【作者】 高猛；

【导师】 李自珍；

【作者基本信息】 兰州大学 ， 应用数学， 2008， 博士

【摘要】 数学生态学研究的主要内容包括两个问题:种群的数量变化和空间分布。种群数量的时间动态的研究,一般以动力学方程等数学模型为基础,相关的研究在过去几十年中取得了许多重要的成果。然而相对于种群的时间动态的研究,种群的空间动态研究的发展则相对滞后。本文重点关注种群的空间动态,即种群的空间模型和空间分布格局分析,其研究内容共包含四章。第一章主要从数学生态学的角度,回顾了种群动态研究的历史,介绍数学生态学研究从非空间模型到空间模型的发展过程。同时比较了几种常用的空间建模方法,并从动力学的角度进行了分类研究。第二章主要研究了两个具有空间结构的种间竞争系统模型。首先,我们将非空间的竞争系统扩展到具有空间结构的竞争系统,其次我们的研究重点从一般的竞争关系转移到一种新的具有循环结构的竞争系统之上。本章使用的第一个模型是积分微分方程模型,第二个模型为具有空间网格结构的元胞自动机模型。通过对模型的分析,我们验证了空间结构和非层次的竞争关系有利于物种共存的理论。相关结果对生物多样性的理论发展提供了依据和支持。第三章介绍了一种基于个体的模型,并利用矩动力学方程,研究了个体在空间中的分布格局的变化。本章使用的基于个体的模型(individual-based model),引入了矩动力学的分析方法,研究了一个具有追逐和逃逸的竞争系统。通过与非空间的模型比较,我们发现,个体之间的相互运动可以延缓竞争排斥的过程,因而有利于物种的共存。第四章主要介绍了空间点过程以及点格局分析在研究种群空间分布中的应用。本章首先给出了两种计算点格局聚集指数的方法,K-function以及邻体距离抽样方法。然后我们给出了一个估计点格局密度的方法,并利用实验数据进行了验证。结果表明,本章给出的极大似然估计,在估计个体密度,计算点格局聚集指数等方面,有很高的准确性和稳定性。本研究给出的方法,在实际野外调查研究中有很强的可操作性,对从事相关领域的研究者有很大帮助。更多还原

【Abstract】 The size and spatial distribution of populations are the two major subjects in mathematical ecology. Classical methods from mathematics have played an important role in studying the problems about population size. Generally, the temporal dynamics of the populations are modeled by the dynamical equations, where many well-known achievements also have been obtained On the contray, few studies have contributed to the subject of spatial distributions of populations and related research is not thrived at all. This PhD thesis, in which four chapters are included, will mainly focus on the spatial dynamics of populations—spatial models and spatial distributions. In chapter one, we briefly reviewed the history of the development of population models from the view point of mathematical ecology. The transition from non-spatial models to spatial models is also included. Moreover, some newly developed methods which are used in modeling spatial dynamics of populations are introduced. All these methods are compared and categorized from the perspective of dynamics theory. In chapter two, two spatially-structured competitive systems are studied: The first one is an integro-differential model while the second one is cellular automata model: After a comprehensive analysis, the theory that spatial structure and non-transitive competition favor coexistence of species is verified. The importance of this research is providing some theoretical evidence and support to biodiversity. In chapter three, a individual-based model (IBM) is introduced and its spatial dynamics and patterns are approximated by a group of moment equations. Actually, the IBM is an interactive particle system, where two competitive species are placed on a plane. Some new results are obtained and a comparison with previous studies about non-spatial system is also conducted. It proves that the dispersal of individuals favor the coexistence of interspecific competitive species. In chapter four, we first introduced the application of spatial point process and spatial analysis in population pattern analysis. The first concern in this chapter is to compute aggregation parameter which reflects the aggregation level of the spatial point pattern. Two new methods, K-function and distance sampling, are proposed. The other concern in this chapter is to give an ideal-estimator of the density. Based on distance sampling (distance from individual to individual), we propose a maximum likelihood estimator of the density. All above methods are assessed by simulated point patterns and mapped point patterns from real forests. The meaning of this research is helping field workers to complete inventory and survey efficiently.更多还原