Who herds the herders ? Albert Kao and Andrew Berdahl Quis custodiet ipsos custodes? - Juvenal, 1 st century C.E.

Two levels of control Herders can exercise control over sheep, but sheep can also self- organize. Sheep can also potentially influence herder movement. herder sheep

Competing hypotheses Exogenous factors: Do herders consistently herd at certain times of day or at certain locations? Endogenous factors: Does the internal state of the herd or the herder determine when herding events occur? Which is more relevant to the actual herding events that we observed?

Exogenous factors Are the herding events synchronized in time?

Exogenous factors There appear to be distinct morning and afternoon herding sessions, with a stop at the watering hole occurring between minutes into the day. While exogenous factors determine the large-scale structure of the herding periods, endogenous factors control the small- scale structure.

Competing hypotheses H1: The herder predominantly controls the herd. The herder often pushes the herd and changes its behavior in some way. H2: The herd predominantly controls the herder. The herd pulls the herder along, and its behavior is relatively independent of the herder’s movements.

Characterizing a herd Herd velocity Herd area Herd diameter Herd polarity Perimeter of herd/diameter of herd Distance from herder to nearest sheep Distance from herder to furthest sheep Distance from herder to center of herd Visual angle of herd from herder’s view

Defining a herding event Herder velocity is > 0.2 m/s Herder is < 300 meters from herd

Hypotheses Revisited H1: The herder predominantly controls the herd. If true, then we predict that there is some systematic change in the characteristics of the herd as a result of a herding event. The herder reorganizes the herd.

Hypotheses Revisited H2: The herd predominantly controls the herder. If true, then we predict that there is no systematic change in the herd from herding events.

Results

Results: Box and Whisker Plots Comparison of before and after herding

Results: Box and Whisker Plots Comparison of before and during herding

Results: SVM We trained various models (linear and nonlinear on 1000 time points and then tested the model using all 6000 time points. The model could successfully predict at most 52% of the data.

Problems with the Analysis Herding events were chosen by hand with a pre- determined criteria Infrequent, unsynchronized, and noisy data Two herders vs. one herder Used herd properties instead of looking at individual properties

Summary Exogenous factors only defines the broad herding patterns, while endogenous factors determine the fine-scale herding patterns. A herd’s properties do not change consistently as a result of a herding event. In other words, the herder does not reorganize the herd in a consistent way. This lends support to the hypothesis that in general, the herder is pulled along by the herd. The low quality of the data could have smeared away patterns that otherwise might have been present.

Acknowledgements (in alphabetical order): Dan, Iain, and Tanya Habiba, Khairi, Mayank, Monda, Victor Ann, Caitlin, Colin, Ipek, Jenni, Qing, Sebastian, Xingli Orestes Steven Mpala staff