Research on the Sex Ratio Variation of Lampetra japonica and Its Reciprocal Altruism Effects Based on the Logistic and Lotka-Volterra Models

The lampreys, a parasitic fish native to the Atlantic Ocean, is an invasive non-native species in the Laurentian Great Lakes of North America and an endangered species in most of its native regions in North America and Europe. This paper addresses the study of demographic changes in the population of lampreys in the Great Lakes basin of North America, which is of reference significance to the control of the population of lampreys in the Great Lakes basin of the United States and the protection of its populations in other regions. Since the sex ratio of lampreys changes according to the external environment, its growth rate in the larval stage is fast or slow to determine its final sex, and its larval growth rate is affected by food availability, this paper adopts the logistic model and the Lotka-Volterra model, and simulates the natural growth of the lampreys population in an ideal state by building a mathematical model and the sex ratio changes, and introduced the intra-species competitive role and inter-species competitive role of lampreys population, through the changes in the number of lampreys population, and further analyzed the advantages, disadvantages and such changes of the sex ratio changes on the evolution of the lampreys population itself and the effects of the evolution of the population on the ecosystem and its stability.