协作增长的种群在网络上的扩张动力学研究

发布时间：2018-06-27 20:57

本文选题：栖息地扩张 + Allee效应　；参考：《兰州大学》2017年硕士论文

【摘要】：种群的栖息地扩张过程可以减轻群体内部的竞争压力、给种群带来新的生存资源甚至帮助种群应对气候变化。因此在自然环境持续变化的情况下种群的扩张能力对种群的存活至关重要。此外种群的栖息地扩张过程也在维持生态系统的多样性、稳定性上有着关键的作用。扩张的结果由种群的个体与个体之间、群体与群体之间的相互作用以及空间结构共同决定。已有的相关工作主要考虑了一维或二维的线性空间,而实际生态系统的空间结构往往非常复杂,但尚未有相关的研究。为了探究真实系统复杂的空间结构对种群扩张过程的影响,本文研究了协作增长的种群在网络上的扩张行为。我们发现不同的系统参数会将种群的长时间动力学行为分为不同的状态:灭绝、局部存活以及全局扩张。通过对扩张过程中快慢变量的分离,我们解析地给出了确定这些不同状态的临界条件。同时我们发现种群全局扩张的临界参数对种群的迁移速率的依赖是非单调的,这意味着存在最优的全局扩张策略。为了尽可能地表征真实系统不同的性质如度的不规则性、局部成团效应、多个种子节点、系统尺寸以及不规则的局部生态环境对种群扩张动力学行为的影响,我们运用理论分析以及数值计算的方法进行了详细的研究。本文的结果揭示了空间结构以及迁移速率对种群栖息地扩张过程的重要影响。最后我们讨论了本文的结论对实际的生态系统控制的意义。
[Abstract]:The process of population habitat expansion can reduce the competitive pressure within the population, bring new living resources to the population and even help the population to cope with climate change. Therefore, the ability of population to expand is very important to the survival of the population under the condition of continuous change of natural environment. In addition, population habitat expansion also plays a key role in maintaining ecosystem diversity and stability. The result of expansion is determined by the interaction and spatial structure of individual and individual of population. The existing work mainly considers the linear space of one or two dimensions, but the spatial structure of the actual ecosystem is often very complex, but there is no related research. In order to investigate the effect of complex spatial structure of real system on population expansion, this paper studies the expansion behavior of cooperative growing population on the network. We find that the long-time dynamical behavior of the population can be divided into different states by different system parameters: extinction, local survival and global expansion. By separating the fast and slow variables in the process of expansion, we analytically give the critical conditions for determining these different states. At the same time, we find that the dependence of critical parameters of global population expansion on population migration rate is non-monotone, which means that there is an optimal global expansion strategy. In order to characterize the effects of different properties of real system, such as degree irregularity, local cluster effect, multiple seed nodes, system size and irregular local ecological environment, on population expansion dynamics, We have carried on the detailed research by the method of theoretical analysis and numerical calculation. The results of this paper reveal the important influence of spatial structure and migration rate on the population habitat expansion process. Finally, we discuss the significance of the conclusion to the actual ecosystem control.
【学位授予单位】：兰州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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