A Study of the Impact of Sex Ratio Based on the Lotka-Volterra Model

In order to analyse the effects of fish sex ratio on ecosystem stability, this paper develops models to investigate the advantages, disadvantages and effects of changing the sex ratio. First, we used a modified Logistic model and differential equations to determine the population dynamics of fish. A Lotka-Volterra model was developed to determine the predation relationship between fish and other species. At the same time, we established a metacellular automata model to analyse the relationship between changes in sex ratio and a variety of factors such as resources and breeding temperature. Based on these analyses, we established a dynamic model of the ecosystem. Secondly, we introduced genetic optimisation of the population to analyse its adaptation to the environment. We used the model established by Verhulst for the change of population with temperature, food and other conditions. Finally, we use a food web model to describe the predation relationship between fish and other species, and a two-party evolutionary game theory model to describe the evolutionary process of fish of different sexes in terms of resource competition, cooperation and adaptation. Based on the above analyses and the Ljapunov index for system stability, it can be seen that a good sex ratio favours the stability of the ecosystem and vice versa.