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Modeling an electrosensory landscape : behavioral and morphological optimization in elasmobranch prey capture

Brandon R. Brown^*

Department of Physics, University of San Francisco, San Francisco, CA 94117, USA

View larger version (13K): [in a new window]   Fig. 1. (A) Dorsal view of simulation geometry. The prey dipole, , defines the origin for all calculations. Three sample canals in the elasmobranch are shown for demonstrative purposes. The vector maps out relevant locations in the canals with respect to the prey origin in equation 1. (B) Close-up view of one sensory organ, including the jelly-filled canal that connects a pore to the ampulla of Lorenzini. The electric field of the prey is loosely illustrated by a pair dashed lines. Each canal/ampulla system is described by a vector running from the pore to the ampulla, and its orientation is denoted by the angle measured with respect to the forward direction of the elasmobranch. In A, the sample canals have orientation angles of roughly 130, 180 and 230°. In B, the canal's orientation angle is roughly 130°.

View larger version (20K): [in a new window]   Fig. 2. Elasmobranch models (A) and ß (B). In A, only every other canal and ampulla system is depicted for presentational clarity. Each canal line forms a vector starting on the modeled elasmobranch's surface and terminating at an ampulla inside the model. Model has one cluster of ampullae; the model measures 20 cm across. Model ß has three separate ampullary clusters spaced 5 cm apart; the model measures 50 cm from side to side and 20 cm from front to back.

View larger version (16K): [in a new window]   Fig. 3. A model elasmobranch making a straight-line approach to the prey dipole , oriented at 45° with respect to north. The light lines illustrate the dipole electric field, and the dark vector denotes the approach vector of the elasmobranch.

View larger version (14K): [in a new window]   Fig. 4. Voltage changes (V) for 36 canal/ampulla systems for the approach described in Fig. 3. Sequential results for (A) 80 cm separation, (B) 50 cm separation and (C) 20 cm separation.

View larger version (20K): [in a new window]   Fig. 5. A model elasmobranch with three approach strategies to a prey dipole parallel to north. Initially, at point A (40 cm east and 40 cm south of ) the model reacts to the dipole field. Point B (40 cm east and 10 cm south of ) is on the path of the elasmobranch if it were to maintain its original course; point C (30 cm east and 10 cm south of ) is on a path maintaining orientation towards the dipole field; point D (20 cm east and 20 cm south of ) is on the path after an abrupt turn to approach the prey directly.

View larger version (14K): [in a new window]   Fig. 6. Voltage changes (V) for 36 canal—ampulla systems for the four points denoted in Fig. 5. Results for (A) the point of first reaction, (B) a model that maintains its initial heading, (C) a model that maintains its orientation to the dipole field and (D) a model that turns to approach the dipole prey directly. Note the changing voltage scales.

View larger version (23K): [in a new window]   Fig. 7. Comparative signal development for two morphologies. The insets depict the scenario and corresponding model in each case, including reference ampullae orientations. (A,B) Voltage changes (V) in ampullae for models and ß, respectively, as they move north at 0.5 ms-1 through a point located 50 cm west and 15 cm south of the prey dipole. The dipole (shown as an arrow) is oriented at 10° east of north. (C,D) Voltage changes in ampullae for models and ß, respectively, as they move north at 0.5 ms-1 through a point located 20 cm south of a prey dipole. The dipole is oriented at 45° east of north.

View larger version (16K): [in a new window]   Fig. 8. (A) Quantitative assessment of the reaction paths shown in Fig. 5 for a mathematically modeled elasmobranch. R, the reinforcement factor, is defined in the text. The fractions denote the percentage of organs maintaining their initial voltage polarities. (B) Quantitative assessment of the elasmobranch's direct approach to a prey dipole illustrated in Fig. 3.

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