Envelope generated by the relative movement of two weakly electric fish. (A) The movement trajectories of two individual fish where fish 1 is stationary and fish 2 is swimming (purple) is shown in the inset box. The distance (magenta) between individuals varies over time as a function of the movement of fish 2. The combined signal (black) is the sum of the EOD signal of fish 1 (S1; 300 Hz) and the EOD of fish 2 (S2; 350 Hz). This combined signal has an emergent amplitude modulation (green) and higher order envelope (red). Note that the black dots show the position of fish 2 (inset) and the distance between the two fish at time 0, respectively. (B) A Fourier transform (FT) analysis shows the power (i.e. the modulus squared of FT) for each of the signals – the combined signal (black), the AM (green) and the envelope (red). (C) A close-up of B, highlighting the power at low frequencies in the envelope due to the relative movement of the fish.

Envelope generated by the interaction of the EODs of three weakly electric fish. (A) Three fish that are not moving are shown in the inset. The magenta and orange lines indicate the constant distance of the two outer fish to the middle fish. The combined signal (black) is the sum of the EOD signals of the three fish, S1 (300 Hz), S2 (350 Hz) and S3 (395 Hz). The combined signal has an amplitude modulation (green) and a higher order envelope (red). (B) A Fourier analysis shows the power for each of the signals – the combined signal (black), the AM (green) and the envelope (red). (C) A close-up of B, highlighting the power at 5 Hz in the envelope due to our choice of EOD frequencies in this simulation.

Interactions of movement and EODs for producing envelopes. In naturalistic conditions, weakly electric fish are often in groups of three or more individuals and are moving relative to one another, producing a complex envelope that contains a social and movement-generated component. (A) There are three fish, with one fish that is stationary and two fish (purple and blue) that are swimming (inset). The distance from fish 1 to each of the swimming fish (magenta and orange) varies as a function of the relative movement. The combined signal (black) contains the EODs of all three fish, an AM (green) and a complex envelope (red), which is composed of both the movement and the difference between the AM frequencies (ddF), from the social EOD interactions. (B) A Fourier analysis shows the power for each of the signals – the combined signal (black), the AM (green) and the envelope (red; consisting of movement and social components). (C) A close-up of B, highlighting the power below 5 Hz, which is due to the relative movement of the three fish, and at 5 Hz, which is due to the social envelope, and results from our choice of EOD frequencies (300, 350, 395 Hz) in this simulation. We have also replotted the power spectrum from the non-moving three fish case (red dotted line; from Fig. 2C) to highlight the potential separation between social and movement-generated envelopes.

The social envelope response (SER). (A) Eigenmannia shift their EOD frequency (ΔF1) in response to envelope stimuli, but the response is dependent on the initial envelope frequency (color coded). Fish show stronger responses to initial envelopes that are lower (i.e. 2 and 4 Hz) in frequency. The response is bidirectional, whereby the frequency shift is down for positive ddFs and up for negative ddFs. (B) The strength of the response (normalized |ΔF1|) varies as a function of combined stimulus amplitude (S2 + S3), where fish show an increased change in EOD frequency for higher stimulus amplitudes. Under natural conditions, increased stimulus amplitude would be achieved by decreasing the distance between individuals, as often happens when they are swimming relative to one another. (C) The SER increases the frequency of the envelope, with the final envelope frequencies (|ddF_f|) typically ending up in a range of 5 to 15 Hz for all initial envelope frequencies (|ddF_i|) tested.

Peripheral electrosensory neurons respond to envelopes. (A) Left: example stimulus in which the envelope (red) increases linearly as a function of time with a 20 Hz sinusoidal AM (green). a.u., arbitrary units. Right: example recording from an electroreceptor in response to this stimulus. It can be seen that the electroreceptor phase locks to high but not to low envelopes. V_m, membrane potential. (B) Peri-stimulus time histogram (PSTH) from the same electroreceptor. It can be seen that the firing rate is constant for low envelope values and increases linearly when the envelope is greater than a threshold value (dashed line). (C) Phase histograms when the envelope is lower than threshold (left) and higher than threshold (right). Phase locking (i.e. the absence of firing at some carrier phases) is observed only when the envelope is higher than threshold.

Hindbrain electrosensory neurons respond to envelopes. (A) Left: morphology of different electrosensory lateral line lobe (ELL) pyramidal cell classes. Note the large differences in dendritic tree length. Superficial pyramidal cells have the largest dendritic trees and are found superficially while deep pyramidal cells have the smallest dendritic trees and are found deep in the pyramidal cell layer. Intermediate pyramidal cells are in between. Right: firing rate and dendritic tree length are strongly negatively correlated. (B) Responses of example superficial (left) and deep (right) ELL pyramidal cells. (C) Phase histograms from these same cells to the AM stimulus. Note that only the superficial pyramidal cell (left) displays strong phase locking because the count is zero for phases between −π/2 and π/2. (D) Envelope response as a function of AM response for ELL pyramidal cells. Note that all cells respond to both. (E) Proposed neural circuit by which ELL pyramidal cells can respond to envelopes. An inhibitory interneuron, the ovoid cell, responds to the envelope via the non-linear action potential generation mechanism and sends this information primarily to superficial ELL pyramidal cells.

Midbrain electrosensory neurons respond to envelopes. (A) The stimulus consists of a noisy AM (green) with corresponding envelope (red). (B) Response from an example Ts neuron to the stimulus shown in A. This neuron responds strongly to the envelope. (C) PSTH response from this same Ts neuron to the stimulus shown in A. (D) Envelope response as a function of AM response from Ts neurons. In contrast with ELL pyramidal cells, three distinct clusters are seen. Some Ts neurons respond selectively to either the envelope (red) or the AM (green) while some respond to both (blue). (E) Model in which a Ts neuron receives input from both ON- and OFF-type ELL pyramidal cells. The strength of the input from ON-cells is given by ρ_ON while the strength of the input from OFF-cells is given by 1–ρ_ON. Both inputs are thus balanced in strength when ρ_ON=0.5. (F) Model results showing the AM (green) and envelope (red) responses as a function of ρ_ON. (G) Model results showing the AM (green) and envelope (red) responses as a function of the baseline firing rate. (H) Proposed schematic diagram by which Ts neurons acquire their response selectivity to envelopes. ON- and OFF-type ELL pyramidal cells respond during the positive and negative phases of the AM, respectively (brown and green). However, both tend to respond more when the envelope is high. Summing these responses gives a response that is independent of AM but will still depend on the envelope (black).