A mathematical model of herding in horse-harem group

Abstract

In animal groups, individual interactions achieve coordinated movements to maintain cohesion. In horse-harem groups, herding is a behaviour in which stallions chase mares from behind; it is considered to assist with group cohesiveness. The mechanisms of the group cohesion were studied using the methods of drone filming and video tracking during herding and two phases of interactions were found based on the mares’ timing of movement initiation. The study shows that mares that move first are those nearest to the stallion; while the movement initiation of the later mares is determined by the distance from the nearest moving mare. Thus, as a second step to the full understanding of group cohesion, we propose a mathematical model of mares herded by a harem stallion, which is a modification of a sheep model during shepherding. Our model is a linear combination of the five components: inertia, repulsion from the stallion, short-range repulsion, synchronisation attraction, and attraction to the centre of the group. We tune the parameters of our proposed models based on the data and successfully reproduce the movements and directional trends of the mares.