“Predator prey games in multiple habitats reveal mixed strategies in diel vertical migration”

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Jérôme Pinti and André W. Visser (March 2019)

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Predator prey games in multiple arenas applied to DVM reveals mixed strategies through frequency dependent processes

Sardines are forage fish feeding on zooplankton and following their prey at day and at night through vertical migrations.

Can we apply economic principles to fish ecology and diel vertical migration? It appears that the way fish and zooplankton behave in the presence of other individuals can be derived from mathematical notions first developed to describe the interactions between several economic players.

In a paper appearing in The American Naturalist, two researchers from the Centre for Ocean Life of DTU (Denmark) modeled the optimal habitat selection strategies of plankton and fish in a water column. Their set-up allows both individual prey (zooplankton) and predators (fish) to choose their position at day and at night. This is the first time that a model has investigated the optimal position of both prey and predators in a water column with such a resolution. The model reproduces features of diel vertical migrations that are observed in nature. For example, at low predation pressure, zooplankton remain near the surface whereas a higher predation pressure induces zooplankton migration between the surface (to feed, at night) and the depths (to hide, during daytime). Fish follow a similar route to maximize their food intake.

Antarctic krill, Euphausia superba, a species of zooplankton performing diel vertical migration to feed at the surface at night and hide from its predators during daytime.
(Credit: Beth Simmons, Palmer Antarctica LTER, CC BY-SA 2.0)

A deeper knowledge of these complex migration processes is necessary as they play a role in global biogeochemical cycles. Zooplankton and fish actively transport carbon to the depths during diel vertical migrations, therefore removing carbon from the surface. The surface being coupled with the atmosphere, this drawdown of carbon helps reducing the atmospheric CO2 concentration. A better understanding of these biological processes will enable scientists to provide better estimates and predictions of atmospheric CO2 concentrations.


Prey and predators continuously react to each other and to their environment, adjusting their behavior to maximize their fitness. In a pelagic environment, organisms can optimize their fitness by performing diel vertical migrations (DVM). We applied a game theoretic approach to investigate the emergent patterns of optimal habitat selection strategies in a multiple habitat arena. Our set-up allows both players to choose their position at day and at night in the water column. The model reproduces features of vertical migrations observed in nature, including residency at depth or at the surface, vertical migrations, mixed strategies and bimodal distributions within a population. The mixed strategies appear as a consequence of frequency-dependent processes and not of any intra-species difference between individuals. The model also reveals a curious feature, where natural selection on individuals can provoke distinct regime shifts and precipitate an irreversible collapse in fitness. In the case presented here, the increasing voracity of the predator triggers a behavioral shift in the prey reducing the fitness of all members of the predator population.