Mean Field Games in Marine Ecology

Diel vertical migration (DVM) is a daily migration between the depths and the surface of the sea on various scales in marine communities ranging from zooplankton to marine mammals. In DVM marine animals remain in deep, dark layers of a water column during daytime period to avoid encountering visual predators and migrate to shallow nutrient-rich regions at dusk to feed.

It is usually assumed that animals optimize some fitness functional and, thus, the interactions between the organisms should be modelled and understood using the game theoretical toolbox. For diel vertical migration the migrational patterns can be thought as strategies the animals select trying to optimize their biological fitness over lifetime period.

This PhD thesis develops a mean field game theoretical framework for expressing diel vertical migration as a vertical differential game the marine animals play against each other. Understanding these ecological games is of great importance to theoretical ecology, which helps predicting responses of the marine ecosystem to various changes in the ecological environment like climate change.