White A, Begon M, Bowers R G
Department of Applied Mathematics and Theoretical Physics, University of Liverpool, U.K.
Proc Biol Sci. 1996 Mar 22;263(1368):325-32. doi: 10.1098/rspb.1996.0050.
A discrete model for a host-pathogen system is developed and is used to represent the dynamics in each patch within a landscape of n x n patches. These patches are linked by between-generation dispersal to neighbouring patches. Important results (compared to similar 'coupled map lattice' studies) include an increase in the likelihood of metapopulation extinction if the natural loss of pathogen particles is low, and the observation of a radial wave pattern (not previously reported) where the wavefront propagates uniformly from a central focus. This result has additional significance in that it permits the system to exhibit 'intermittency' between two quasi-stable spatial patterns: spirals and radial waves. With intermittent behaviour, the dynamics may look consistent when viewed at one time scale, but over a longer time scale they can alter dramatically and repeatedly between the two patterns. There is also evidence of clear links between spatial structure and temporal metapopulation behaviour in both the intermittent and 'pure' regions, verified by results from an algorithmic complexity measure and a spectral analysis of the temporal dynamics.
我们构建了一个宿主 - 病原体系统的离散模型，并用它来描述一个由(n×n)个斑块组成的景观中每个斑块内的动态变化。这些斑块通过代际扩散与相邻斑块相连。重要结果（与类似的“耦合映射格点”研究相比）包括：如果病原体颗粒的自然损失较低，集合种群灭绝的可能性会增加；观察到一种径向波模式（此前未报道过），波前从中心焦点均匀传播。这一结果具有额外的重要意义，因为它使系统能够在两种准稳定空间模式之间表现出“间歇性”：螺旋和径向波。在间歇性行为中，在一个时间尺度上观察时，动态可能看起来是一致的，但在更长的时间尺度上，它们会在两种模式之间剧烈且反复地变化。在间歇性区域和“纯”区域，空间结构与集合种群的时间行为之间也有明显联系的证据，这通过算法复杂度度量和时间动态的频谱分析结果得到了验证。
