A Study of Ecosystems Based on the Sex Transition of Lampreys

In this paper, we focus on the effect of the sex ratio of lampreys on the ecosystem and establish a population dynamics ecosystem model. The problem is solved using the following models: Model I - Logistic growth model for population, Model II - Lotka-Volterra model considering gender, Model III - population symbiosis model, and Model IV - population model with degenerate stage structure. For Problem 1, on the basis of Model I, this paper first establishes the Lotka-Volterra model with Model II, excluding the denaturation stage. Considering that the sex ratio of lampreys is influenced by the external environment and the growth rate of the larval stage, this paper includes information about lampreys being capable of undergoing sex conversion based on Model II. Additionally, it constructs a population model IV with a denaturation stage structure. Next, the results of Model II and Model IV are compared. It is concluded that in situations with limited resources, sex conversion can help maintain a stable population. Problem 2 is actually an extension of problem 1. According to the findings of problem 1, this paper concludes that the benefit of sex ratio conversion is its ability to quickly stabilize the population size. Comparing the sex ratio data before and after the 500-year gender transition, it can be found that the sex ratio transition will lead to serious imbalance, and the sex ratio imbalance may lead to the extinction of species. For Problem 3, which analyzes stability in the larger ecosystem of Problem 1, we compared the phase diagrams before and after the sex switch. We found that the number of lamprey baits stabilized after the sex switch was performed. It is concluded that the conversion of sex ratios is beneficial to the stability of the ecosystem. For problem 4, this paper first constructs Model I, which is a logistic growth model for the population.