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

Abstract

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.

Inferring symmetric and asymmetric interactions between animals and groups from positional data

“…If the use of space by a group of animals is affected by the proximity of another group, the changing level of clustering may be captured in the measure. Convex hull areas have previously been applied to analyze sheep positional data [21] and are used extensively in ecology as a means of estimating the home range and the utilization distributions of an individual animal or a group of animals [39–43]. CHA was calculated using the positions of all the animals of a particular species over periods of 1, 3 or 5 hours.…”

“…A Voronoi tessellation is a partitioning of a plane into areas of influence about a set of sites, where for each site there is a corresponding polygon of points that are closer to that site than any other [39, 43]. The area of the Voronoi polygon formed about an individual animal can be used as a measure for its isolation [39].…”

“…The area of the Voronoi polygon formed about an individual animal can be used as a measure for its isolation [39]. Voronoi tessellations for neighbourhood construction have been used successfully for characterizing flocking and school behavior in birds, fish and for animal movement prediction and modelling [36, 39, 43, 46, 47].…”

Order Through Disorder: The Characteristic Variability of Systems

“…Finally, randomness in the motion of animals is relevant to the movement of individuals within animal groups. It promotes the compactness of a herd by enabling the disintegration of small clusters in favor of a more compact structure and, by that, reducing the distances to center for the herd (Ose and Ohmann, 2017).…”

Collective Motion as an Ultimate Effect in Crowded Selfish Herds

“…Several modelling studies have examined how and why selfish herds emerge from the interaction of prey individuals. For example, instead of the attraction to the nearest neighbour 1 , reasonably complicated movement rules based on group densities and individual positions have been demonstrated as necessary for the emergence of large groups in two-dimensional space, the environment of most terrestrial animals 13–17 . In consideration of the ultimate reasons, a growing number of simulations have demonstrated that under the selfish herd scenario, the evolution of prey agents’ movement strategies can result in stable states where selfish agents assemble large and dense groups 18–22 .…”