Modelling Holling type II functional response in deterministic and stochastic food chain models with mass conservation

The Rosenzweig-MacArthur predator-prey model is the building block in modeling food chain, webs and ecosystems. There are a number of hidden assumptions involved derivation. For instance prey population growth logistic without predation but also with predation. In order to reveal these we will start modelling resource-predator-prey system closed spatially homogeneous environment. This allows us keep track nutrient flow. With an instantaneous remineralisation products excreted environment by populations dead body mass there conservation mass. for dimension reduction yields balance model. When furthermore searching handling processes much faster that changing rates, trophic interaction described Holling type II functional response, assumed derivation uses extended deterministic predators as variables where ratio predator/prey masses used mechanistic time-scale parameter. starting point stochastic We investigate effects random switching between predator dying. Prey consumption ambient resources still therefore hybrid. transient dynamics studied numerical Monte Carlo simulations quasi-equilibrium distribution quantities calculated. individual scaling parameter formulation. quantification mean-field approximation criterion justification replacement