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基于Penna模型的一类捕食被捕食模型

One Kind of Predator-Prey Model Based on Penna Model

作者: 专业:应用数学 导师:贺明峰 年度:2010  院校: 大连理工大学

Keywords

        Penna TJP于1995年提出了一个用0-1串来表示个体基因的模型,称为Penna模型。该模型是一个单物种的生物演化模型,利用计算机模拟的手段,从个体基因着手,研究了种群的发展变化情况。Penna模型被提出后,经常被用于说明现实中的一些现象,并用来阐述现象背后的意义方面有着广泛的发展和应用。将Penna模型与二维格子相结合从个体的层次来研究捕食被捕食模型中整个种群的演化是一种有效的方法。在第一章,简单介绍了Penna模型的内容及结果;第二三章,在基于Penna模型和二维格子的方法上,研究了捕食被捕食模型中群体的动态变化情况。这两部分是我自己的工作。第二章,将Penna模型和二维格子应用到捕食被捕食模型(模型由草-羊-狼三个群体组成),研究了草资源量的多少对系统演化的影响。发现草的多少直接影响羊和狼的存活:草资源充足,三群体可以很好的共存;草资源不足,物种会趋于灭绝。第三章,在第二章的基础上,假设草资源量充足,赋予羊逃逸能力,赋予狼捕食能力,用两个高斯函数分别模拟它们。首先模拟了两种模型的动态演化情况,分析发现羊和狼不一定总能共生,两个群体能否共生与与羊的防御能力和狼的捕食能力大小有关。在第二三部分,分别研究了羊的防御能力和狼的捕食能力对模型演化的影响。通过模拟发现羊的防御能力决定两群体能否共生:羊的防御能力过大或过小都不利于两物种的共生;羊的防御能力过强,狼群体成功捕食食物的个体较少,一定时间后群体会因饥饿而灭绝;羊的防御能力太弱,在演化刚开始时,狼的捕食成功率很大,羊被大量捕食,个体数目急剧下降,此时,狼群体因几乎无法捕食到食物急剧灭亡。而由于狼的捕食随机等情况的限制,总有存活的羊个体,在没有狼的情况下,羊会大量繁殖并稳定下来。羊的防御能力一定时,狼的捕食能力对两群体的存活有直接的影响:狼的捕食能力太强或过弱不利于群体的共生。狼的捕食能力过强,一定时间内,大量的羊被捕食而亡,羊群体数目急剧下降,同时,狼群体中因能够觅取的食物量太少,大量的个体会饥饿而亡,最终整个群体灭绝;狼的捕食能力太弱,模型的整个演化期间,能够成功捕食的狼个体数目总是很少,而大量的个体会因无法成功获取食物来补充能量而死亡,一定时间后,狼群体灭绝。同时,经过模拟发现,将模型中的参数μ1和μ2分别设置为羊和狼的性成熟期后的年龄,两群体的逃逸能力和捕食能力比较强,对群体的共生比较有利。
    Penna T J P proposed a model in 1995 using 0-1 Bit-String to represent genome of individuals. The model is about organic evolution of a single species and studies the population’s dynamical evolution by computer. Since Penna model was proposed, it is often used used to illustrate some realities, and used to elaborate the meaning behind the model’s development and application. The method, which studies the whole population’s development from the respect of the individual using Penna model and a two-dimension lattice is very effective.In the first chapter we describe the content of Penna model simply and give out its results, in chapterⅡandⅢ, based on Penna models and two-dimension lattice, we have studied the population’s evolution in the Predator-Prey model. The two parts are my own work.In the chapterⅡ, we apply Penna model on a two-dimension lattice in the Predator-Prey model(there are three groups of grass, sheep and wolf), and have studied that the amount of grass has a direct impact on the population of sheep and wolf:if grass is sufficient, the three groups can have a good coexistence; otherwise, groups may become extinct.In chapterⅢ, on the basis of sufficient grass, and we endow the sheep escaping capability and the wolf predation capability, with two Gauss functions simulating them. Firstly, we simulate the model’s dynamical evolution when the wolf’s predation capability respectively gets two different values, and find that sheep are not always able to live with wolves as the two groups’coexistence depends on the sheep’s escaping capability and the wolf’s predation capability. Then, we study how escaping capability and predation capability impact the evolution. Whether the two groups can coexist is firstly decided by the sheep’s escaping capacity:if sheep’s escaping capacity is too weak, at early time of the evolution, with very high rate of successful in wolves’predations, a large number of sheep are preyed, then the sheep’s population drops sharply, and the wolf’s group gets extinct drastically because of deficiency on food. Because the wolf’s predation is randomly, there are always sheep alive. After the extinction of wolf, the population of sheep will flourish and finally become stable. Furthermore, when sheep’s escaping capability is fixed, wolfs predation capability has a direct impact on the two groups:whether it too strong or too weak is not conductive to two species’symbiosis. If the predation capability is too strong, lots of sheep are dead because of being preyed on. At the same time, as there are few sheep for wolves to eat, lots of wolves die because of hunger, ultimately the whole group becomes extinct; if the wolf’s predation capability is too weak, during the whole evolution, the individuals of wolf which can get food successfully are always very few, while a large number of individuals will die because they can not obtain food successfully for energy supplying, afterwards, the wolf gets extinct. In addition, after some analysis we find when the model’s parameters are respectively set to the values around sexual maturity of the two groups, the escaping capacity and predation capability both are very strong and conducive to two species’symbiotic.
        

基于Penna模型的一类捕食被捕食模型

摘要4-5
Abstract5-6
1 绪论8-15
    1.1 生物数学的发展简介8
    1.2 Penna模型8-15
        1.2.1 标准的Penna模型8-10
        1.2.2 有性Penna模型10-11
        1.2.3 Penna模型的结论11-13
        1.2.4 Penna模型的发展13-15
2 基于Penna模型和二维格子的简单捕食被捕食模型15-24
    2.1 捕食被捕食模型的发展15-16
    2.2 格子上的捕食被捕食模型16-20
        2.2.1 格子的定义16-17
        2.2.2 基于Penna模型的捕食被捕食模型中个体的定义17-19
        2.2.3 模型的演化规则19-20
    2.3 基于Penna模型的格子上捕食被捕食模型的动态演化及分析20-24
        2.3.1 模型的动态演化20-21
        2.3.2 模型初步分析21-24
3 基于Penna模型和二维格子的一类捕食被捕食模型24-45
    3.1 狼的捕食能力和羊的逃逸能力定义24-34
        3.1.1 模型简单分析25-34
    3.2 捕食能力和逃逸能力与系统状态34-38
        3.2.1 羊的逃逸能力对系统稳定性的影响34-36
        3.2.2 狼的捕食能力对系统稳定性的影响36-38
    3.3 任两个参数变化时模型演化情况38-44
    3.4 结论44-45
结论45-46
参考文献46-49
攻读硕士学位期间发表学术论文情况49-50
致谢50-52
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