Leopard Seal at the Ice Edge: Dive Oxygen Budget, Prey Patch Depletion and the Marginal Value Theorem

Oxygen Budget and Dive Physiology

Leopard seals, like many marine mammals, face a critical balance between their need for oxygen and the energy required for diving. During a dive, these seals rely on their stored oxygen in the blood and muscles. The oxygen budget is calculated based on the seal's metabolic rate and the duration of the dive. As the dive progresses, the concentration of oxygen in the seal’s tissues decreases, leading to a point where anaerobic metabolism begins, causing a buildup of lactic acid, known as the lactate penalty.

The aerobic dive limit (ADL) is the maximum time that an animal can remain underwater while maintaining sufficient oxygen levels for aerobic respiration. Beyond this limit, the seal would need to surface and replenish its oxygen stores before diving again.

Prey Patch Depletion

Leopard seals hunt in patches of prey, such as silverfish, which are often depleted over time. The rate at which these patches are depleted can significantly impact the seal's dive strategy. If a patch is rapidly depleting, the seal must decide whether to stay and risk running out of food or leave to find a new, more abundant patch.

The marginal value theorem (MVT) helps explain this decision-making process. It suggests that animals will continue foraging in a patch as long as the expected return from staying is greater than the cost of leaving. When the net gain from additional time spent in the patch becomes negative, it's optimal to leave and search for new patches.

The Marginal Value Theorem

The MVT is a key concept in behavioral ecology that predicts how animals allocate their time between different resources. In the context of leopard seals, it helps explain why they might choose to stay longer at a patch with high initial prey density but lower overall productivity compared to patches with lower initial density but higher sustained productivity.

By using MVT, researchers can model the optimal dive duration and frequency that maximizes energy intake while minimizing oxygen expenditure.

Monte Carlo Simulation

To simulate the complex interactions between leopard seal diving behavior, prey patch depletion, and the MVT, a Monte Carlo simulation is employed. This statistical method allows for the probabilistic modeling of dive outcomes based on various parameters such as initial oxygen levels, metabolic rates, and prey availability.

The Monte Carlo diver in the simulation helps to calculate the optimal bottom time that maximizes energy intake while considering the lactate penalty and the depletion rate of the silverfish patch.

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