Structured population models for predator-prey interactions. The case of Daphnia and size selective planktivorous fish

In this thesis a model of the dynamics of size-structured population subject to selective predation is built and analyzed. The study is motivated by biological phenomena concerning limnology and oceanography, and in particular diversity of first consumers in aquatic ecosystems. An individual-based model of size-selective visual predator-harvester based on the concept of optimal foraging is proposed. Farther, a simplification of the model, described in terms of operators on the space of measures, is derived based on Holling II-type functional response to eliminate inherent difficulties of individual-based approach. The results are compared against experimental evidence. Considerations involving populations dynamics, namely growth, birth and mortality, are examined in the framework of measure-valued solutions to transport equation and various distances arising from optimal transportation theory. To this end, efficient algorithms for solving transportation problem on a real line are found and finally, numerical schemes based on particle methods for structured population models are improved. Moreover, approximation theory for Radon measures is developed.