How do sheepdogs round up a flock of sheep? Our recent paper, Strömbom et al. (2014), provides some answers to this question. The paper proposes a simple mathematical model based on the idea that that the dog does two things: drive and collect. When the sheep are in a compact group (which they often are when a dog is around) the dog gets behind the flock so that it can drive the flock towards the target. If the herd becomes too spread out the dog goes to a point which collects the furthest out sheep back towards the group. The result is a zigzagging motion as the dog takes the sheep towards the pen.
The video above gives a comparison between simulated and real sheep/sheepdog interactions. In the article we give a detailed comparison of data collected with GPS and our model, and show how the responsive zigzagging works. We currently have a pretty good understanding of how both sheep and sheepdogs behave in standard rounding up situations. However, we still haven't fully solved the problem of how a shepherd might round up really big groups. The video below shows one attempt to solve this problem, where the
If you want to find out more the best starting place is to watch the videos in the supplementary material in the paper, then have a look at the paper itself. If you want a more gentle introduction, there was a fair amount of media coverage when the paper when it came out. Some of the best articles are at BBC, The Independent and Jason Goldman. I also wrote a short blog post, addressing some of the responses we got in the comments section of the newspaper articles. No, as you can see in the simulations below, we aren't quite ready to replace sheepdogs with robots!