Geodesic
The Role of Avoidance and Learning Behaviours on the Formation and Movement of Biological Aggregations
R. Eftimie1 ; A. Coulier2
1 Division of Mathematics, University of Dundee, Dundee, DD1 4NR, UK
2 Institut National des Sciences Appliquées de Rouen, 76800, Saint-Étienne-du-Rouvray, France
Mathematical modelling of natural phenomena, Tome 10 (2015) no. 2, pp. 27-44.

Voir la notice de l'article provenant de la source EDP Sciences

Communication forms the basis of any animal aggregation. However, not all organisms communicate the same way. Moreover, different psychological and physiological characteristics of individuals can lead to avoidance behaviours between different individuals. This can have implications on the formation and structure of large biological aggregations. In this article, we use a mathematical model to investigate the effects of avoidance behaviour by a subpopulation, on the spatial dynamics of the whole population. We show that avoidance (exhibited even by a small fraction of the population) can alter the spatio-temporal patterns of the whole groups, leading to new patterns difficult to predict from the case without avoidance. Generally, these patterns show the segregation of the populations into different aggregations (spatially separated) or inside the same aggregation. Moreover, we investigate numerically the situation where individuals can learn to tolerate their neighbours. In this case, we observe an unexpected spatial segregation inside moving aggregations of individuals that tolerate their neighbours and those that avoid their neighbours.
DOI : 10.1051/mmnp/201510203

R. Eftimie 1 ; A. Coulier 2

1 Division of Mathematics, University of Dundee, Dundee, DD1 4NR, UK
2 Institut National des Sciences Appliquées de Rouen, 76800, Saint-Étienne-du-Rouvray, France 
@article{MMNP_2015_10_2_a2,
     author = {R. Eftimie and A. Coulier},
     title = {The {Role} of {Avoidance} and {Learning} {Behaviours} on the {Formation} and {Movement} of {Biological} {Aggregations}},
     journal = {Mathematical modelling of natural phenomena},
     pages = {27--44},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2015},
     doi = {10.1051/mmnp/201510203},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp/201510203/}
}
TY  - JOUR
AU  - R. Eftimie
AU  - A. Coulier
TI  - The Role of Avoidance and Learning Behaviours on the Formation and Movement of Biological Aggregations
JO  - Mathematical modelling of natural phenomena
PY  - 2015
SP  - 27
EP  - 44
VL  - 10
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp/201510203/
DO  - 10.1051/mmnp/201510203
LA  - en
ID  - MMNP_2015_10_2_a2
ER  - 
%0 Journal Article
%A R. Eftimie
%A A. Coulier
%T The Role of Avoidance and Learning Behaviours on the Formation and Movement of Biological Aggregations
%J Mathematical modelling of natural phenomena
%D 2015
%P 27-44
%V 10
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp/201510203/
%R 10.1051/mmnp/201510203
%G en
%F MMNP_2015_10_2_a2
R. Eftimie; A. Coulier. The Role of Avoidance and Learning Behaviours on the Formation and Movement of Biological Aggregations. Mathematical modelling of natural phenomena, Tome 10 (2015) no. 2, pp. 27-44. doi : 10.1051/mmnp/201510203. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/201510203/

[1] M. Aldana, V. Dossetti, C. Huepe, V. M. Kenke, H. Larralde Phys. Rev. Lett. 2007 095702 1

[2] I. Barber OIKOS 2003 331 337

[3] Ch. Becco, N. Vanderwalle, J. Delcourt, P. Poncin Physica A 2006 487 493

[4] U. Börner, A. Deutsch, H. Reichenbach, M. Bär Phys. Rev. Lett 2002 078101

[5] D.J.T. Sumpter, J. Buhl, D. Biro, I.D. Couzin Theory Biosci. 2008 177 186

[6] J. Buhl, D. J. T. Sumpter, I. D. Couzin, J. J. Hale, E. Despland, E. R. Miller, S. J. Simpson Science 2006 1402 1406

[7] P-L. Buono, R. Eftimie Math. Models Methods Appl. Sci. 2014 327 357

[8] P-L. Buono, R. Eftimie SIAM J. Appl. Dyn. Syst. 2014 1542 1582

[9] José A. Carrillo, Massimo Fornasier, Giuseppe Toscani, Francesco Vecil. Particle, kinetic, and hydrodynamic models of swarming. Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences (Giovanni Naldi, Lorenzo Pareschi, Giuseppe Toscani, eds.) Modeling and Simulation in Science, Engineering and Technology Birkhäuser Boston 2010, 297–336 (English).

[10] Z. Chen, H. Liao, T. Chu Physica A 2012 3988 3994

[11] Y.-L. Chuang, M.R. D’Orsogna, D. Marthaler, A.L. Bertozzi, L.S. Chayes Physica D 2007 33 47

[12] A. Czirók, M. Vicsek, T. Vicsek Physica A 1999 299 304

[13] R. Eftimie J. Math. Biol. 2012 35 75

[14] R. Eftimie Math. Model. Nat. Phenom. 2013 32 51

[15] R. Eftimie J. Theor. Biol. 2013 42 53

[16] R. Eftimie, G. De Vries, M.A. Lewis Proc. Natl. Acad. Sci. 2007 6974 6979

[17] R. Eftimie, G. De Vries, M.A. Lewis J. Math. Biol. 2009 37 74

[18] R. Eftimie, G. De Vries, M.A. Lewis, F. Lutscher Bull. Math. Biol. 2007 1537 1566

[19] R.C. Fetecau Math. Models Methods Appl. Sci. 2011 1539 1

[20] F. Ginelli, H. Chaté Phys. Rev. Lett. 2010 168103

[21] E. Goodale, G. Beauchamp, R.D. Magrath, J.C. Nieh, G.D. Ruxton Trends Ecol. Evol. 2010 354 361

[22] N.M. Harrison, M.J. Whitehouse Anim. Behav. 2011 675 682

[23] J.K. Hellerstein, D. Newmark The review of Economics and Statistics 2008 459 477

[24] O. Igoshin, A. Mogilner, R. Welch, D. Kaiser, G. Oster Proc. Natl. Acad. Sci. USA 2001 14913 14918

[25] J. Krause Oecologia 1993 356 359

[26] J.R. Krebs Can. J. Zool. 1973 1275 1288

[27] P.J.O. Miller Behav. Ecol. Sociobiol. 2002 262 270

[28] R. Muzinic J. Cons. Int. Expl. Mer. 1977 147 155

[29] M. Nagy, Z. Akos, D. Biro, T. Vicsek Nature 2010 890 983

[30] J.K. Parrish Env. Biol. Fishes 1989 79 86

[31] P.H.C. Pereira, J.L.L. Feitosa, D.V. Medeiros, B.P. Ferreira Acta Ethologica 2013 53 56

[32] C.W. Reynolds Computer Graphics 1987 25 34

[33] R.M. Seyfarth, D.L. Cheney, P. Marler Science 1980 801 803

[34] H. Sridhar, G. Beauchamp, K. Shanker Anim. Behav. 2009 337 347

[35] D.J.T. Sumpter Phil. Trans. R. Soc. B 2006 5 22

[36] T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, O. Shochet Phys. Rev. Lett. 1995 1226 1229

[37] T. Vicsek, A. Czirok, I.J. Farkas, D. Helbing Physica A 1999 182 189

[38] G. Vines Anim. Behav. 1980 1175 1183

[39] D.P. Whitfield Trends in Ecology & Evolution 1987 13 18

[40] S.R. Witkin The Condor 1977 490 493

[41] A.J. Wood, G.J. Ackland Proc. R. Soc. B 2007 1637 1642

Cité par Sources :