Abstract
Models of collective animal motion can greatly aid in the design and interpretation of behavioural experiments that seek to unravel, isolate, and manipulate the determinants of leader-follower relationships. Here, we develop an initial model of zebrafish social behaviour, which accounts for both speed and angular velocity regulatory interactions among conspecifics. Using this model, we analyse the macroscopic observables of small shoals influenced by an “informed” agent, showing that leaders which actively modulate their speed with respect to their neighbours can entrain and stabilise collective dynamics of the naïve shoal.
Article PDF
Similar content being viewed by others
References
B.L. Partridge, Sci. Amer. 246, 114 (1982)
I. Aoki, B. Jpn. Soc. Sci. Fish. 48, 1081 (1982)
A. Huth, C. Wissel, J. Theor. Biol. 156, 365 (1992)
J.K. Parrish, S.V. Viscido, D. Grünbaum, Biol. Bull. 202, 296 (2002)
I.D. Couzin, J. Krause, R. James, J. Theor. Biol. 218, 1 (2002)
D.J.T. Sumpter, Collective Animal Behaviour (Princeton University Press, 2009)
N. Miller, R. Gerlai, PLoS ONE 7, e48865 (2012)
J. Gautrais, F. Ginelli, R. Fournier, S. Blanco, M. Soria, H. Chaté, G. Theraulaz, PLoS Comput. Biol. 8, e1002678 (2012)
C.W. Reynolds, Comp. Graph. 21, 25 (1987)
T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, O. Shochet, Phys. Rev. Lett. 75, 4 (1995)
S. Reebs, Anim. Behav. 59, 403 (2000)
A. Czirók, T. Vicsek, Physica A 281, 17 (2000)
G. Grégoire, H. Chaté, Y. Tu, Physica D 181, 157 (2003)
T. Vicsek, A. Zafeiris, Physics Reports 517, 71 (2012)
C. Ioannou, V. Guttal, I. Couzin, Science 337, 1212 (2012)
E.A. Codling, J.W. Pitchford, S.D. Simpson, Ecology 88, 1864 (2007)
A. Berdahl, C.J. Torney, C.C. Ioannou, J.J. Faria, I.D. Couzin, Science 339, 574 (2013)
A. Eriksson, M. Nilsson Jacobi, J. Nystrom, K. Tunstrom, Behav. Ecol. 21, 1106 (2010)
R. Lukeman, Y.X. Li, L. Edelstein-Keshet, PNAS 107, 12576 (2010)
Y. Katz, K. Tunstrøm, PNAS 108, 18721 (2011)
J.E. Herbert-Read, A. Perna, PNAS 108, 18726 (2011)
I.D. Couzin, J. Krause, N.R. Franks, S.A. Levin, Nature 433, 513 (2005)
I.D. Couzin, C.C. Ioannou, G. Demirel, T. Gross, C.J. Torney, A. Hartnett, L. Conradt, S.A. Levin, N.E. Leonard, Science 334, 1578 (2011)
G. Polverino, N. Abaid, V. Kopman, S. Macrì, M. Porfiri, Bioinspir. Biomim. 7, 036019 (2012), ISSN 1748-3190
S. Butail, G. Polverino, P. Phamduy, D. Sette, M. Porfiri, D. Del Sette, F. Del Sette, Behav. Brain Res. 275, 90550I (2014)
F. Ladu, T. Bartolini, S.G. Panitz, F. Chiarotti, S. Butail, S. Macrì, M. Porfiri, Zebrafish 00, 1 (2015)
D. Swain, I. Couzin, N. Leonard, P. IEEE 100, 150 (2012)
M. Aureli, F. Fiorilli, M. Porfiri, Physica D 241, 908 (2012)
G. Polverino, M. Porfiri, Bioinspir. Biomim. 8, 044001 (2013), ISSN 1748-3190
S. Butail, T. Bartolini, M. Porfiri, PLoS ONE 8, e76123 (2013)
M. Aureli, M. Porfiri, EPL 92, 40004 (2010)
N.W.F. Bode, D.W. Franks, A.J. Wood, Behav. Ecol. Sociobiol. 66, 835 (2012)
D.S. Calovi, U. Lopez, P. Schuhmacher, H. Chate, G. Theraulaz, J. R. Soc. Interface 12, 20141362 (2015)
A.K. Zienkiewicz, D.A. Barton, M. Porfiri, M. Di Bernardo, J. Math. Biol., 1432 (2014)
F.E. Fish, J.F. Fegely, C.J. Xanthopoulos, Comp. Biochem. Phys. A 100, 633 (1991)
M. Sfakiotakis, D.M. Lane, J.B.C. Davies, IEEE J. Oceanic Eng. 24, 237 (1999)
J.E. Herbert-Read, S. Krause, L.J. Morrell, T.M. Schaerf, J. Krause, A.J.W. Ward, P.R.S. B, Proc. R. Soc. B: Biol. Sci. 280, 20122564 (2013)
A. Strandburg-Peshkin, C.R. Twomey, N.W.F. Bode, A.B. Kao, Y. Katz, C.C. Ioannou, S.B. Rosenthal, C.J. Torney, H.S. Wu, S.A. Levin, et al., Curr. Biol. 23, R709 (2013)
J. Gautrais, C. Jost, M. Soria, A. Campo, S. Motsch, R. Fournier, S. Blanco, G. Theraulaz, J. Math. Biol. 58, 429 (2009)
V. Mwaffo, R.P. Anderson, S. Butail, M. Porfiri, J. R. Soc. Inter. 12, 20140884 (2014)
K. Wong, M. Elegante, B. Bartels, S. Elkhayat, D. Tien, S. Roy, J. Goodspeed, C. Suciu, J. Tan, C. Grimes, et al., Behav. Brain Res. 208, 450 (2010)
F. Ladu, S. Butail, S. Macrí, M. Porfiri, Alcohol. Clin. Exp. Res. 38, 1 (2014)
V. Mwaffo, S. Butail, M. Di Bernardo, M. Porfiri, Zebrafish 12, 250 (2015)
D.S. Calovi, U. Lopez, S. Ngo, C. Sire, H. Chaté, G. Theraulaz, New J. Phys. 16, 015026 (2014)
A. Kolpas, M. Busch, H. Li, I.D. Couzin, L. Petzold, J. Moehlis, PLoS ONE 8, e58525 (2013)
D. Garcia, Comput. Stat. Data. An. 54, 1167 (2010)
L. Bai, D. Breen, J. Graphics, GPU, and Game Tools 13, 53 (2008), ISSN 2151-237X
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Zienkiewicz, A., Barton, D., Porfiri, M. et al. Leadership emergence in a data-driven model of zebrafish shoals with speed modulation. Eur. Phys. J. Spec. Top. 224, 3343–3360 (2015). https://doi.org/10.1140/epjst/e2015-50093-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2015-50093-5