Laura Kantzler, LJLL, Sorbonne Université
Modelling of the Size-spectrum Evolution in Marine Ecosystems
Trophic interactions between animals in the ocean were matter of interest since the 60′, where it was quickly discovered that the individuals’ body size acts as ‘master trait’ in food webs of animals, giving rise to emergent distributions of biomass, abundance and production of organisms.
We propose and investigate a deterministic jump-growth model of Boltzmann type, aiming to capture this emergence phenomenon in aquatic ecosystems. The equation of interest is derived from individual based dynamics governed by a stochastic process. Following the observation of the body mass being the crucial trait in these dynamics it is based on the assumption that binary interactions between individuals in the ecosystem take place: A predator feeding on a prey, which then results in growth of the predator with assimilating a certain (usually very small) amount of its prey’s mass as well as plankton production. Analytical results in various parameter regimes are discussed and numerical simulations underlying these observations are given.