Effects of random motion in traveling and grazing herds

Abstract

We examine the role that randomness or noise in individual motion may play in forming effective grazing strategies for herd members as they collectively move toward a destination. Through a model where animals are attracted to Voronoi neighbors as well as a destination endpoint, we show that including a significant random motion component can speed up the movement of a herd toward this destination, increase the efficiency that food is acquired during the travel, and facilitate a natural herd shape that mitigates predation risk. Specifically, if the influence of the Voronoi neighbors on individual motion is equal to the pull toward the destination, we find that optimal travel time and food consumption efficiency occurs for noise approximately twice as strong as the influence of herd members to each other, in a range of herd sizes from 10 to 100. We find that reducing the destination influence lowers this optimal noise only slightly, with random motion still exceeding the influence of neighbors. For a destination influence exceeding that of the Voronoi neighbors, an additional travel mode appears with minimal noise and aligned velocities in which the herd marches directly toward the endpoint. Our results are consistent with observational evidence of random motion in several animal groups, and motivate its generalization to traveling and grazing herds.

Fission–fusion dynamics in sheep: the influence of resource distribution and temporal activity patterns

“…Hence, in other contexts, such as grazing, the sheep are physically farther apart but are still able to perceive cues from other group members, for instance after detecting a predator, and display some cohesion by moving together. Even so, group members rarely move in the average direction of the group but rather with large variation along a common route [ 33 ] making the 3–5 m radius inappropriate to capture these dynamics. We were interested in these larger groups providing benefits for the individual, rather than physical interactions among group members and thus used an inner radius of 30 m. In addition, we conducted a robustness check using radii between 5 and 60 m displayed in electronic supplementary material, figures S1–S6.…”