Trophic interactions between animals in the ocean were matter of interest since 6 decades. 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 structural equation 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 that the body mass is 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 production of a certain amount of organisms or nutrients, nursing the ecosystem at a very small scale. This model reproduces the so-called “cascade-effect”, which is frequently observed in ecosystems and describes the suppression of specific trophic positions in the ecosystem as result of an indirect influence from one trophic level to the second next lower or higher.
Some analytical results in specific parameter regimes are discussed and numerical simulations underlying these observations are given.