Model for the spatial pattern formed by a small herd in grazing cattle

The spatial pattern of a small cattle herd within a fenced grazing pasture was investigated using a mathematical model. Only changes in the distance between the two most distant individuals in the pasture, i.e. troop length, were observed. Troop length is a measure of closeness of individuals within a herd. In the model, we assumed that the troop length was determined by: (1) attractive activities (desire to be in a group) and repulsive activities (maintenance of individual space) operating among individuals in the herd; and (2) random activities unrelated to the attractive and repulsive activities. A relationship between these two elements was incorporated into a diffusion equation, and the theoretical frequency distribution of the troop length was derived. The model was tested using experimental data collected in a strip-wise pasture. Activities of a cattle herd were visually divided into three categories such as resting, feeding and moving states. Parameters representing the attractive and repulsive activities, and the equilibrium of troop length were estimated using the model for the three states. The frequency distribution of troop length was compared between the three states and with the frequency distribution derived under the assumption of a random spatial pattern. It was concluded that: (1) the changes in troop length could be described by the newly derived model; (2) the spatial pattern of a cattle herd in an actual pasture was not random but aggregated; and (3) the closeness of individuals within a herd was loosened in the following order: resting, feeding and moving states.