A Plant Invasion Model In Ecosystem

Population ecology is a discipline which studies the regulation mechanism and variation of population structure and quantity. Recently, varieties of models are applied to analyze the interactions between species quantitatively and qualitatively. In this paper, we first introduce the Lotka-Volterra system, which is a classical model to describe the interaction. Besides, other predator and prey models, which are the bases of population ecology study, are also presented.In Chapter 2, some phenomenon of species invasion in China are introduced. The huge threaten and destruction to original ecosystem from the species invasion has caught worldwide attentions. The invasion is considered as one of the major reasons for the loss of species and genomic diversity. Then we introduce several mathematical models to describe the species invasion.The invasion is studied mainly based on these models.In Chapter 3, we introduce a three level food web with detritus and analyze its characteristics by Monte Carlo method. Comparing with the food web which has no detritus, it is observed that the food web with detritus is much more stable than the ordinary one. Furthermore, we find the species in the middle and upmost trophic levels are key factors to the stability of the system. Considering the stability of the model with detritus, our results in this chapter support the opinion that the more complex system is more stable than the simple one. It is necessary to add detritus to the predator and prey system in the further study.In Chapter 4, we present a lattice model of food web with alien plants invasion and analyze the model via Monte Carlo simulations and Mean Field Theory. The original food web contains herbivore, plant and detritus. Our results reveal that the species invasion will cause different changes under different conditions. There exists five kinds of phenomenon in our experiment. The system’s status could be only detritus left, only alien plants left, all plants exist harmoniously, initial plants die out while other ingredients still be alive with the alien plants, or the alien plants become extinct while the original system keeps working. In these consequences, researchers should pay attention to the system collapse caused by the unsuccessful species invasion, which probably be the reason to some ecosystems break down.