The effects of simple objects on the electric field of Apteronotus

How might electric fish determine, from patterns of transdermal voltage changes, the size, shape, location, and impedance of a nearby object? I have investigated this question by measuring and simulating electric images of spheres and ellipsoids near an Apteronotus leptorhynchus. Previous studies have shown that this fish's electric field magnitude, and perturbations of the field due to objects, are complicated nonliner functions of distance from the fish. These functions become much simpler when distance is measured from the axes of symmetry of the fish and the object, instead of their respective edges. My analysis suggests the following characteristics of high frequency electric sense and electric images. 1. The shape of electric images on the fish's body is relatively independent of a spherical object's radius, conductivity, and rostrocaudal location. 2. An image's relative width increases linearly with lateral distance, and might therefore unambiguously encode object distance. 3. Only objects with very large dielectric constants cause appreciable phase shifts, and the degree of shift depends strongly on water conductivity. 4. Several parameters, such as the range of electric sense, may depend on the rostrocaudal location of an object. Large objects may be detectable further from the head than the tail, and conversely, small objects may be detectable further from the tail than head. 5. Asymmetrical objects produce different electric images, correlated with their cross-sections, for different orientations and phases of the electric field. 6. The steep attenuation with distance of the field magnitude causes spatial distortions in electric images, somewhat analogous to the perspective distortion inherent in wide angle optical lenses.