# Modeling Population Dynamics and Assessing Ecological Impacts of Lampreys via Sex Ratio Regulation
## 2 Assumptions and Symbols  
To simplify the problem, we adopt the following basic assumptions, each of which is justified. Other assumptions based on different models will be listed in the following model-related sections.  
**Assumption 1:**_Food availability is the main factor affecting the growth rate of sea lamprey larvae._  
Justification: In nature, food availability directly affects the growth rate and survival of individuals. For many aquatic organisms, food availability is a key limiting factor in determining growth and development rates. Particularly for juvenile fish, adequate food supply can promote rapid growth and increase chances of survival, whereas food scarcity can limit growth rates and even lead to high mortality rates.  
**Assumption 2:**_Variations in the sex ratio have a direct impact on the rate of reproduction and the size of the population._  
Justification: Sex ratio is one of the key factors affecting the reproductive potential of a population. A balanced sex ratio ensures adequate reproductive opportunities, while a skewed sex ratio may reduce the reproductive success of a population, which in turn affects population size and growth rate.  
**Assumption 3:**_Overlook the impact of disease spread and movement within and outside populations on the size of the population._  
Justification: Although disease and migration have significant effects on population dynamics, ignoring these factors during the initial modeling phase simplifies the model and makes it easier to analyze and understand. This simplifying assumption allows the researcher to focus on food availability and sex ratio, two factors that more directly affect population growth.  
**Assumption 4:**_Limit environmental carrying capacity._  
Justification: Any ecosystem has a finite amount of resources, which limits the maximum sustainable size of populations living in that system. Environmental carrying capacity takes into account the limits of the resources available in an ecosystem and is an important predictor of population growth and stability.  
**Assumption 5:**_Individuals at an identical developmental phase in a population are considered equal._  
Justification: This assumption assumes that there are no significant genetic or phenotypic differences between individuals within a population, and thus that each individual is the same in terms of growth rate, survival rate, and so on. This simplification reduces the complexity of the model and is a practical approximation for large-scale population dynamics studies, although it may ignore inter-individual differences.  
**Assumption 6:**_Once established, the sexes remain unchanged._  
Justification: This reflects the biological reality of most vertebrates that the sex of an individual will not change once it is determined early in a life stage. This assumption simplifies the modeling of sex dynamics because it excludes the potential effects of sex transitions on population structure and dynamics.  
The main notations used in this paper are listed in Table 1.  
Additionally, sources of data used in the paper are websites such as the Great Lakes Fishery Commission and so on.