Modelling animal movement as a persistent random walk in two dimensions: expected magnitude of net displacement

We present semi-empirical model of persistent random walk for studying anim al movements in two-dimensions. The model incorporates an arbitrary distrib ution for the angles between successive steps in the tracks. Inclusion of a turning angle distribution enables explicit computation of the effect of p ersistence in the direction of travel on the expected magnitude of net disp lacement of the animal over time. We employed a form-analogous approach to obtain expressions for the expected net displacement and derived root mean square of the expected displacement of an animal at the end of a multi-step random walk in which turning angles were drawn from the Lemicon of Pascal, the elliptical, the von Mises,and the wrapped Cauchy distributions. The ac curacy of these expressions for the expected magnitude of net displacement was tested by comparison with simulated results of persistent random walks where turning angles were drawn form the wrapped Cauchy distribution. Our r esults should be useful in predicting two-dimensional distribution of movin g animals for which frequency distributions of the turning angles can be me asured. (C) 2000 Elsevier Science B.V. All rights reserved.