Dynamic food web model based on Lotka Volterra model

Abstract

Lampreys are regarded as parasites with significant impacts on the ecosystem in some lake habitats, and analyzing the relationship between the population characteristics of lampreys and the ecosystem is of great significance for improving the ecological environment and maintaining the ecological balance. The sex ratio of lampreys varies depending on the external environment. To gain insight into the issue of sex ratios of lampreys in ecosystems and their dependence on local conditions, this paper firstly develops a Lotka-Volterra model to characterize the effects of changes in the sex ratio of lampreys on predators. The dynamics of male and female lampreys were modeled separately. A reproduction rate impact factor k was introduced to describe the effect of the poison TFM on lamprey populations, considering human intervention. A pattern of change in predator population size was derived: the proportion of males was negatively correlated with the number of predators. Considering that the larvae and adults of the lamprey are in different ecological niches, the model was further optimized to establish a dynamic food web model containing multiple trophic levels, and to derive the changes in the number of groups in the ecosystem over time. These data were used to construct a comprehensive evaluation index of ecological stability, establish an AHP-PCA integrated model, calculate the weights of each index, and analyze the comprehensive evaluation index. It was concluded that the proportion of males in the lamprey population fluctuated regularly over time, and when the proportion of males in the lamprey population increased, the comprehensive evaluation index declined, forming a fluctuating trend like that of the lamprey population.