The electric image in weakly electric fish: Perception of objects of complex impedance

Weakly electric fish explore the environment using electrolocation, They produce an electric field that is detected by cutaneous electroreceptors; external objects distort the field, thus generating an electric image. The electric image of objects of complex impedance was investigated using a realistic model, which was able to reproduce previous experimental data. The transcutaneous voltage in the presence of an elementary object is modulated in amplitude and waveform on the skin. Amplitude modulation (measured as the relative change in the local peak-to-peak amplitude) consists of a 'Mexican hat' profile whose maximum relative slope depends on the distance of the fish from the object. Waveform modulation depends on both the distance and the electrical characteristics of the object. Changes in waveform are indicated by the amplitude ratio of the larger positive and negative phases of the local electric organ discharge on the skin. Using the peak-to-peak amplitude and the positive-to-negative amplitude ratio of this discharge, a perceptual space can be defined and correlated with the capacitance and resistance of the object. When the object is moved away, the perceptual space is reduced but keeps the same proportions (homothetically): for a given object, the positive-to-negative amplitude ratio is a linear function of the peak-to-peak amplitude. This linear function depends on the electrical characteristics of the object. However, there are 'families' of objects with different electrical characteristics that produce changes in the parameters of the local electric organ discharge that are related by the same linear function. We propose that these functions code the perceptual properties of an object related to its impedance.