Sex ratios of sea lampreys vary in response to the external environment. In order to analyze sex ratio and its dependence on local conditions, we need to develop models that reflect the relationship between sex ratio and resource availability. In this paper, we establish a link between individual sex and the availability of larval food resources. Then, we extend the object of study from individuals to populations and express the dynamics of the sex ratio as a differential equation. We introduce other factors affecting the sex ratio to refine the relationship between reproductive rates and sex ratios. To better model the growth of the lamprey population, we developed a Gompertz model that initially approximates the growth rate of the exponential function. And the introduction of the Allee effect provides a more comprehensive view of population growth.
This paper focuses on word difficulty prediction and classification on the basis of capturing a year's word game data. Although Wordle was all the rage, recent tracking data shows that the Wordle popularity appears to be declining gradually, and the number of players has a downward trend. To promote the healthy development of Wordle and assist game developers in adjusting their game strategies in time, this paper establishes a word difficulty prediction model. Before Wordle difficulty prediction model is established, we preprocessed the data, rasterizing the area to be studied. In phase I, we introduced a PSO-LSTM prediction model and performed specific training, achieving an accuracy rate of over 85%. After coding the letters in “EERIE”, we successfully obtained the percentage of word “EERIE” on March 1,2023 will appear. The second phase uses hierarchical clustering analysis to subcategorize words by difficulty. The difficulty of words is then divided into five levels based on the folded graph of clustering coefficients derived from the elbow rule. Finally, this paper presents a model accuracy test and suggests the idea that this model can predict the data of serial relationship within the existence time and can be extended to the evaluation and weighted ranking under the influence of other factors.
The study of species population change is one of the most classic topics in biology. In this paper, we consider not only intra-race competition but also competition between two species. It is assumed that the resources in the environment are finite in this paper. Improved on the Logistic Population Growth Model from Malthusian model, we built the Competitive Hunter Model for trout and bass referring to the Lotka-Volterra Model. In this paper, we presented the assumptions of the model and analyzed the equilibrium points of the model in numerical analysis and the typical trajectories in phase planes in graphical analysis.
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