Allee效应对种群动力系统复杂性的影响

发布时间：2018-01-15 16:16

本文关键词：Allee效应对种群动力系统复杂性的影响　出处：《甘肃农业大学》2015年硕士论文　论文类型：学位论文

【摘要】：近年来,随着全球环境破坏的加剧,物种丧失速度随之加快,资源问题也日益突出,这促使人类对资源的持久利用及可再生资源的循环利用问题有了深入的考虑,尤其是对生物资源的开发利用,开发不当更容易导致物种灭绝。另一方面,大量的实验研究和野外观测表明,Allee效应在生态系统中广泛存在,濒危物种更容易受到Allee效应的影响。Allee效应对物种的续存是潜在的干扰因素,在很大程度上将增加种群局部甚至全局灭绝的可能性。再者,具有Allee效应种群的收获问题更是敏感,引起生态学家及保护生物学家的广泛关注。此外,种群的合作行为的进化是种群进化生物学最重要的理论命题之一,受Allee效应种群的合作行为的进化目前还未引起广泛的关注。本论文选题于种群动力系统中一致关注的新焦点及未深入涉及的新领域,对其进行了系统地研究。首先详细讨论了Allee效应的提出、演化、以及它在种群动力学系统、单种群模型中的应用;然后基于具有正效应的捕食-食饵系统建立了具有收获及Allee效应的捕食系统;最后,分析了Allee效应对单种群模型中合作行为进化的影响。通过讨论其平衡点的存在性和稳定性,及数值模拟研究了Allee效应对种群动力系统的影响。研究结果表明:(1)具有Holling-IV型功能反应函数的捕食-食饵动力系统模型,由于捕食正效应较大,两物种之间会出现周期性振荡现象(存在极限环);减少捕食正效应,系统就会达到稳定的平衡状态;但若增加系统中食饵种群的环境容纳量,可能由于食饵种群的自然防御功能的增强,导致捕食者种群因食物匮乏而灭绝。(2)对捕食-食饵系统中的食饵种群进行适当地收获,反而会增加系统的稳定性,使得系统更容易达到稳定状态,也会推迟分叉及混沌现象的出现。并应用稳定性分析和庞特里亚金极大值原理得出了系统的生物经济平衡点及最优捕获策略。(3)受强Allee效应影响的系统需更长的时间才能从不稳定状态到达稳定状态;增加Allee效应,系统出现周期性振荡现象;继续增强Allee效应,食饵种群呈负增长,种群趋向局部灭绝,系统将崩溃;而受弱Allee效应影响时,系统更容易达到平衡态,但会使食饵种群的增长率减少,不过仍保持正值。(4)当进行收获的捕食-食饵系统受到弱Allee效应的影响,增强弱Allee效应强度,系统出现振荡现象,且随着Allee效应强度的增强,系统的振荡频率越强。对于原本稳定平衡的系统,弱Allee效应也会抑制系统达到稳定状态,即达到稳定态需要更长的时间。(5)在恶劣的环境条件下,Allee效应将导致物种灭绝;在相对优越的外部环境中,Allee效应的存在促进合作行为的进化,且随着Allee效应强度的增强,更有利于合作行为的入侵,不过过强的Allee效应依旧会导致物种灭绝。
[Abstract]:In recent years, with the intensification of global environmental damage, the rate of species loss has been accelerated, and the problem of resources has become increasingly prominent. This makes us think deeply about the sustainable utilization of resources and the recycling of renewable resources, especially the exploitation and utilization of biological resources. On the other hand, the improper exploitation of biological resources is more likely to lead to species extinction. A large number of experimental studies and field observations show that the Allee effect exists widely in the ecosystem. Endangered species are more vulnerable to the influence of Allee effect. Allee effect is a potential interference factor to the survival of species, to a large extent will increase the possibility of local or even global extinction of the population. The harvesting of populations with Allee effect is more sensitive and has attracted wide attention of ecologists and conservation biologists. The evolution of cooperative behavior of population is one of the most important theoretical propositions in evolutionary biology of population. The evolution of cooperative behavior due to the Allee effect has not attracted much attention. This thesis focuses on the new focus and the new field that has not been deeply involved in the population dynamic system. Firstly, the Allee effect is presented, its evolution and its application in population dynamics system and single population model are discussed in detail. Then, based on the predator-prey system with positive effect, a predator-prey system with harvest and Allee effect is established. Finally, the influence of Allee effect on the evolution of cooperative behavior in a single population model is analyzed, and the existence and stability of the equilibrium point are discussed. The effect of Allee effect on the population dynamic system is studied by numerical simulation. The results show that the predator-prey dynamic system model with Holling-IV type functional response function is obtained. Because of the large positive effect of predation, there will be periodic oscillation between the two species (there is a limit cycle); Reducing the positive predation effect, the system will reach a stable equilibrium state; However, if the environmental capacity of prey population is increased, it may be due to the enhancement of natural defense function of prey population. As a result, the predator population becomes extinct because of lack of food.) the predator population in the predator-prey system can be harvested properly, which will increase the stability of the system and make the system more stable. The bifurcation and chaos will also be delayed. By using the stability analysis and the Ponteriagin maximum principle, the bio-economic equilibrium point and the optimal capture strategy of the system are obtained. It takes a longer time for the system affected by the strong Allee effect to reach the stable state. With the increase of Allee effect, periodic oscillation occurs in the system. If the Allee effect continues to be enhanced, the prey population will increase negatively, the population will tend to become local extinct, and the system will collapse. Under the influence of weak Allee effect, the system is easier to achieve equilibrium state, but will reduce the growth rate of prey population. However, when the prey-prey system is affected by the weak Allee effect, the intensity of the weak Allee effect is enhanced and the system oscillates. The stronger the intensity of Allee effect is, the stronger the oscillation frequency of the system is. For the previously stable system, the weak Allee effect will restrain the system from reaching a stable state. That is to say, it takes a longer time to reach the stable state. (5) the Allee effect will lead to the extinction of species under the harsh environment. In the relatively superior external environment, the existence of Allee effect promotes the evolution of cooperative behavior, and with the increase of the intensity of Allee effect, it is more conducive to the invasion of cooperative behavior. But an excessive Allee effect could still lead to extinction.
【学位授予单位】：甘肃农业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175

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