Oceanic diel vertical migrations arising from a predator-prey game

The deep scattering layer is an ubiquitous aggregation of zooplankton and forage fish in the ocean. It features the striking phenomenon of diel vertical migration, where animals remain in deep, dark water in daylight hours and migrate upwards at dusk. The common explanation for this is that prey avoid vulnerability to visual predators.

Here, we develop a game-theoretic explanation for the deep scattering layer and its diel vertical migrations, focusing on one generic predator species and one generic prey species. The model is formulated in continuous time and space, and by neglecting the cost of locomotion, it allows fine-grained predictions of vertical distributions.

The Nash equilibrium features a distinct deep scattering layer which undertakes diel vertical migrations, the range of which increases with predator abundance. Maximum feeding rates are predicted to occur at dawn and dusk. Predator interference emerges from the game dynamics in the form of a complicated functional dependency of gross encounter rates on predator abundance.

In turn, the growth rate of the prey decreases monotonically with predator abundance. In addition to providing a mechanistic explanation for the striking phenomenon of diel vertical migrations, the model yields quantitative predictions of vertical distributions and diel patterns in feeding intake, which may be compared with acoustic data, observed individual behavior, or stomach data.