# Modeling Population Dynamics and Assessing Ecological Impacts of Lampreys via Sex Ratio Regulation
## 1 Introduction
### Review  
The population of sea lampreys, a blood-feeding species that consumes the blood of other fish, plays a crucial role in maintaining the balance of the ecosystems they inhabit. As a result, the environmental effects of sea lampreys are garnering more focus from pertinent management bodies, making their population control a key concern in managing lake ecosystems. However, due to the inherent complexity of ecosystems and the need to account for the interplay of multiple factors, qualitative methods alone are insufficient for capturing the underlying dynamics.  
Ecosystem modeling offers a promising alternative by incorporating both structural components and functional processes into a unified framework, enabling a more quantitative and systematic approach to ecological research. Scholars have explored ecosystem modeling across various dimensions, covering terrestrial [2], aquatic [3], and aerial [4] environments, and extending across domains such as agriculture [5], forestry [6], and fisheries [3]. Research has ranged from single-species studies to large-scale community and ecosystem modeling [7]. With increasing ecological challenges in recent years, such modeling approaches have become essential tools for both understanding and conserving ecosystems.  
In terms of modeling techniques, several approaches have been developed: [PERSON] [4] employed hierarchical Bayesian models to incorporate parameter uncertainty and layered ecological structures, finding no significant time trend in house sparrow abundance. [PERSON] et al. [8] used ecological network models to simulate how invasive species influence prey (e.g., rabbits) abundance, considering important feedback mechanisms. [PERSON] [9] employed the linear generalized Lotka-Volterra model to demonstrate its predictive capability in multi-species systems.  
However, these researchers frequently overlooked the ripple effects on the environment caused by changes in abundance. This paper addresses that gap by explicitly consid  
Figure 1: Global distribution chart of lampreys. The numbers in the figure represent the number of adult lampreys, with the unit being hundreds. Red signifies a broad distribution of lampreys, yellow indicates a moderate dispersion, and green denotes a limited distribution.  
ering how population changes, especially those driven by sex ratio variation, can further affect ecosystem dynamics. While [PERSON] et al. [10] also employed the Lotka-Volterra framework to study total population and assess the influence of sex ratio changes, their model overlooked the life-history stages and developmental heterogeneity that characterize sea lamprey population structure. In this study, we incorporate a detailed life-cycle representation of sea lampreys, considering their distinct behavioral and ecological traits at different developmental stages. This integrated modeling approach offers a robust framework for simulating the ecological impact of adaptive sex ratio variation and provides deeper insights into sea lamprey population dynamics and their role within ecosystems.