Hostname: page-component-7bb8b95d7b-fmk2r Total loading time: 0 Render date: 2024-10-01T13:28:11.180Z Has data issue: false hasContentIssue false
  • English
  • Français

The Effect of Different Communication Mechanisms on the Movement and Structure of Self-Organised Aggregations

Published online by Cambridge University Press:  28 November 2013

R. Eftimie
Get access

Abstract

The formation, persistence and movement of self-organised biological aggregations are mediated by signals (e.g., visual, acoustic or chemical) that organisms use to communicate with each other. To investigate the effect that communication has on the movement of biological aggregations, we use a class of nonlocal hyperbolic models that incorporate social interactions and different communication mechanisms between group members. We approximate the maximum speed for left-moving and right-moving groups, and show numerically that the travelling pulses exhibited by the nonlocal hyperbolic models actually travel at this maximum speed. Next, we use the formula for the speed of a travelling pulse to calculate the reversal time for the zigzagging behaviour, and show that the communication mechanisms have an effect on these reversal times. Moreover, we show that how animals communicate with each other affects also the density structure of the zigzags. These findings offer a new perspective on the complexity of the biological factors behind the formation and movement of various aggregations.

Keywords

travelling pulseszigzag pulseswave speednonlocal hyperbolic systemcommunication
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 6: Ecology , 2013 , pp. 5 - 24
Copyright
© EDP Sciences, 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aldana, M., Huepe, C., Phase transitions in self-driven many-particle systems and related non-equilibrium models: a network approach, J. Stat. Phys., 112 (2003), No. 1-2, 135–153. CrossRefGoogle Scholar
Aoki, I., A simulation study on the schooling mechanism in fish, Bull. Japan Soc. Sci. Fish, 48 (1982), 1081–1088. CrossRefGoogle Scholar
Bazazi, S., Bartumeus, F., Hale, J.J., Couzin, I.D., Intermittent motion in desert locusts: behavioural complexity in simple environments, PLOS Comput. Biol., 8 (2012), No. 5, e1002498. CrossRefGoogle ScholarPubMed
Bode, N.W.F., Franks, D.W., Wood, A.J., Making noise: emergent stochasticity in collective motion, J. Theor. Biol., 267 (2010), No. 3, 292–299. CrossRefGoogle ScholarPubMed
Bode, N.W.F., Wood, A.J., Franks, D.W., The impact of social networks on animal collective motion, Anim. Behav., 82 (2011), 29-38. CrossRefGoogle Scholar
Bousquet, C.A.H., Sumpter, D.J.T., Manser, M.B., Moving calls: a vocal mechanism underlying quorum decisions in cohesive groups, Proc. R. Soc. B, 278 (2011), No. 1711, 1482–1488. CrossRefGoogle ScholarPubMed
Brown, C., Laland, K.N., Social learning in fishes: a review, Fish and fisheries, 4 (2003), 280-288. CrossRefGoogle Scholar
Buhl, J., Sumpter, D. J. T., Couzin, I. D., Hale, J. J., Despland, E., Miller, E. R., Simpson, S. J., From disorder to order in marching locusts, Science, 312 (2006), 1402-1406. CrossRefGoogle ScholarPubMed
Buhl, J., Sword, G.A., J. Simpson, S., Using field data to test locust migratory band collective movement models, Interface Focus, 2 (2012), No. 6, 757–763. CrossRefGoogle ScholarPubMed
P.-L. Buono, R. Eftimie, Analysis of Hopf-Hopf bifurcations in nonlocal hyperbolic models for self-organised aggregations, Math. Models Methods Appl. Sci. (2013), To Appear.
Chaverri, G., Gillam, E.H., Kunz, T.H., A call-and-response system facilitates group cohesion among disc-winged bats, Behav. Ecol., 24 (2013), No. 2, 481–487. CrossRefGoogle Scholar
Couzin, I. D., Krause, J., James, R., Ruxton, G.D., Franks, N. R., Collective memory and spatial sorting in animal groups, J. Theor. Biol., 218 (2002), 1-11. CrossRefGoogle ScholarPubMed
Czirók, A., Barabási, A.-L., Vicsek, T., Collective motion of self-propelled particles: kinetic phase transition in one dimension, Physical Review Letters, 82 (1999), No. 1, 209–212. CrossRefGoogle Scholar
D’Orsogna, M.R., Chuang, Y.L., Bertozzi, A.L., Chayes, L.S., Self-propelled particles with soft-core interactions: patterns, stability and collapse, Phys. Rev. Lett., 96 (2006), No. 10, 104302. CrossRefGoogle Scholar
Dossetti, V., Cohesive motion in one-dimensional flocking, J. Phys. A: Math. Theor., 45 (2012), 035003. CrossRefGoogle Scholar
Eftimie, R., Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review, J. Math. Biol., 65 (2012), No. 1, 35–75. CrossRefGoogle ScholarPubMed
Eftimie, R., de Vries, G., Lewis, M. A., Complex spatial group patterns result from different animal communication mechanisms, Proc. Natl. Acad. Sci., 104 (2007), No. 17, 6974–6979. CrossRefGoogle Scholar
Eftimie, R., de Vries, G., Lewis, M. A., Lutscher, F., Modeling group formation and activity patterns in self-organizing collectives of individuals, Bull. Math. Biol., 69 (2007), No. 5, 1537–1566. CrossRefGoogle Scholar
Eftimie, R., de Vries, G., Lewis, M.A., Weakly nonlinear analysis of a hyperbolic model for animal group formation, J. Math. Biol., 59 (2009), 37–74. CrossRefGoogle ScholarPubMed
Erban, R., Othmer, H. G., From individual to collective behavior in bacterial chemotaxis, SIAM J. Appl. Math., 65 (2004), No. 2, 361–391. CrossRefGoogle Scholar
Fetecau, R., Eftimie, R., An investigation of a nonlocal hyperbolic model for self-organization of biological groups, J. Math. Biol., 61 (2009), No. 4, 545–579. CrossRefGoogle ScholarPubMed
Fetecau, R.C., Collective behavior of biological aggregations in two dimensions: a nonlocal kinetic model, Math. Model. Method. Appl. Sci., 21 (2011), No. 07, 1539. CrossRefGoogle Scholar
Gazi, V., Passino, K.M., A class of attraction/repulsion functions for stable swarm aggregations, Int. J. Control, 77 (2004), No. 18, 1567–1579. CrossRefGoogle Scholar
Gueron, S., Levin, S. A., Rubenstein, D. I., The dynamics of herds: from individuals to aggregations, J. Theor. Biol., 182 (1996), 85-98. CrossRefGoogle Scholar
Hemelrijk, C. K., Kunz, H., Density distribution and size sorting in fish schools: an individual-based model, Behay. Ecol., 16 (2005), No. 1, 178–187. CrossRefGoogle Scholar
Hillen, T., Invariance principles for hyperbolic random walk systems, J. Math. Ana. Appl., 210 (1997), 360-374. CrossRefGoogle Scholar
Hoare, D.J., Couzin, I.D., Godin, J.G., Krause, J., Context-dependent group size choice in fish, Anim. Behav., 67 (2004), 155–164. CrossRefGoogle Scholar
Horstmann, D., Stevens, A., A constructive approach to traveling waves in chemotaxis, J. Nonlinear. Sci., 14 (2004), No. 1, 1–25. CrossRefGoogle Scholar
Huth, A., Wissel, C., The simulation of the movement of fish schools, J. Theor. Biol., 156 (1992), 365-385. CrossRefGoogle Scholar
＿, The simulation of fish schools in comparison with experimental data, Ecol. Model., 75/76 (1994), 135–145. CrossRef
Inada, Y., Steering mechanisms of fish schools, Complexity International, 8 (2001), 1–9. Google Scholar
Iwasa, M., Iida, K., Tanaka, D., Hierarchical cluster structures in a one-dimensional swarm oscillator model, Phys. Rev. E, 81 (2010), No. 4, 046220. CrossRefGoogle Scholar
Keller, E.F., Segel, L.A., Traveling bands of chemotactic bacteria: A theoretical analysis, J. Theor. Biol., 30 (1971), 235-248. CrossRefGoogle Scholar
Kerth, G., Ebert, C., Schmidtke, C., Group decision making in fission-fusion societies: evidence from two-field experiments in Bechstein’s bats, Proc. R. Soc. B, 273 (2006), 2785-2790. CrossRefGoogle ScholarPubMed
Levine, H., Rappel, W.-J., Cohen, I., Self-organization in systems of self-propelled particles, Phys. Rev. E, 63 (2000), No. 1, 01701. CrossRefGoogle ScholarPubMed
Lui, R., Wang, Z.A., Travelling wave solutions from microscopic to macroscopic chemotaxis models, J. Math. Biol., 61 (2010), No. 5, 739–761. CrossRefGoogle Scholar
Lukeman, R., Li, Y.-X., Edelstein-Keshet, L., Inferring individual rules from collective behaviour, Proc. Natl. Acad. Sci., 107 (2010), No. 28, 12576–12580. CrossRefGoogle Scholar
Nagai, T., Ikeda, T., Travelling waves in a chemotactic model, J. Math. Biol., 30 (1991), No. 2, 169–184. CrossRefGoogle Scholar
New, S.T.D., Peters, R.A., A framework for quantifying properties of 3-dimensional movement-based signals, Current Zoology, 56 (2010), No. 3, 327–336. Google Scholar
O’Loan, O.J., Evans, M.R., Alternating steady state in one-dimensional flocking, J. Phys A: Math. Gen., 32 (1999), No. 8, L99. CrossRefGoogle Scholar
Parrish, J. K., Viscido, S. V., Grunbaum, D., Self-organized fish schools: An examination of emergent properties, Bioll. Bull., 202 (2002), 296-305. CrossRefGoogle Scholar
B. Pfistner, A one dimensional model for the swarming behaviour of Myxobacteria, Biological Motion, Lecture Notes on Biomathematics, 89 (W. Alt, G. Hoffmann, eds.), Springer, 1990, pp. 556-563.
Pomeroy, H., Heppner, F., Structure of turning in airborne rock dove (Columba Livia) flocks, The Auk, 109 (1992), 256-267. Google Scholar
Raymond, J.R., Evans, M.R., Flocking regimes in a simple lattice model, Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 73 (2006), No. 3/2, 036112. CrossRefGoogle Scholar
Reuter, H., Breckling, B., Self organization of fish schools: an object-oriented model, Ecol. Model., 75/76 (1994), 147159. CrossRefGoogle Scholar
Reynolds, C. W., Flocks, herds and schools: A distributed behavioral model, Computer Graphics, 21 (1987), 25-34. CrossRefGoogle Scholar
Saragosti, J., Calvez, V., Bournaveas, N., Buguin, A., Silberzanand, P., Perthame, B., Mathematical description of bacterial traveling pulses, PLOS Computational Biology, 6 (2010), No. 8, e1000890. CrossRefGoogle Scholar
Schwetlick, H.R., Travelling waves for chemotaxis-systems, Proc. Appl. Math. Mech, 3 (2003), 476-478. CrossRefGoogle Scholar
Stocker, S., Models for tuna school formation, Math. Biosci, 156 (1999), 167-190. CrossRefGoogle Scholar
Topaz, C. M., Bertozzi, A. L., Swarming patterns in a two-dimensional kinematic model for biological groups, SIAM J. Appl. Math., 65 (2006), No. 1, 152–174. CrossRefGoogle Scholar
Topaz, C. M., Bertozzi, A. L., Lewis, M. A., A nonlocal continuum model for biological aggregation, Bull. Math. Bio., 68 (2006), 1601-1623. CrossRefGoogle Scholar
Torney, C., Neufeld, Z., D. Couzin, I., Context-dependent interaction leads to emergent search behaviour in social aggregates, Proc. Natl. Acad. Sci., 106 (2009), No. 52, 22055–22060. CrossRefGoogle Scholar
Viscido, S. V., Parish, J. K., Grunbaum, D., Individual behavior and emergent properties of fish schools: a comparison of observation and theory, Mar. Ecol. Prog. Ser., 273 (2004), 239-249. CrossRefGoogle Scholar
Xue, C., Hwang, H.J., Painter, K.J., Erban, R., Travelling waves in hyperbolic chemotactic equations, Bull. Math. Biol., 73 (2011), No. 8, 1695–1733. CrossRefGoogle ScholarPubMed