Dynamics Of Stoichiometric Model Of Producer-grazer

The mismatch of the nutrient content of producer and of grazer influences the conversion rate of grazer, the dynamics of producer-grazer system and also the structure and the function of ecosystem. In this paper, population dynamical models are established based on ecological stoichiometry to examine the effect of nutrient enrichment on the dynamics of producer-grazer system.The paper is composed of four chapters.In Chapter1, the background and methods of the study, and main results of this paper are presented.In Chapter2, the conversion rate of grazer in the LKE model, unsmooth and limited by only one nutrient at any time, is modified by a smooth and limited by two nutrients at any time. Qualitative analysis shows that system has com-plex dynamical behaviors, such as multiple equilibria, Hopf bifurcation and saddle-node bifurcation. Numerical simulation indicates that at lower phosphorus den-sity, energy enrichment leads the grazer through (deterministic extinction)/(steady state)/(cycle)/(steady state)/(deterministic extinction), at higher phosphorus den-sity energy enrichment leads the grazer through (deterministic extinction)/(steady state)/(cycle), and nutrient enrichment leads the grazer through (deterministic ex-tinction)/(steady state)/(cycle) when the energy density is not too small. Nutrient enrichment can destabilize the dynamics and Rozensweig paradox of enrichment holds in a limited range of light/nutrient parameters.In Chapter3, by integrating the evolutionary dynamics with the ecological stoichiometric theory, we build an ecological and an evolutionary producer-grazer model. Our outcomes expound the impact of nutrient enrichment on the coevo-lution of evolutionary dynamics, i.e., CSS-stability, evolutionary branching and evolutionary cycle. Our study reveals that total phosphorus asserts a considerable impact on both the ecological dynamics and the evolutionary dynamics. The stud-ies show that the higher total phosphorus is always in favor of the coexistence of producer-grazer system in the ecological dynamics without considering the evolu-tionary processes. Increasing the density of total phosphorus may produce complex evolutionary dynamics and trigger the dimorphic populations, a cyclic changes, or sensitive dependence on the initial conditions.In Chapter4, since macrophytes provide a refuge for zooplankton against the predation of fish, the functional response of fish is deduced. By ecological sto-ichiometry, a phytoplankton-zooplankton-fish model is presented. The existence and stability of the equilibria are explored in qualitative analysis. Our work in-dicates that nutrient enrichment, macrophytes density and the diet composition of fish influence the dynamical behaviors of the system. Our results show that transplanting macrophytes producing refuge effect may be not effective to protect zooplankton and control algae blooms, so a comprehensive approach is considered, which refers to nutrient density and the diet composition of fish.At the end of this paper, the remark of main results and further work are presented, many related references are listed.