# Modeling Population Dynamics and Assessing Ecological Impacts of Lampreys via Sex Ratio Regulation
## 3 Resource-Dependent Sex Ratio Dynamics Model (RDSRD Model)
### Results Analysis
Modifying the parameters of the model enables the forecasting of how various environmental scenarios and management strategies impact the lampreys' population composition and number. It can be seen that food sufficiency leads to an increase in the number of sea lampreys and eventually stabilization, and the male ratio increases and stabilizes, while food scarcity leads to a decrease in the number of sea lampreys and an increase in the male-to-female ratio followed by a decrease and a gradual tendency toward 1:1. Furthermore, we set up two types of lampreys with identical conditions except for the trait of whether the sex ratio changed over time. First, we introduce two comparative indicators, including environmental resource utilization and reproductive success. Figure 5: Growth and sex ratio of lampreys under different conditions of food availability. Environmental Resource Utilization \(\eta\): the ratio of a population's number \(N\) to its environmental holding capacity \(K\). We adopted Assumption 4. Reproductive success (\(RS\)): the product of hatching success \(\gamma\) and mating success \(\delta_{3}\) in Equation (4). The expression is as follows:  
\[\eta=\frac{N}{K} \tag{24}\]  
\[RS=\gamma\cdot\delta_{3} \tag{25}\]  
Figure 7 illustrates the variations in population sizes of two species over time under experimental conditions with the same initial sex ratio and initial age composition when sea lampreys with sex ratios that can change in response to the environment compete with sea lampreys with unchanging sex ratios. From Figure 7, it can be seen that in the first 30 years, the population size of both lampreys tended to become larger, and the population size of sea lampreys with a variable sex ratio was significantly larger than that of those with a non-variable sex ratio. Thirty years later, the population size of sea lampreys with a non-vari  
Figure 6: Age distribution of lamprey populations over time. \[\frac{df}{dt}=0 \tag{20}\]0 Changes in population size over time during competition between two populations. that of those with a variable sex ratio, and gradually tended to be in dynamic equilibrium, whereas the population size of lampreys with a variable sex ratio gradually became smaller and smaller, approaching nearly extinct status. Figure 8 compares the differences of the following indices between the two populations:  
Stability of population sex ratio: We set the initial male ratio of both lampreys to 0.7 and found that the male ratio of lampreys with an unchanged sex ratio gradually returned to normal, i.e., 0.5, while the male ratio of lampreys with a changeable sex ratio in the external environment was maintained at 0.7, with a tendency to increase. Stability of age composition structure: For the juvenile ratio of both lampreys, we set the initial juvenile ratio of both at 0.96 and found that the juvenile ratio of lampreys with no change in sex ratio stayed at 0.96. Reproductive success: Our finding indicates that the reproductive success rate of lampreys with an unchanged sex ratio gradually decreased, and the decrease was large, while the reproductive success rate of lampreys with a changeable sex ratio was maintained at about 0.7. Environmental resource utilization: Regarding the resource utilization of the two species, it was found that the resource utilization of lampreys, which did not change their sex ratio, showed a decreasing trend and remained low for the first 20 years. On the other hand, the resource utilization of lampreys that can change their sex ratio following the external environment showed a significant upward trend, dynamically increasing from 10% to 70%. From this, we can further conclude that the advantages of a variable sex ratio in lamp-prey populations include increased adaptability to environmental changes, the optimization of resource use, and reproductive success by adjusting the sex ratio.