Collective responses of flocking sheep (Ovis aries) to a herding dog (border collie)

This repository contains the code for the manuscript: Jadhav, V., Pasqua, R., Zanon, C., Roy, M., Tredan, G., Bon, R., Guttal, V. and Theraulaz, G., 2024. Collective responses of flocking sheep to a herding dog. bioRxiv, pp.2024-05. bioRXiv preprint

The codes are tested to run on MATLAB Version: 23.2.0.2485118 (R2023b).

Raw data

UWB tag data for all the trials are available in /main_text/sheepR.dat. The first, second, third, fourth and fifth columns in sheepR.dat are trial number, sheep ID, time (s), and position along the x (m) and y (m) axis, respectively.

To convert the data in sheepR.dat into .mat format, run /main_text/pre_ana.m followed by /main_text/pre_ini_ana.m. This will give sheep_all_dat.mat. As our analysis focuses on the active phase, during which the dog was driving the sheep and staying behind the flock relative to its direction of movement, we select active phase trajectories from sheep_all_dat.mat. To do this, run /main_text/drivs_dat.m, which generates drives_data.mat

Both data files sheep_all_dat.mat and drives_data.mat should be in both\main_text and sm folders to reproduce figures in those folders. We have already added these files to both the folder.

Code for Figure 1b

Run \main_text\figure_1b to reproduce representative trajectories of sheep, barycenter and dog shown in Figure 1b.

Codes for Figure 2

Time series and probability density functions of the observables characterizing collective behavior of sheep and their reaction to the dog: run main_text\figure_2ae.m to generate Figure 2a-e and run \main_text\figure_2fj.m to generate Figure 2f-j of the main text.

Code for Figure 3

Relative angular positions and headings of the barycenter of the flock and the dog: Run main_text\figure_3.m to generate Figure 3 of the main text.

Code for Figure 4

Turning rates of the barycenter of the flock and the dog: run \main_text\figure_4.m to generate Figure 4 of the main text. Ensure that Violin.m and violinplot.m (Bechtild, Bastian, 2016) are in path.

Codes for Figure 5

Hierarchical leader-follower relationships

1. Run \main_text\figure_5c to generate leader-follower networks for all drives. Set variable no_shp_dg = no_shp to observe the leader-follower network without the dog and comment the above variable to observe the leader-follower network with the dog. This code generates Figure 5c and Supplementary Figure 5.
2. Run \main_text\figure_5de to generate Figure 5 d-e of the main text and Supplementary Figures 6 and 7. To generate Fig 5e, the relationship between mean $d_i$ and indegree for the model, simulation data is already uploaded in the folder main_text. However, to run the simulations and calculate Pearson's correlation between mean $d_i$ and indegree, do the following:
   1. Run \sm\simulation_hm.m. Simulation data is stored as hm_n_14.mat for group size 14.
   2. Load hm_n_14.mat in \sm\model_network_ana.m and run the code.

Codes for Figure 6

Simulation results of the shepherding model To generate Figure 6 of the main text do the following:

1. Run \model\simulation_hm.m. Simulation data is stored as hm_n_14.mat for group size 14.
2. Load hm_n_14.mat in \sm\model_results.m and run the code.

Modified herding model (Supplementary Section 3)

To simulate the modified model described in Supplementary Section 3, run sm\simulation_hm_sim.m. Simulation data is stored as hm_sim_14_rd_3.mat for $N = 14$ and radius of repulsion from the dog , $R_{\rm D} = 3$. For $N = 20$ and $30$, change model parameters as suggested in the code (see, Supplementary Fig.9 caption and Supplementary Table 1). To generate Supplementary Figure 9, run \sm\model_network_ana.m with data from appropriate $N$.

Supplementary Figures

Run codes in the folder \sm to generate Supplementary Figures. Ensure that sheep_all_dat.mat and drives_data.mat are in the path.

1. \sm\sm_fig_spd_coh.m generates Supplementary Figure 2
2. \sm\sm_fig_cc.m generates Supplementary Figures 3, 4, and 16.
3. \sm\sm_fig_dij.m generates Supplementary Figure 8 and 11.
4. \sm\all_trajectories.m generates Supplementary Figure 14.

References

1. Bechtold, Bastian, 2016. Violin Plots for Matlab, Github Project https://github.com/bastibe/Violinplot-Matlab, DOI: 10.5281/zenodo.4559847