Greenman J V, Norman R A
Department of Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA, Scotland, UK.
J Theor Biol. 2007 Aug 7;247(3):492-506. doi: 10.1016/j.jtbi.2007.03.031. Epub 2007 Mar 30.
Destabilising a biological system through periodic or stochastic forcing can lead to significant changes in system behaviour. Forcing can bring about coexistence when previously there was exclusion; it can excite massive system response through resonance, it can offset the negative effect of apparent competition and it can change the conditions under which the system can be invaded. Our main focus is on the invasion properties of continuous time models under periodic forcing. We show that invasion is highly sensitive to the strength, period, phase, shape and configuration of the forcing components. This complexity can be of great advantage if some of the forcing components are anthropogenic in origin. They can be turned into instruments of control to achieve specific objectives in ecology and disease management, for example. Culling, vaccination and resource regulation are considered. A general analysis is presented, based on the leading Lyapunov exponent criterion for invasion. For unstructured invaders, a formula for this exponent can typically be written down from the model equations. Whether forcing hinders or encourages invasion depends on two factors: the covariances between invader parameters and resident populations and the shifts in average resident population levels brought about by the forcing. The invasion dynamics of a structured invader are much more complicated but an analytic solution can be obtained in quadratic approximation for moderate forcing strength. The general theory is illustrated by a range of models drawn from ecology and epidemiology. The relationship between periodic and stochastic forcing is also considered.
通过周期性或随机性强迫使生物系统失稳，可能会导致系统行为发生显著变化。强迫作用在先前存在排斥的情况下可实现共存；它可通过共振激发大规模系统响应，可抵消表观竞争的负面影响，还可改变系统被入侵的条件。我们主要关注周期性强迫下连续时间模型的入侵特性。我们表明，入侵对强迫分量的强度、周期、相位、形状和配置高度敏感。如果某些强迫分量源自人为因素，这种复杂性可能具有很大优势。例如，它们可转化为控制手段，以实现生态和疾病管理中的特定目标。我们考虑了捕杀、疫苗接种和资源调控。基于入侵的主导李雅普诺夫指数准则进行了一般分析。对于无结构的入侵者，通常可从模型方程写出该指数的公式。强迫作用是阻碍还是促进入侵取决于两个因素：入侵者参数与本地种群之间的协方差以及强迫作用引起的本地种群平均水平的变化。有结构入侵者的入侵动态要复杂得多，但对于中等强迫强度，可在二次近似中获得解析解。一系列来自生态学和流行病学的模型阐释了这一一般理论。我们还考虑了周期性强迫与随机性强迫之间的关系。
