具有个体尺寸避难所的捕食者—食饵系统的数学建模与进化动力学研究

发布时间：2018-04-25 19:38

本文选题：捕食者-食饵模型 + 竞争性的避难所结构　；参考：《江苏大学》2017年硕士论文

【摘要】：捕食者的捕食行为是导致食饵种群早期死亡的一个重要原因.食饵种群通常会使用避难所来减少被捕获的风险.在种群动力学中,以个体尺寸为特征的避难所结构对系统的影响是研究的热点之一.本文主要研究捕食者-食饵种群中突变食饵入侵常驻食饵的能力在很大强度上依赖于特异性参数对食饵尺寸避难所保护下可捕获比例成分间的调节.首先,本文介绍捕食者-食饵系统的研究背景及意义和常微分方程的相关理论知识.在考虑种群基因表现型的基础上,又介绍了进化动力学的相关理论与知识.然后,种群的某种基因表现型能力决定的个体尺寸差异会导致捕食者不同的成功捕获率.通过种群模型来研究食饵的尺寸避难所结构是如何影响捕食者-食饵种群的进化,其中避难所的结构依赖于可捕获的比例,把尺寸避难所保护下的可捕获比例分成两种情况:一种是食饵各自避难所结构下的可捕获比例,另一种是食饵不同尺寸避难所保护下可捕获比例的加权平均,通过定义特异性参数来调节它们两者之间的权重.并且通过运用常微分稳定性理论,得出突变食饵可入侵的充分条件,在此基础上得出突变食饵入侵并且生存导致常驻食饵和捕食者的灭绝,突变食饵与捕食者共存且常驻食饵灭绝,常驻食饵与突变食饵共存且捕食者灭绝以及三者共存的结果.其次,考虑食饵与捕食者内部单一基因型策略的个体尺寸避难所结构.假设种群的环境容纳量、捕食率和个体尺寸避难所都直接依赖于基因型策略.因此,建立具有进化系统的捕食者-食饵模型来研究由不同基因型策略决定的避难所结构对种群之间进化动力学的影响.进一步,通过进化动力学的观点可发现决定尺寸避难所结构的基因型奇异策略在特异性参数调节可捕获比例成分下,存在着进化不稳定策略、连续稳定策略和进化分支,以及可能发生进化自杀的一些条件.最后,依据研究内容总结全文。
[Abstract]:Predator's predatory behavior is an important cause of early death of the prey population. The prey population usually uses refuge to reduce the risk of being captured. In population dynamics, the impact of the structure of the individual size on the system is one of the hotspots of the study. This paper mainly studies the mutation of the predator prey population. The ability of the prey to invade the permanent bait depends heavily on the regulation of the capable proportions between the specific parameters of the prey size shelters. First, this paper introduces the research background and significance of the predator prey system and the relevant theoretical knowledge of the ordinary differential equation. The related theory and knowledge of evolutionary dynamics. Then, the individual size difference determined by a certain gene expressive ability of the population can lead to the successful capture rate of the predator. The percentage obtained is divided into two cases under the protection of dimensional refuge: one is the capture ratio under the shelter structure of the bait, the other is the weighted average of the capture ratio protected by the different size shelters of the bait, and the weights between them are adjusted by defining the specific parameters. On the basis of the differential stability theory, we obtain the sufficient conditions for the mutational bait to invade. On this basis, the mutant bait invasion and survival lead to the extinction of the permanent bait and predator, the mutated bait coexists with the predator, the permanent bait is extinct, the permanent bait and the mutant bait coexist, the predator is extinct, and the three coexistence results. Secondly, the examination of the results. The structure of individual size asylum in the single genotype strategy of predator and predator. It is assumed that the environmental capacity of the population, the predation rate and the individual size refuge are directly dependent on the genotype strategy. Therefore, a predator prey model with an evolutionary system is established to study the structure of the shelters determined by different genotyping strategies to the population. The effect of evolutionary dynamics. Further, through the viewpoint of evolutionary dynamics, it is found that the genetic singularity strategy that determines the structure of the size asylum has an evolutionary instability strategy, a continuous stabilization strategy and a branch of evolution, and some conditions for possible evolutionary suicide. The full text is summed up according to the content of the study.

【学位授予单位】：江苏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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