Aggregation by chemotactic random walk: Drifting clusters and chemotactic friction

Dynamics of the group-formation of animals by the secretion of aggregation pheromone are studied by a chemotactic random walk model in which the location of each individual is traced. If the number of individuals is reasonably large (several tens), the behavior of the model is qualitatively different from that of the corresponding reaction-diffusion model in which demographic stochasticity owing to finiteness of the number of individuals is neglected. In a typical time-course starting from uniform initial distribution, animals may quickly aggregate into many small clusters. Subsequently these clusters drift around randomly, merge with one another upon encounter, slow down movement, and finally form one or a few large clusters. Both directed movement and random drift of a single cluster of animals slow down owing to the pheromone produced by itself in the near past, which we call chemotactic friction. An approximate formula for the magnitude of slowdown is derived and confirmed by computer simulation.