Mathematical Model Of Ecological Population

Population ecology is one kind of population science which from some kind of meaning take a regional group as the research objects. Modern Population ecology is one branch of the population ecology research which includes regulating mechanism of interaction between populations and temporal dynamics of population. It is the core and foundation of the ecology research. In the modern mathematics of ecological population, establishing and solving the model plays a very important role. Under the natural condition, any population is not isolated but closely related with other populations in the biological communities. Therefore, strictly speaking, single species population exists only in the laboratory. However, in order to understand the population dynamics, it is a traditional method to research and analysis from single population. This dissert introduces the basic characteristics of populations, starting from the single species population and the population dynamic model of generation isolation and overlapping in time. Based on the two models of the logistic growth, it investigates several other single species models:Malthus model, Gompertz model, Rosenzweig model, Anti-Rosenzweig model and Logistic model with Allee effect. The results show that the Malthus model is actually not large enough to be reasonable only in the general population; Gompertz model on the graph showing the distribution of anti-S-shaped, and has good applicability in reflecting the general characteristics of the growth curve and Logistic curve which has similar characteristics; Compared with the Logistic model, Anti-Rosenzweig model is a further development of the Logistic model, it changes the density dependent factors, so it is closer to the experimental results; Logistic model with Allee effect is a kind of consideration for a population of cooperation within the dynamics of life, which describes the negative population growth caused by the decline in reproductive success when the population level falls below a certain value. On the basis of these models, this dessert analyses the internal and external population fluctuations. The species mix would definitely leads to the inter-specific relationship taking food, space and other resources as the core. Theoretically speaking, the impact of any species to other species only have three forms, namely, the intermediate state favorable harmful, with or without the benefit of harmless. Therefore, the inter-specific relationship just has the three forms of possible combinations. The most common relationship between ecological populations includes inter-specific competition, predation and parasitism. This dissertation discusses the competition relationship and analysis the quantitative relationship between the two competing populations. For two biological groups coexists in the environment at the same time, this dissertation establishes a equation to discuss the competition relation between the two groups, results show that the number of population A has a inhibition on the growth of B populations, and the effect of inhibition is proportional to the population size of A, the number of B also has a inhibition on the growth of A which is proportional to the population size of A. Based on the model, this dissertation conducts qualitative analysis on the four cases and discusses the variation of population size in the four cases.