitude and time course as the frequency increases seen during the jamming avoidance response. Single unit recordings from this region revealed one cell type which preferentially responded to stimuli that cause the acceleration phase of the jamming avoidance response (electric organ discharge frequency increase). A second cell type responded preferentially to stimuli which cause EOD frequency decrease, and both cell types were tuned to stimuli which evoked maximal jamming avoidance behaviors.The results of the horseradish peroxidase experiments showed that the recording and stimulation sites correspond to the previously described nucleus electrosensorius. Our results confirm the earlier finding that this nucleus receives output from the torus semicircularis and we also found that the N. electrosensorius projects to the mesencephalic prepacemaker nucleus. The prepacemaker projects to the medullary pacemaker nucleus which generates the commands that evoke electric organ discharges.The anatomical and physiological results described here establish this diencephalic region as a link between the major sensory processing region for the jamming avoidance response, the torus semicircularis, and a mesencephalic pre-motor region, the prepacemaker nucleus.Abbreviations AM amplitude modulation - DF Delta F - ELLL electrosensory lateral line lobe - EOD electric organ discharge - JAR jamming avoidance response - NE nucleus electrosensorius - PPN prepacemaker nucleus - PN pacemaker nucleus     

EOD modulations of brown ghost electric fish: JARs, chirps, rises, and dips.

Weakly electric "wave" fish make highly regular electric organ discharges (EODs) for precise electrolocation. Yet, they modulate the ongoing rhythmicity of their EOD during social interactions. These modulations may last from a few milliseconds to tens of minutes. In this paper we describe the different types of EOD modulations, what they may signal to recipient fish, and how they are generated on a neural level. Our main conclusions, based on a species called the brown ghost (Apteronotus leptorhynchus) are that fish: (1) show sexual dimorphism in the signals that they generate; (2) make different signals depending on Whether they are interacting with a fish of the opposite sex or, within their own sex, to a fish of that which is dominant or subordinate to it; (3) are able to assess relative dominance from electrical cues; (4) have a type of plasticity in the pacemaker nucleus, the control center for the EOD, that occurs after stimulation of NMDA receptors that causes a long-lasting (tens of minutes to hours) change in EOD frequency; (5) that this NMDA receptor-dependent change may occur in reflexive responses, like the jamming avoidance response (JAR), as well as after certain long-lasting social signals. We propose that NMDA-receptor dependent increases in EOD frequency during the JAR adaptively shift the EOD frequency to a new value to avoid jamming by another fish and that such increases in EOD frequency during social encounters may be advantageous since social dominance seems to be positively correlated with EOD frequency in both sexes.     

Responses of electrosensory neurons in the torus semicircularis of Eigenmannia to complex beat stimuli: testing hypotheses of temporal filtering

The weakly electric fish, Eigenmannia, changes its frequency of electric organ discharges (EODs) to increase the frequency difference between its EODs and those of a jamming neighbor. This jamming avoidance response is greatest for frequency differences (i.e., beat rates) of approximately 4 Hz and barely detectable at beat rates of 20 Hz. A neural correlate of this behavior is found in the torus semicircularis, where most neurons act as low-pass or band-pass filters over this range of beat rates.This study examines two mechanisms that could possibly underlie low-pass temporal filtering: 1) Inhibition by a high-pass interneuron. 2) Voltage and time-dependent conductances associated with ligand-gated channels. These mechanisms were tested by recording intracellularly while employing stimuli consisting of simultaneous low and high beat rates. A neuron's response to the low beat rate was not diminished by the addition of the higher frequency jamming signal (thereby superimposing a high rate of amplitude and phase modulation onto the lower rate), and the inhibitory interneuron hypothesis is, therefore, not supported. Also, the responses to the high beat rate were not facilitated during maintained depolarization in response to the low beat rate.In some cases, particularly band-pass neurons, accommodation processes appeared to contribute to the decline in the amplitude of psps at high beat rates.     

Behavioral responses to jamming and ‘phantom’ jamming stimuli in the weakly electric fish <Emphasis Type="Italic">Eigenmannia</Emphasis>

The jamming avoidance response (JAR) of the weakly electric fish Eigenmannia is characterized by upward or downward shifts in electric organ discharge (EOD) frequency that are elicited by particular combinations of sinusoidal amplitude modulation (AM) and differential phase modulation (DPM). However, non-jamming stimuli that consist of AM and/or DPM can elicit similar shifts in EOD frequency. We tested the hypothesis that these behavioral responses result from non-jamming stimuli being misperceived as jamming stimuli. Responses to non-jamming stimuli were similar to JARs as measured by modulation rate tuning, sensitivity, and temporal dynamics. There was a smooth transition between the magnitude of JARs and responses to stimuli with variable depths of AM or DPM, suggesting that frequency shifts in response to jamming and non-jamming stimuli represent different points along a continuum rather than categorically distinct behaviors. We also tested the hypothesis that non-jamming stimuli can elicit frequency shifts in natural contexts. Frequency decreases could be elicited by semi-natural AM stimuli, such as random AM, AM presented to a localized portion of the body surface, transient changes in amplitude, and movement of resistive objects through the electric field. We conclude that ‘phantom’ jamming stimuli can induce EOD frequency shifts in natural situations.     

Sensory cues for the gradual frequency fall responses of the gymnotiform electric fish, Rhamphichthys rostratus

The sensory cues for a less known form of frequency shifting behavior, gradual frequency falls, of electric organ discharges (EODs) in a pulse-type gymnotiform electric fish, Rhamphichthys rostratus, were identified. We found that the gradual frequency fall occurs independently of more commonly observed momentary phase shifting behavior, and is due to perturbation of sensory feedback of the fish's own EODs by EODs of neighboring fish. The following components were identified as essential features in the signal mixture of the fish's own and the neighbor's EOD pulses: (1) the neighbor's pulses must be placed within a few millisecond of the fish's own pulses, (2) the neighbor's pulses, presented singly at low frequencies (0.2–4 Hz), were sufficient, (3) the frequency of individual pulse presentation must be below 4 Hz, (4) amplitude modulation of the sensory feedback of the fish's own pulses induced by such insertions of the neighbor's pulses must contain a high frequency component: sinusoidal amplitude modulation of the fish's own EOD feedback at these low frequencies does not induce gradual frequency falls. Differential stimulation across body surfaces, which is required for the jamming avoidance response (JAR) of wave-type gymnotiform electric fish, was not necessary for this behavior. We propose a cascade of high-pass and low-pass frequency filters within the amplitude processing pathway in the central nervous system as the mechanism of the gradual frequency fall response.Abbreviations EOD electric organ discharge - f frequency of EOD or pacemaker command signal - JAR jamming avoidance response - S ₁ stimulus mimicking fish's own EOD - f ₁ frequency of S₁ - S ₂ stimulus mimicking neighbor's EOD - f ₂ frequency of S₂     

Electrosensory phase sensitivity in the weakly electric fish Eigenmannia in the detection of signals similar to its own

The electric organ discharge (EOD) of the South American knifefish Eigenmannia sp. is a permanently present wave signal of usually constant amplitude and frequency (similar to a sine wave). A fish perceives discharges of other fish as a modulation of its own. At frequency identity (F = 0 Hz) the phase difference between a fish's own electric discharge and that of another fish affects the superimposed waveform. It was unclear whether or not the electrosensory stimulus-intensity threshold as behaviourally determined depends on the phase difference between a fish's own EOD and a sine-wave stimulus (at F = 0 Hz). Also the strength of the jamming avoidance response (JAR), a discharge frequency shift away from a stimulus that is sufficiently close to the EOD frequency, as a function of phase difference was studied. Sine-wave stimuli were both frequency-clamped and phase-locked to a fish's discharge frequency (F = 0 Hz). In food-rewarded fish, the electrosensory stimulus-intensity threshold depended significantly on the phase difference between a fish's discharge and the stimulus. Stimulus-intensity thresholds were low (down to 3 V/cm, peak-to-peak) when the superimposed complex wave changed such that the shift in zero-crossings times relative to the original EOD was large but amplitude change minimal; stimulus-intensity thresholds were high (up to 16.9 V/cm, peak-to-peak) when the shift in zero-crossings times was small but amplitude change maximal. Similar results were obtained for the non-conditioned JAR: at constant supra-threshold stimulus intensities and F = 0 Hz, the phase difference significantly affected the strength of the JAR, although variability between individuals was higher than that observed in the conditioned experiments.Abbreviations ACP active phase coupling - EOD electric organ discharge - JAR jamming avoidance response - F frequency (fish) — frequency (stimulus) [Hz] - p-p peak-to-peak     

Electric field interactions in pairs of electric fish: modeling and mimicking naturalistic inputs

Weakly electric fish acquire information about their surroundings by detecting and interpreting the spatial and temporal patterns of electric potential across their skin, caused by perturbations in a self-generated, oscillating electric field. Computational and experimental studies have focused on understanding the electric images due to simple, passive objects. The present study considers electric images of a conspecific fish. It is known that the electric fields of two fish interact to produce beats with spatially varying profiles of amplitude and phase. Such patterns have been shown to be critical for electrosensory-mediated behaviours, such as the jamming avoidance response, but they have yet to be well described. We have created a biophysically realistic model of a wave-type weakly electric fish by using a genetic algorithm to calibrate the parameters to the electric field of a real fish. We use the model to study a pair of fish and compute the electric images of one fish onto the other at three representative phases within a beat cycle. Analysis of the images reveals rostral/caudal and ipsilateral/contralateral patterns of amplitude and phase that have implications for localization of conspecifics (both position and orientation) and communication between conspecifics. We then show how the common stimulation paradigm used to mimic a conspecific during in vivo electrophysiological experiments, based on a transverse arrangement of two electrodes, can be improved in order to more accurately reflect the important qualitative features of naturalistic inputs, as revealed by our model.     

Electrocommunication and Social Behaviour in Marcusenius senegalensis (Mormyridae,Teleostei)

The electric organ discharges (EODs) of Marcusenius senegalensis, a West African freshwater fish, are bipolar pulses of short duration (220 ± SE 13 μs). In males (n = 10; 10.1–13.1 cm standard length — which is around the size of getting mature), the duration of EOD pulses was of significantly greater variance than in females (n = 9; 9.8–12.8 cm standard length). Male EODs also showed a tendency for a longer duration than female EODs. Groups of three as well as of 14 M. senegalensis formed temporary schools in a ‘naturally’ equipped 720-1 tank. While swimming slowly in a loose school during their nocturnal active phase, fish discharged in irregular long-short-long inter-EOD interval patterns. Near neighbours displayed a tendency to discharge in intervals of similar duration (nearest neighbour distance < 1/2 fish length). On removal of a plastic partition that had separated a pair of fish for at least 3 days, mutual threat displays followed by fighting were observed. During threatening, the fish alternated regularly between bursts of a high discharge rate and short discharge breaks; the rate of change was 4/s. The subdominant animal in a group of two was attacked frequently and often ceased discharging when the dominant fish approached. Courtship behaviour involving gonadally mature fish was accompanied by high-discharge-rate displays with intervals of constant duration in both fish, and the reciprocal display of ‘preferred’ EOD latencies in the 12 ms range. The results demonstrate electric communication by distinct inter-discharge interval patterns in the social behaviour of this mormyrid fish.     

The potential coding utility of intercell cross-correlations in the retina

The action potentials (impulses) produced by pairs of neighboring retinal ganglion cells often show a tendency either to fire in close temporal synchrony or to avoid temporal synchrony. This cross-correlation (a rate of coincidences that differs from that expected by chance) has been exploited as a window into retinal processing, but its possible functional significance has proven elusive. Previous work has failed to show that the coincidences serve as a direct code for visual stimuli. In this analysis it is shown that the coincidences serve neither as a key for reducing variability nor as a key for improving the coding by the individual cells. The residual impulse trains (trains with coincidences deleted) are more variable than the raw impulse trains and provide an inferior coding to that of the raw impulse trains. There is negative correlation between the firing rate of the residual impulse trains and that of the coincidence impulse trains, which is consistent with the lower variance of the raw impulse trains. There is no consistent cross-correlation between the rates of residual impulse trains of cells in pairs showing cross-correlation; however, it is found that this observation does not discriminate among models for generating coincidences.     

Temporal Hyperacuity in the Gymnotiform Electric Fish, Eigenmannia

SYNOPSIS. The gymnotiform electric fish, Eigenmannia, exhibitsextraordinary sensitivity to small timing differences betweensensory signals. The jamming avoidance response, gradual frequencyshifts of the electric organ discharges, requires the detectionof temporal disparities between sensory signals impinging upondifferent electroreceptors. This behavior occurs reliably evenwith temporal disparities being smaller than one microsecond.Since individual sensory receptors are not capable of encodingsuch minute timing with certainty, the high behavioral sensitivitymust, therefore, emerge from signal processing within the centralnervous system. Individual neurons, at the top of a well definedneuronal hierarchy have been found to be sensitive to temporaldisparities in the range of 1 microsecond. The response propertiesof these neurons as well as behavioral results suggest thatspatial convergence of sensory information plays a major rolein the emergence of this temporal hyperacuity.     

Independently evolved jamming avoidance responses employ identical computational algorithms: a behavioral study of the African electric fish,Gymnarchus niloticus

An African electric fish, Gymnarchus, and a South American electric fish, Eigenmannia, are believed to have evolved their electrosensory systems independently. Both fishes, nevertheless, gradually shift the frequency of electric organ discharge away when they encounter a neighbor of a similar discharge frequency. Computational algorithms employed by Gymnarchus for this jamming avoidance response have been identified in this study for comparison with those of extensively studied Eigenmannia.

1. Gymnarchus determines whether it should raise or lower its discharge frequency based solely upon the signal mixture of its own reafferent and the exafferent signal from a neighbor, and does not internally refer to the pacemaker command signal which drives its own discharge.
2. The signal mixture is analyzed in terms of the time courses of amplitude modulation and phase modulation at each area of the body surface.
3. Phase of the signal mixture at each area is compared with that of another area for the detection of phase modulation.
4. Unambiguous information necessary for the jamming avoidance response is extracted by integrating information from all body areas each of which yields ambiguous information.
5. These computational features are identical to those of Eigenmannia, suggesting that the neural circuit for jamming avoidance responses may have evolved from preexisting mechanisms for electrolocation in both fishes.

     

A model for the variability of maintained discharges and responses to flashes of light

Previous studies of the variability of firing of retinal ganglion cells have led to apparently contradictory conclusions. To a first approximation, maintained discharges derive their variability from a noise source that is linearly added to the signal setting the mean firing rate. On the other hand, the variability of responses to abrupt changes in lighting seems to result from a nonlinear interaction between signal and noise. In both the cat and the goldfish retinae, the variance of rate is a fractional power function of the mean response amplitude (impulses/s). The exponent of that power function depends on the duration of the period in which the response is sampled after each transition in luminance; longer durations have a larger exponent. These results are difficult to explain with any simple model. The variability of the maintained discharges also deviates from the predictions of simple additivity. We propose a model for the variability of responses to abrupt changes in lighting that incorporates variability of the form observed for maintained discharges. The parameters of our model that provide the best fits to the variability of responses also provide a reasonable fit to the variability of maintained discharges. Thus, a single explanation can account for the variability of maintained discharges and responses of ganglion cells.