Research On Population Dynamics of Lamprey Based on Differential Equations

Abstract

The sea lamprey is a species with unique ecological characteristics, and its population dynamics are influenced by various factors, including sex ratio strategies, resource availability, and interactions with other species. This study constructs two types of models to investigate the dynamic changes in sea lamprey populations. Firstly, a model for male and female individuals based on Logistic differential equations is developed, considering the impact of sex ratio transition rates on population size. The results indicate that, after accounting for the sex ratio transition rate, the proportion of male sea lampreys increases from 60% to 68.8%. Secondly, a food availability parameter is defined to explore the impact of larval food resources on sex transition rates. A differential equation model considering the food chain between zooplankton and fish is constructed. The results show that when food resources are insufficient, the proportion of male sea lampreys rises significantly (to 80.7%), while the numbers of parasitic fish and competing species increase by 73.0% and 23.2%, respectively. This research provides a scientific basis for a deeper understanding of the population dynamics of sea lampreys and offers valuable insights for their ecological management and conservation.