Adaptive Prediction of Lamprey Population Based on Combination of Time-lag Differential Equation and Machine Learning

In scenarios where long-term prediction is required, models generated by time-lag differential equations can be combined with machine learning for prediction, and machine learning techniques are used for future state prediction and control strategy optimization. To extend its application, this combined model is used in this paper to analyze the mechanism by which a population of lamprey adapts to environmental changes by altering the sex ratio to induce damped oscillatory effects. Firstly, a model outlining the effect of sex-adaptive capacity on population size is developed in this paper, and a time-lag differential equation model is based on this framework. Next, a food chain model explaining changes in sex ratio was constructed using the Lotka-Volterra model. And then, this paper considers the juvenile and adult stages of the lamprey eel as different species and analyses whether there is a time lag between them, thus integrating time-lag differential equations in the initial model, thus building a food web model. Finally, the model parameters were adjusted to discuss the effect of sex ratio on the ecosystem. This study better combines time-lag differential equations with machine learning, which is motivated to address the difficulty of long-term prediction in ecosystems due to the time-lag effect, as compared to traditional methods. The combination of accurate description of lagged behavior in dynamic systems and powerful data-driven prediction capabilities enables the study to better reveal the nonlinear dynamic relationships among complex variables, accomplishing the prediction of future trends of complex variables and providing a reference for similar prediction scenarios.