Modelling Collective Behaviour in Shepherding and Horse Herding

Clark Kendrick Go

Many species in the animal kingdom have evolved to live and travel together in groups called herds. They perform herding behaviours that would be advantageous to them in certain ecological conditions. In most groups, there are herders and followers. Here, we present two models of collective behaviour from the perspective of the herder and followers in two different animal groups. 

First, we consider the herding of sheep by a shepherd dog. We develop a model on how a herder might have acquired such a herding behaviour using imitation learning. We show that given expert demonstrations from a phenomenological model, our imitation learning model reproduces the switching behaviour necessary to be able to complete the herding task. Furthermore, our model does simply copy expert demonstrations but is able to generalise well to herd more sheep than those in the given demonstrations. 

Second, we model the behaviour of female horses as a response to herding by a harem stallion. We propose a mathematical model, a modification of the phenomenological model, where the horses’ motion is expressed as a sum of a linear combination of forces. We then optimise the coefficients of the forces based on actual data. Results show that our model is able to recreate the trajectories and directional trends of the original data set. 

Finally, we discuss the relevance and implications of these models in animal behaviour studies.