A study on the Ecosystem of the Lampreys Based on Lotka-Volterra Modeling

Abstract

This study provides insights into the ecosystem impacts of adaptive sex ratio variation in lampreys through mathematical and ecological modeling. The predator-prey relationship between prey, lampreys and indigenous populations was simulated using the Lotka-Volterra model, revealing the effect of increasing male sex ratio on the significant increase in prey population size and the variation in the three population cycles. The model was further linearized to determine the stability of the ecosystem under different sex ratios by calculating Jacobi matrices and eigenvalues and found that the ecosystem tends to be stable when the male ratio is within a specific range. Analysis of the model with the addition of parasites showed that an increase in male ratio promotes an increase in prey population size, has a smaller effect on competitors, and slightly reduces parasite numbers. These findings provide an important reference for understanding the effects of adaptive sex ratio variation on ecosystems and population interactions.