利用元胞自动机研究一类捕食食饵模型中的斑块扩散现象
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兰州大学数学与统计学院,兰州大学数学与统计学院

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国家自然科学基金资助项目(40930533);国家科技支撑计划资助项目(2009BAC53B03)


Using cellular automata to study patchy spread in a predator-prey system
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School of Mathematics and Statistics,Lanzhou University;China,School of Mathematics and Statistics,Lanzhou University;China

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    利用概率元胞自动机模型对空间隐式的、食饵具Allee效应的一类捕食食饵模型进行模拟,发现随着相关参数的变化,种群的空间扩散前沿由连续的扩散波逐渐转变为一种相互隔离的斑块向外扩散,这种斑块扩散现象与以往的扩散模式有所不同。研究结果表明:(1)在斑块扩散的情况下,相关参数的微小变化会导致种群灭绝或者形成连续的扩散波,即斑块扩散发生在种群趋于灭绝和连续扩散之间;(2)当种群的空间扩散方式为斑块扩散时,种群的扩散速度会变慢,与其他扩散方式下的速度有着明显的区别。该研究结果对生物入侵控制和外来物种监测有重要的启发和指导作用。

    Abstract:

    The study of basic mechanisms and patterns underlying species spread in space are of central importance in the theory of biological invasions. Homogeneous environments frequently allow the establishment of classic reaction-diffusion models that show invasive species spreading at a linear rate and on continuous circular population fronts. However, there is growing evidence that in some cases invasion can take place via the formation, interaction and propagation of non-continuous patches of high species density that are separated by regions of nearly zero density. This type of spread is called ‘patchy spread’ or ‘patchy invasion’. It was shown by Petrovskii et al. that patchy spread can arise in deterministic reaction-diffusion models such as predator-prey systems with the Allee effect and multi-species systems. In this paper, a discrete probability cellular automata model (a discrete model widely used in mathematics, physics, complexity science and theoretical biology) is established to investigate the spreading patterns of a spatially implicit predator-prey system with the Allee effect in prey that exhibit patchy spread. We address the following questions: (1) Under what circumstances can patchy spread be observed? (2) Are there essential differences in spread speed under different spread patterns?
    Extensive simulations were used to study parameter conditions under which patchy spread can be found, and the differences between different spreading regimes. We found that under patchy spread conditions, slight variations of parameters were sufficient to destroy this regime and either restore the propagation of continuous fronts or drive the species to extinction. Thus, patchy spread can be qualified as an invasion at the edge of extinction. In this paper, predator mortality was chosen as a control factor and all other parameters treated as fixed. When predator mortality was large, prey were not fully controlled by predators, continuous circular waves were formed, and prey densities were distributed homogeneously behind the wave front. A reduction in predator mortality resulted in a pulse of expanding circular fronts. Further decreases in predator mortality led to increasing break-ups of the inside of the spread wave and inhibited the formation of continuous circular waves, ultimately resulting in the complete break-up of continuous spread waves and the establishment of a patchy spread pattern. The transition from a continuous front propagation pattern to a patchy spread pattern was characterized by a remarkable drop in invasion speed.
    Our results provide a theoretical basis for biological invasion control and exotic species monitoring and suggest the consideration of an exotic species management and control strategy based on the deliberate introduction of a specialist predator. While an exotic species is distributed in a patchy pattern at high densities, it poses the risk of an outbreak in the absence of natural enemies or environmental restrictions. The intensity of population management measures should be increased when an invasive species enters a patchy spread pattern until effective biological control with the aim of extermination can be put into practice.

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杨立,李维德.利用元胞自动机研究一类捕食食饵模型中的斑块扩散现象.生态学报,2012,32(6):1773~1782

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