Phase -Depth 0 mOxygen 100 %Fish caught 0FPS 0

Drag to orbit, wheel or pinch to zoom. Side cross-section: ice edge on the left, silver fish school at the patch depth. Time runs faster than real life. The seal and fish are enlarged against the 40 m scale only by the camera, not by the model.

Leopard Seal at the Ice Edge

Every dive costs travel time and oxygen; every extra second on the patch catches fewer fish. Find the bottom time that gives the best catch per hour, and see why a seal should not push its oxygen limit.

Patch and dive

Oxygen and recovery

Strategy

Live readouts

Catch rate against bottom time

Orange curve: long-term intake rate (kJ per second, whole dive cycle). Thin blue curve: energy caught so far on the patch (scaled). Green line: optimum bottom time. White line: your choice. Red dashed line: aerobic dive limit.

Self-checks (independent of the animation)

running...

The science

Marginal value theorem (Charnov 1976). A forager that must leave a patch to travel to the next one maximises its long-term intake rate γ = g(t_b) / (t_travel + t_b) by leaving when the instantaneous rate has fallen to the average: g'(t_b*) = γ*. Longer travel means a longer stay. For a patch that depletes exponentially, g(t) = G(1 - e^-t/τ), and with no oxygen limit the optimum solves e^x = 1 + c + x with x = t_b/τ and c = t_travel/τ (a Lambert W function).

Diving makes travel time and cost depend on the stay. The oxygen store S (mL O₂ per kg) is used at the diving metabolic rate m, so the aerobic dive limit is ADL = S/m. Within it, recovery at the surface is roughly proportional to the dive: t_surf = a T_dive. Beyond it, lactate builds up and recovery grows faster, modelled here as a T + b (T - ADL)²/ADL. The intake rate is then γ(t_b) = g(t_b) / (T_dive + t_surf) with T_dive = 2ℓ/v + t_b, where ℓ is the length of the swim path to the patch.

Monte Carlo check. Each fish in the patch is caught after a random exponential time with mean τ, so the expected catch is exactly g(t). A simulated diver makes hundreds of dives and its measured rate is compared with the formula.

Honest simplifications. All numbers (patch energy, depletion time, oxygen store, dive metabolic rate, recovery ratio, lactate penalty) are illustrative, typical in order of magnitude for a large phocid seal, not measurements of leopard seals. The model ignores the energy cost of swimming, prey of different sizes, hunting other prey (penguins and seals are also eaten by leopard seals; this lab studies only the fish dive), buoyancy changes, and learning. The seal is animated with rigid flippers.

Models: Blender 5.2 (seal, fish, ice edge; baked textures). Rendering: Three.js r160.

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