A random walk description of individual animal movement accounting for periods of rest
A random walk description of individual animal movement accounting for periods of rest
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考虑休息时间的个体动物运动的随机游走描述
DOI：
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发表时间：
2016
影响因子：
3.5
通讯作者：
Paulo Laerte Natti
中科院分区：
文献类型：
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作者：
Paulo F. C. Tilles;S. Petrovskii;Paulo Laerte Natti
动物并不是一直在移动，而是在实际移动的时间（觅食）和休息的时间（例如进食或睡觉）之间交替。虽然休息时间的存在在文献中被广泛承认，甚至已成为最近越来越多的关注的焦点，理论方法来描述动物运动通过计算扩散核和/或均方位移（MSD）很少考虑休息。在这项研究中，我们的目标是弥合这一差距。我们考虑一个复合随机过程，其中活跃的扩散或“回合”（由一定的基线概率密度函数（PDF）的动物扩散）交替与不动的时期。对于这个过程，我们推导出一个一般方程，确定这个复合运动的pdf。在两个特殊但重要的情况下，如由高斯核描述的标准布朗运动和由柯西分布描述的Levy飞行方程进行了详细分析。对于布朗运动，我们表明，在大的时间渐近的影响休息的结果在重新调整的扩散系数。该运动作为两个扩散渐近性之间的次扩散过渡而发生。有趣的是，Levy飞行案例显示了类似的性质，这表明我们的发现具有一定的普遍性。
Animals do not move all the time but alternate the period of actual movement (foraging) with periods of rest (e.g. eating or sleeping). Although the existence of rest times is widely acknowledged in the literature and has even become a focus of increased attention recently, the theoretical approaches to describe animal movement by calculating the dispersal kernel and/or the mean squared displacement (MSD) rarely take rests into account. In this study, we aim to bridge this gap. We consider a composite stochastic process where the periods of active dispersal or ‘bouts’ (described by a certain baseline probability density function (pdf) of animal dispersal) alternate with periods of immobility. For this process, we derive a general equation that determines the pdf of this composite movement. The equation is analysed in detail in two special but important cases such as the standard Brownian motion described by a Gaussian kernel and the Levy flight described by a Cauchy distribution. For the Brownian motion, we show that in the large-time asymptotics the effect of rests results in a rescaling of the diffusion coefficient. The movement occurs as a subdiffusive transition between the two diffusive asymptotics. Interestingly, the Levy flight case shows similar properties, which indicates a certain universality of our findings.