Survival Relationships and Ecosystems of the lampreys on the Basis of Several Models

The population of lampreys, one of the only remaining jawless vertebrates in the world, has survived on Earth for hundreds of millions of years, predating the dinosaurs. This remarkable endurance has made lampreys a significant topic of discussion among biologists, particularly for their relevance to the study of biological evolution and ecological stability. In this paper, the predation and competition relationship between lampreys and their natural enemies is described using the Lotka-Volterra model, and the cyclic amplitude law of the male ratio in lampreys and their predators is resolved. Additionally, an Agent-Based Model is employed to simulate the dynamics of the lamprey population, revealing a pattern of "Peak - Sharp Decline - Tendency Toward Equilibrium." Finally, the stability of the lamprey's internal ecology is analyzed using the Jacobi matrix and eigenvalues, demonstrating the model's optimality presented in this paper and providing theoretical support and reference for future lamprey research.