On taking up position in a group: A continuous‐time Markov model for biased random movement

A model is developed for movement by members of a group when this movement is random but is affected by a preference for a particular region of the space occupied by the group. Asymptotic distributions are derived from a continuous-time Markovian model for the case in which a group member may move to any unoccupied location in one jump, and a method for estimating the degree of attraction of the preferred region is given. Such a group is described as ‘fluid’. A viscous' group is defined as one in which interchanges take place one step at a time. Movement in such groups was simulated on a computer and some results are given, including the apparently paradoxical finding that an approach tendency will be more strongly evident at asymptote if access to the preferred region is difficult than if it is easy.