The selfish herd: Noise effects in Local Crowded Horizon and Voronoi models

Randomness or noise in the motion of herding animals is more important than commonly assumed. We show through simulations that noise promotes the compactness of a herd by facilitating the breakup of small clusters in favor of a more compact whole, reducing the mean median distances to center (MMDC) for the herd. Adding noise to movement models can also decrease risk from predators emerging locally by reducing Domains of Danger (DODs); we specifically show that adding noise to the Voronoi (V) movement model gives favorable DOD results comparable to that of the Local Crowded Horizon (LCH) model. In addition, we show that adding noise to these models can significantly reduce risk from predators emerging outside the herding area through head-to-head competition in mixed herds, with effects that can be larger than the choice of model itself. Our results are consistent with recent observational studies in several different animal populations that suggest random motion plays a significant role in the movement of individuals within these groups. Because of its significance, noise must be considered whenever model effectiveness is discussed or comparisons between movement models are made.