【作者】 霍丽慧；

【导师】 赵惠燕；

【作者基本信息】 西北农林科技大学 ， 应用数学， 2010， 硕士

【摘要】 捕食被捕食是自然界中普遍存在的种间相互作用关系之一,如食蚜蝇与蚜虫的关系。由于捕食者(如食蚜蝇)各阶段的生物学特性不同,其食性、食量、搜索率、发现率等完全不同,因此考虑具有年龄结构的捕食者与猎物模型有非常重要的理论意义和实用价值。但是,现有的捕食者与猎物模型总是假设只有成年捕食者捕食猎物而幼年不捕食,这不符合实际情况。本研究根据食蚜蝇仅在幼年捕食的生物学特点,建立了一个幼年捕食者捕食猎物的具年龄结构模型,并对其进行数学分析,解释昆虫数量动态,以期为有害生物综合治理提供理论依据。通过对食蚜蝇具有幼年捕食特性的捕食者的生物学特性的分析,建立了幼年捕食者捕食猎物模型,并对模型的稳定性、永久持续生存的条件以及数量变动条件和机理进行了分析,得到如下主要结论:首先,建立了一个幼年捕食者捕食猎物的具有年龄结构的数学模型。其次,根据系统的初始条件和特点,证明了系统解的正性和有界性,符合系统的生态意义。再次,得到了系统的三个平衡点。其中,平衡点E1为不稳定;满足一定条件时,边界平衡点E2为局部渐近稳定,此时随着时间的增加,蚜虫种群将幸存并趋于环境容纳量K,而食蚜蝇种群将灭绝,也即害虫种群将会爆发;在一定条件下,正平衡点E3亦为局部渐近稳定的,此时随着时间的增加,蚜虫和食蚜蝇种群均存活并趋于平衡态E3,此时可得到一个重要参数:天敌和害虫的益害比。利用益害比可以将害虫种群控制在平衡点附近,防止害虫种群的大爆发。所以益害比是一个控制害虫的阈值密度,也是生物防治效果中最为重要的评价参数。最后,应用一直生存理论,得到了系统永久持续生存的条件。在此条件下,捕食者与猎物种群都不会绝灭,将持续生存。并通过给定相应参数,对系统进行了数值模拟分析。综上,根据捕食性食蚜蝇的生物学特点,本研究建立了一个幼年捕食者捕食猎物的年龄结构模型,通过对其进行数学分析,讨论了系统的平衡点及其稳定性,并建立了系统持续生存的条件。以此解释昆虫种群动态,为有害生物综合治理提供了理论依据。更多还原

【Abstract】 Predator-prey is one of the most prevalent interactions among species in the nature. For example, syrphid fly and aphid. Because the predator’s biological characteristics of each age are different, it is of very important theoretical significance and practical value to take into account the predator-prey models with age structure. For example, their feeding habits, appetite, searching rate and detection rate are absolutely different. However, the existing predator prey models with age structure always assume that only mature predators catch prey. This is inconsistent with observed fact. In this paper we establish a syrphid fly-aphid model with age structure based on the biological characteristics of the predatory syrphid fly that only the immature predators can catch prey. We also explain the insect population dynamics by a mathematical analysis of the models, in order to provide a theoretical basis for Integrated Pest Management.Through the analyses of syrphid fly’s biological characteristics that only the immature predators can catch prey. We establish a model with age structure that only the immature predators can catch prey. We also analyze the criterion for the stability and permanence of populations and the quantity change conditions and mechanism. Obtains the following conclusions:Firstly, a model with age structure that only the immature predators can catch prey was established.Secondly, according to the given initial conditions and characteristics of the system, we have proven that the solutions of the system are always positive and bounded.This is consistent with the ecological significance of the system.Thirdly, we get three equilibrium points of the system when we suppose the right-hand side is zero. The results show that one equilibrium point E1 is unstable, and the boundary equilibrium point E2 is locally asymptotically stable under certain conditions. With time increasing at the boundary equilibrium point, the aphid populations tend to survive and achieve the maximum capacity, while the syrphid fly species will get extinct, that would be the outbreak of the pest populations which should be prevented. The results also indicate that the positive equilibrium point E3 is locally asymptotically stable under certain conditions. With time increasing at this point, both the aphid and syrphid fly populations will tend to survive and approach a positive equilibrium E3. At this point we can also get the ratio of natural enemies by the pest, which is a very important parameter and can help control the pest population to reach the positive equilibrium point so as to prevent the outbreak of the pest population. So this ratio is a threshold value density to control harmful insect and the most important appraisal parameter in the effect of biological control.Last but not the least; we get the criterion for the permanence of populations using uniform persistence theory. Under the condition, both the predator and the prey populations will not be survive. Given certain corresponding parameters, we can draw some results of the system with numerical simulation analysis.To sum up, based on the biological characteristics of the predatory syrphid fly, in this article we establish a syrphid fly-aphid system with age structure, in which only the immature predators catch prey. Through mathematical analysis, we discuss the equilibrium points and stability of the system, and build a criterion for the permanence of populations. We can explain the insect population dynamics by these results. All of these results provide a foundation for Integrated Pest Management.更多还原