Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, United Kingdom.
Ecology. 2010 Oct;91(10):3106-13. doi: 10.1890/09-1729.1.
Random walks are used to model movement in a wide variety of contexts: from the movement of cells undergoing chemotaxis to the migration of animals. In a two-dimensional biased random walk, the diffusion about the mean drift position is entirely dependent on the moments of the angular distribution used to determine the movement direction at each step. Here we consider biased random walks using several different angular distributions and derive expressions for the diffusion coefficients in each direction based on either a fixed or variable movement speed, and we use these to generate a probability density function for the long-time spatial distribution. We demonstrate how diffusion is typically anisotropic around the mean drift position and illustrate these theoretical results using computer simulations. We relate these results to earlier studies of swimming microorganisms and explain how the results can be generalized to other types of animal movement.
从趋化性细胞的运动到动物的迁移。在二维有偏随机游走中，平均漂移位置的扩散完全取决于用于确定每步运动方向的角分布的矩。在这里，我们考虑了使用几种不同的角分布的有偏随机游走，并根据固定或可变的运动速度推导出每个方向的扩散系数的表达式，我们使用这些来生成长时间空间分布的概率密度函数。我们展示了在平均漂移位置周围扩散通常是各向异性的，并使用计算机模拟来说明这些理论结果。我们将这些结果与先前对游泳微生物的研究联系起来，并解释了如何将这些结果推广到其他类型的动物运动。
