Estimation of distance and electric impedance of capacitive objects in the weakly electric fish .

During active electrolocation, the weakly electric fish judges the distance and impedance of nearby objects. Capacitive objects, which modulate local amplitude and waveform of the fish's electric probing signals, cast amplitude and waveform images onto the fish's electroreceptive skin. For an unambiguous estimation of the impedance and distance of an object, the animal has to deal with multiple dependencies of object and image parameters. Based on experimentally recorded amplitude and waveform images, we investigated possible strategies of the fish to unequivocally determine both the distance and the impedance of capacitive objects. We show that the relative slope in amplitude images, but not in waveform images, is independent of object impedance and is a measure of object distance. Distance-invariant impedance estimators were obtained by two different analytical strategies. The peak modulations of both image types were 'calibrated' with the relative slope of the amplitude image. Impedance estimators were obtained whenever these pairs of image features (peak and relative slope) were related dynamically over two consecutive distances. A static impedance estimator termed 'electric colour' is postulated to arise from the relationship of an amplitude and waveform image. Our results confirm that electric colour is indeed unaffected by object distance. For electric colour estimation we suggest a minimalistic approach of just relating the peak modulations of both image types to the basal amplitude and waveform condition. Our results are discussed with regard to the anatomical and physiological organization of the fish's electrosensory neuronal pathways and behavioural strategies of electrolocating fish.