# Modeling Population Dynamics and Assessing Ecological Impacts of Lampreys via Sex Ratio Regulation
## 8 Conclusions and Discussion  
Overall, we created a complex model, which contains the dynamics of the sex ratio and examines the effects of changes in the sex ratio on population and ecosystem stability. Through competitive modeling, we conclude that in resource-rich environments, changes in sex ratios can lead to rapid population expansion. However, in resource-limited environments, changes in sex ratios may lead to long-term reductions in the reproductive capacity of populations. Simulations also suggest that changes in the sex ratio of sea lampreys can help co-occurring species suppress overgrowth and adapt to complex environmental changes. In addition, the ecosystem was most stable when the male ratio was close to 0.6, and these findings provide useful guidance for developing ecological management strategies. Previous studies by [PERSON] et al. [20] did not portray how the sex ratio varies over time; however, our study clearly gives a picture of how the sex ratio varies over time under food shortage and sufficiency. Our research illustrates and validates that in shorter time cycles, females under restricted growth conditions face higher mortality because they require more energy for the development of reproductive organs [21], and the food-restricted group exhibits a higher male-to-female ratio. Over extended periods, changes in the sex ratio itself may affect the population as a whole, with a sharp decrease in population size, which in turn affects the amount of food available to individual sea lampreys, increasing the number of females. Alternatively, the sharp decrease in its population may have led to a specific sex-determination mechanism in the lampreys, making it more inclined to produce females to ensure the reproduction of the race. In addition, the numerical solution of the system of differential equations using the fourth-order Runge-Kutta method ensured the accuracy and stability of the model calculations, which provided reliable results for the complex ecological dynamics model. It was found that hatchery sea lampreys and juvenile sea lampreys accounted for a large proportion of the overall population size, with the sum of both exceeding 80%. This is most likely a protective mechanism for the organisms, breeding large numbers of eggs and larvae to cope with crises, adapt to nature, and ensure that there is a sufficient number of adult individuals. In the sex ratio model, we focus on the characteristic changes in the sex ratio of sea lampreys with the external environment and simulate the external environmental parameters by introducing large fluctuations. Such an approach enhances the model's  
Figure 17: Sensitivity of the model under the condition of applying different disturbances \(\beta\) to the survival environment food. adaptability, more accurately mirrors the unpredictability and extremity of the environment within the real ecosystem, and bolsters the model's accuracy. The decrease in males and increase in females resulted in increased survival pressure on downstream prey while providing sufficient food for their upstream predators. This suggests that sea lampreys and their upstream and downstream populations produce mutual constraints on the number of organisms through this predatory relationship. In contrast, changes in the sex ratio did not have a specific effect on the symbiotic organisms and only affected the behavior of a portion of the parasitic organisms. The findings of our research indicate that optimal ecosystem stability occurs with a male sex ratio of 0.6. In the future, we will likely be able to adjust the number of species and ensure ecological balance through this specific constraint relationship. Our study still faces certain limitations, as we overlooked how the living conditions of sea lampreys influence their gender ratio, in contrast to various studies [1; 22], indicating a strong correlation between sex determinants and their living environment.