Theoretical Ecology

, Volume 7, Issue 3, pp 239–252 | Cite as

Effects of successive predator attacks on prey aggregations

  • Christophe Lett
  • Magali Semeria
  • Andréa Thiebault
  • Yann Tremblay


We study the cumulative effect of successive predator attacks on the disturbance of a prey aggregation using a modelling approach. Our model intends to represent fish schools attacked by both aerial and underwater predators. This individual-based model uses long-distance attraction and short-distance repulsion between prey, which leads to prey aggregation and swarming in the absence of predators. When intermediate-distance alignment is added to the model, the prey aggregation displays a cohesive displacement, i.e., schooling, instead of swarming. Including predators, i.e. with repulsion behaviour for prey to predators in the model, leads to flash expansion of the prey aggregation after a predator attack. When several predators attack successively, the prey aggregation dynamics is a succession of expanding-grouping-swarming/schooling phases. We quantify this dynamics by recording the changes in the simulated prey aggregation radius over time. This radius is computed as the longest distance of individual prey to the aggregation centroid, and it is assumed to increase along with prey disturbance. The prey aggregation radius generally increases during flash expansion, then decreases during grouping until reaching a constant lowest level during swarming/schooling. This general dynamics is modulated by several parameters: the frequency, direction (vertical vs. horizontal) and target (centroid of the prey aggregation vs. random prey) of predator attacks; the distance at which prey detect predators; the number of prey and predators. Our results suggest that both aerial and underwater predators are more efficient at disturbing fish schools by increasing their attack frequency at such level that the fish cannot return to swarming/schooling. We find that a mix between aerial and underwater predators is more efficient at disturbing a fish school than a single type of attack, suggesting that aerial and underwater foragers may gain mutual benefits in forming foraging groups.


Animal aggregation Animal group School Flock Swarm Attraction-repulsion model 



We thank the developers of the SwarmWatch 1.0 software ( that we used to visualize our model outputs, and particularly Péter Szabó. We thank two anonymous reviewers for their very helpful comments.

Supplementary material

12080_2014_213_MOESM1_ESM.avi (2.2 mb)
Video 1 Simulation S1 (Table 3) with successive predator attacks occurring every 5 s. The prey aggregation dynamics is a succession of expanding-grouping-swarming phases. (AVI 2264 kb)
12080_2014_213_MOESM2_ESM.avi (2.2 mb)
Video 2 Simulation S1 with successive predator attacks occurring every 0.5 s. The prey aggregation eventually forms a quasi-permanent ring structure. (AVI 2244 kb)
12080_2014_213_MOESM3_ESM.avi (2.2 mb)
Video 3 Simulation S2 with successive predator attacks occurring every 0.5 s. (AVI 2236 kb)
12080_2014_213_MOESM4_ESM.avi (2.2 mb)
Video 4 Simulation S3 (including alignment in prey-prey interactions) with successive predator attacks occurring every 5 s. The prey aggregation dynamics is a succession of expanding-grouping-schooling phases. (AVI 2265 kb)


  1. Au DWK, Pitman RL (1986) Seabird interactions with dolphins and tuna in eastern tropical Pacific. Condor 88(3):304–317. doi: 10.2307/1368877 CrossRefGoogle Scholar
  2. Axelsen BE, Anker-Nilssen T, Fossum P, Kvamme C, Nøttestad L (2001) Pretty patterns but a simple strategy: predator–prey interactions between juvenile herring and Atlantic puffins observed with multibeam sonar. Can J Zool 79(9):1586–1596. doi: 10.1139/cjz-79-9-1586 CrossRefGoogle Scholar
  3. Bainbridge R (1960) Speed and stamina in three fish. J Exp Biol 37(1):129–153Google Scholar
  4. Ballerini M, Calbibbo N, Candeleir R, Cavagna A, Cisbani E, Giardina I, Lecomte V, Orlandi A, Parisi G, Procaccini A, Viale M, Zdravkovic V (2008) Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study. Proc Natl Acad Sci U S A 105(4):1232–1237. doi: 10.1073/pnas.0711437105 PubMedCentralPubMedCrossRefGoogle Scholar
  5. Boesch C (1994) Cooperative hunting in wild chimpanzees. Anim Behav 48(3):653–667. doi: 10.1006/anbe.1994.1285 CrossRefGoogle Scholar
  6. Boyd IL, Arnould JPY, Barton T, Croxall JP (1994) Foraging behavior of Antartic fur seals during periods of contrasting prey abundance. J Anim Ecol 63(3):703–713. doi: 10.2307/5235 CrossRefGoogle Scholar
  7. Camperi M, Cavagna A, Giardina I, Parisi G, Silvestri E (2012) Spatially balanced topological interaction grants optimal cohesion in flocking models. Interface Focus 2(6):715–725. doi: 10.1098/rsfs.2012.0026 PubMedCentralPubMedCrossRefGoogle Scholar
  8. Camphuysen CJ, Webb A (1999) Multi-species feeding associations in North Sea seabirds: jointly exploiting a patchy environment. Ardea 87(2):177–198Google Scholar
  9. Clua E, Grosvalet F (2001) Mixed-species feeding aggregation of dolphins, large tunas and seabirds in the Azores. Aquat Living Resour 14(1):11–18. doi: 10.1016/s0990-7440(00)01097-4 CrossRefGoogle Scholar
  10. Coetzee JC, Merkle D, Hutchings L, van der Lingen CD, van den Berg M, Durholtz MD (2010) The 2005 KwaZulu-Natal sardine run survey sheds new light on the ecology of small pelagic fish off the east coast of South Africa. Afr J Mar Sci 32(2):337–360. doi: 10.2989/1814232x.2010.502639 CrossRefGoogle Scholar
  11. Coleman RA, Browne M, Theobalds T (2004) Aggregation as a defense: limpet tenacity changes in response to simulated predator attack. Ecology 85(4):1153–1159. doi: 10.1890/03-0253 CrossRefGoogle Scholar
  12. Creel S, Creel NM (1995) Communal hunting and pack size in African wild dogs, Lycaon Pictus. Anim Behav 50:1325–1339. doi: 10.1016/0003-3472(95)80048-4 CrossRefGoogle Scholar
  13. Dejean A, Fénéron R (1999) Predatory behaviour in the ponerine ant, Centromyrmex bequaerti: a case of termitolesty. Behav Process 47(2):125–133. doi: 10.1016/s0376-6357(99)00060-1 CrossRefGoogle Scholar
  14. Dejean A, Lachaud J-P (2011) The hunting behavior of the African ponerine ant Pachycondyla pachyderma. Behav Process 86(2):169–173. doi: 10.1016/j.beproc.2010.11.004 CrossRefGoogle Scholar
  15. Domenici P (2001) The scaling of locomotor performance in predator–prey encounters: from fish to killer whales. Compar Biochem Phys A 131(1):169–182. doi: 10.1016/s1095-6433(01)00465-2 CrossRefGoogle Scholar
  16. Eaton RC, Emberley DS (1991) How stimulus direction determines the trajectory of the Mauthner-initiated escape response in a teleost fish. J Exp Biol 161:469–487PubMedGoogle Scholar
  17. Estes RD (1991) The behavior guide to African mammals. University of California Press, BerkeleyGoogle Scholar
  18. Fanshawe JH, Fitzgibbon CD (1993) Factors influencing the hunting success of an African wild dog pack. Anim Behav 45(3):479–490. doi: 10.1006/anbe.1993.1059 CrossRefGoogle Scholar
  19. Fish FE (1993) Power output and propulsive efficiency of swimming bottle-nosed dolphins (Tursiops truncatus). J Exp Biol 185:179–193Google Scholar
  20. Fréon P, Misund OA (1999) Dynamics of pelagic fish distribution and behaviour: effects on fisheries and stock assessment. Fishing News Books. Blackwell, LondonGoogle Scholar
  21. Fryxell JM, Mosser A, Sinclair ARE, Packer C (2007) Group formation stabilizes predator–prey dynamics. Nature 449(7165):1041–U1044. doi: 10.1038/nature06177 PubMedCrossRefGoogle Scholar
  22. Gerlotto F, Bertrand S, Bez N, Gutierrez M (2006) Waves of agitation inside anchovy schools observed with multibeam sonar: a way to transmit information in response to predation. ICES J Mar Sci 63(8):1405–1417CrossRefGoogle Scholar
  23. Grimm V, Berger U, Bastiansen F, Eliassen S, Ginot V, Giske J, Goss-Custard J, Grand T, Heinz SK, Huse G, Huth A, Jepsen JU, Jørgensen C, Mooij WM, Müller B, Pe’er G, Piou C, Railsback SF, Robbins AM, Robbins MM, Rossmanith E, Ruger N, Strand E, Souissi S, Stillman RA, Vabø R, Visser U, DeAngelis DL (2006) A standard protocol for describing individual-based and agent-based models. Ecol Model 198(1–2):115–126CrossRefGoogle Scholar
  24. Grimm V, Berger U, DeAngelis DL, Polhill JG, Giske J, Railsback SF (2010) The ODD protocol: a review and first update. Ecol Model 221(23):2760–2768. doi: 10.1016/j.ecolmodel.2010.08.019 CrossRefGoogle Scholar
  25. Hamilton WD (1971) Geometry for the selfish herd. J Theor Biol 31:295–311PubMedCrossRefGoogle Scholar
  26. Handegard NO, Boswell KM, Ioannou CC, Leblanc SP, Tjostheim DB, Couzin ID (2012) The dynamics of coordinated group hunting and collective information transfer among schooling prey. Curr Biol 22(13):1213–1217. doi: 10.1016/j.cub.2012.04.050 PubMedCrossRefGoogle Scholar
  27. Harrison NM, Whitehouse MJ, Heinemann D, Prince PA, Hunt GL, Veit RR (1991) Observations of multispecies seabird flocks around South Georgia. Auk 108(4):801–810Google Scholar
  28. Hemelrijk CK, Hildenbrandt H (2012) Schools of fish and flocks of birds: their shape and internal structure by self-organization. Interface Focus 2(6):726–737. doi: 10.1098/rsfs.2012.0025 PubMedCentralPubMedCrossRefGoogle Scholar
  29. Hodges CL, Woehler EJ (1994) Associations between seabirds and cetaceans in the Australian sector of the southern Indian Ocean. Mar Ornithol 22:205–212Google Scholar
  30. Hoffman W, Heinemann D, Wiens JA (1981) The ecology of seabird feeding flocks in Alaska. Auk 98(3):437–456. doi: 10.2307/4086112 Google Scholar
  31. Huth A, Wissel C (1992) The simulation of the movement of fish schools. J Theor Biol 156:365–385CrossRefGoogle Scholar
  32. Inada Y, Kawachi K (2002) Order and flexibility in the motion of fish schools. J Theor Biol 214(3):371–387PubMedCrossRefGoogle Scholar
  33. Ioannou CC, Guttal V, Couzin ID (2012) Predatory fish select for coordinated collective motion in virtual prey. Science 337(6099):1212–1215. doi: 10.1126/science.1218919 PubMedCrossRefGoogle Scholar
  34. Krause J, Ruxton GD (2002) Living in groups. Oxford University Press, OxfordGoogle Scholar
  35. Kunz H, Hemelrijk CK (2003) Artificial fish schools: collective effects of school size, body size, and body form. Artif Life 9(3):237–253PubMedCrossRefGoogle Scholar
  36. Kunz H, Hemelrijk CK (2012) Simulations of the social organization of large schools of fish whose perception is obstructed. Appl Anim Behav Sci 138:142–151CrossRefGoogle Scholar
  37. Lee DN, Reddish PE (1981) Plummeting gannets: a paradigm of ecological optics. Nature 293(5830):293–294. doi: 10.1038/293293a0 CrossRefGoogle Scholar
  38. Lee S-H, Pak HK, Chon T-S (2006) Dynamics of prey-flock escaping behavior in response to predator’s attack. J Theor Biol 240(2):250–259PubMedCrossRefGoogle Scholar
  39. Lett C, Auger P, Gaillard JM (2004) Continuous cycling of grouped vs. solitary strategy frequencies in a predator–prey model. Theor Popul Biol 65(3):263–270PubMedCrossRefGoogle Scholar
  40. Lett C, Mirabet V (2008) Modelling the dynamics of animal groups in motion. S Afr J Sci 104(5/6):192–198Google Scholar
  41. Luque SP, Guinet C (2007) A maximum likelihood approach for identifying dive bouts improves accuracy, precision and objectivity. Behaviour 144:1315–1332. doi: 10.1163/156853907782418213 CrossRefGoogle Scholar
  42. Magurran AE, Pitcher TJ (1987) Provenance, shoal size and the sociobiology of predator-evasion behavior in minnow shoals. Proc R Soc Lond Ser B-Biol Sci 229(1257):439–465. doi: 10.1098/rspb.1987.0004 CrossRefGoogle Scholar
  43. Major PF (1978) Predator–prey interactions in two schooling fishes, Caranx ignobilis and Stolephorus purpureus. Anim Behav 26(AUG):760–777. doi: 10.1016/0003-3472(78)90142-2 CrossRefGoogle Scholar
  44. Mirabet V, Auger P, Lett C (2007) Spatial structures in simulations of animal grouping. Ecol Model 201(3–4):468–476CrossRefGoogle Scholar
  45. Moffett MW (1988) Foraging dynamics in the group-hunting myrmicine ant, Pheidologeton diversus. J Insect Behav 1(3):309–331CrossRefGoogle Scholar
  46. Muro C, Escobedo R, Spector L, Coppinger RP (2011) Wolf-pack (Canis lupus) hunting strategies emerge from simple rules in computational simulations. Behav Process 88(3):192–197. doi: 10.1016/j.beproc.2011.09.006 CrossRefGoogle Scholar
  47. Niizato T, Gunji Y-P (2011) Metric-topological interaction model of collective behavior. Ecol Model 222(17):3041–3049. doi: 10.1016/j.ecolmodel.2011.06.008 CrossRefGoogle Scholar
  48. Niizato T, Gunji Y-P (2012) Fluctuation-driven flocking movement in three dimensions and scale-free correlation. PLoS One 7(5):e35615. doi: 10.1371/journal.pone.0035615 PubMedCentralPubMedCrossRefGoogle Scholar
  49. Nishimura SI, Ikegami T (1997) Emergence of collective strategies in a prey–predator game model. Artif Life 3:243–260PubMedCrossRefGoogle Scholar
  50. Nøttestad L, Axelsen BE (1999) Herring schooling manoeuvres in response to killer whale attacks. Can J Zool 77(10):1540–1546. doi: 10.1139/cjz-77-10-1540 CrossRefGoogle Scholar
  51. O’Donoghue SH, Drapeau L, Peddemors VM (2010) Broad-scale distribution patterns of sardine and their predators in relation to remotely sensed environmental conditions during the KwaZulu-Natal sardine run. Afr J Mar Sci 32(2):279–291. doi: 10.2989/1814232x.2010.501584 CrossRefGoogle Scholar
  52. Okunishi T, Yamanaka Y, Ito S (2009) A simulation model for Japanese sardine (Sardinops melanostictus) migrations in the western North Pacific. Ecol Model 220(4):462–479. doi: 10.1016/j.ecolmodel.2008.10.020 CrossRefGoogle Scholar
  53. Oro D (1995) Audouin’s gulls Larus audouinii associate with sub-surface predators in the Mediterranean Sea. J Ornithol 136(4):465–467. doi: 10.1007/bf01651595 CrossRefGoogle Scholar
  54. Packer C, Ruttan L (1988) The evolution of cooperative hunting. Am Nat 132(2):159–198. doi: 10.1086/284844 CrossRefGoogle Scholar
  55. Partridge BL (1982) The structure and function of fish schools. Sci Am 246(6):114–123PubMedCrossRefGoogle Scholar
  56. Pennycuick CJ (1987) Flight of auks (Alcidae) and other northern seabirds compared with southern Procellariiformes: ornitholdolite observations. J Exp Biol 128:335–347Google Scholar
  57. Peraltilla S, Bertrand S (2014) In situ measurements of the speed of Peruvian anchovy schools. Fish Res 149:92–94. doi: 10.1016/j.fishres.2013.09.002 CrossRefGoogle Scholar
  58. Pitcher TJ, Misund OA, Fernø A, Totland B, Melle V (1996) Adaptive behaviour of herring schools in the Norwegian Sea as revealed by high-resolution sonar. ICES J Mar Sci 53(2):449–452. doi: 10.1006/jmsc.1996.0063 CrossRefGoogle Scholar
  59. Pitcher TJ, Wyche CJ (1983) Predator avoidance behaviour of sand-eel schools: why school seldom split? In: Noakes DLG, Lindquist BG, Helfman GS, Ward JA (eds) Predators and prey in fishes. Junk, The Hague, pp 193–204CrossRefGoogle Scholar
  60. Quérouil S, Silva MA, Cascão I, Magalhães S, Seabra MI, Machete MA, Santos RS (2008) Why do dolphins form mixed-species asssociations in the Azores? Ethology 114(12):1183–1194. doi: 10.1111/j.1439-0310.2008.01570.x CrossRefGoogle Scholar
  61. Rands SA, Cowlishaw G, Pettifor RA, Rowcliffe JM, Johnstone RA (2003) Spontaneous emergence of leaders and followers in foraging pairs. Nature 423(6938):432–434. doi: 10.1038/nature01630 PubMedCrossRefGoogle Scholar
  62. Rohr JJ, Fish FE, Gilpatrick JW (2002) Maximum swim speeds of captive and free-ranging delphinids: critical analysis of extraordinary performance. Mar Mammal Sci 18(1):1–19. doi: 10.1111/j.1748-7692.2002.tb01014.x CrossRefGoogle Scholar
  63. Ropert-Coudert Y, Grémillet D, Kato A, Ryan PG, Naito Y, Le Maho Y (2004) A fine-scale time budget of Cape gannets provides insights into the foraging strategies of coastal seabirds. Anim Behav 67:985–992CrossRefGoogle Scholar
  64. Sand H, Wikenros C, Wabakken P, Liberg O (2006) Effects of hunting group size, snow depth and age on the success of wolves hunting moose. Anim Behav 72:781–789. doi: 10.1016/j.anbehav.2005.11.030 CrossRefGoogle Scholar
  65. Scheel D, Packer C (1991) Group hunting behavior of lions: a search for cooperation. Anim Behav 41:697–709. doi: 10.1016/s0003-3472(05)80907-8 CrossRefGoogle Scholar
  66. Schellinck J, White T (2011) A review of attraction and repulsion models of aggregation: methods, findings and a discussion of model validation. Ecol Model 222(11):1897–1911. doi: 10.1016/j.ecolmodel.2011.03.013 CrossRefGoogle Scholar
  67. Stander PE (1992) Cooperative hunting in lions: the role of the individual. Behav Ecol Sociobiol 29(6):445–454CrossRefGoogle Scholar
  68. Stanford CB (1995) The influence of chimpanzee predation on group size and antipredator behavior in red Columbus monkeys. Anim Behav 49(3):577–587. doi: 10.1016/0003-3472(95)90033-0 CrossRefGoogle Scholar
  69. Stensland E, Angerbjörn A, Berggren P (2003) Mixed species groups in mammals. Mammal Rev 33(3–4):205–223. doi: 10.1046/j.1365-2907.2003.00022.x CrossRefGoogle Scholar
  70. Treherne JE, Foster WA (1981) Group transmission of predator avoidance behaviour in a marine insect: the Trafalgar effect. Anim Behav 29(AUG):911–917. doi: 10.1016/s0003-3472(81)80028-0 CrossRefGoogle Scholar
  71. Tu S-Y, Sayed AH (2011) Cooperative prey herding based on diffusion adaptation. In: 2011 I.E. International Conference on Acoustics, Speech, and Signal Processing. International Conference on Acoustics Speech and Signal Processing ICASSP. pp 3752–3755.Google Scholar
  72. Vabø R, Nøttestad L (1997) An individual based model of fish school reactions: predicting antipredator behaviour as observed in nature. Fish Oceanogr 6(3):155–171CrossRefGoogle Scholar
  73. Vaughn R, Würsig B, Packard J (2010) Dolphin prey herding: prey ball mobility relative to dolphin group and prey ball sizes, multispecies associates, and feeding duration. Mar Mammal Sci 26(1):213–225. doi: 10.1111/j.1748-7692.2009.00317.x CrossRefGoogle Scholar
  74. Vaughn RL, Muzi E, Richardson JL, Würsig B (2011) Dolphin bait-balling behaviors in relation to prey ball escape behaviors. Ethology 117(10):859–871. doi: 10.1111/j.1439-0310.2011.01939.x CrossRefGoogle Scholar
  75. Vaughn RL, Shelton DE, Timm LL, Watson LA, Wuersig B (2007) Dusky dolphin (Lagenorhynchus obscurus) feeding tactics and multi-species associations. N Z J Mar Freshw Res 41(4):391–400CrossRefGoogle Scholar
  76. Vaughn RL, Würsig B, Shelton DS, Timm LL, Watson LA (2008) Dusky dolphins influence prey accessibility for seabirds in admiralty bay, New Zealand. J Mammal 89(4):1051–1058. doi: 10.1644/07-mamm-a-145.1 CrossRefGoogle Scholar
  77. Viscido SV, Miller M, Wethey DS (2001) The response of a selfish herd to an attack from outside the group perimeter. J Theor Biol 208(3):315–328. doi: 10.1006/jtbi.2000.2221 PubMedCrossRefGoogle Scholar
  78. Viscido SV, Parrish JK, Grünbaum D (2005) The effect of population size and number of influential neighbors on the emergent properties of fish schools. Ecol Model 183(2–3):347–363CrossRefGoogle Scholar
  79. Viscido SV, Parrish JK, Grünbaum D (2007) Factors influencing the structure and maintenance of fish schools. Ecol Model 206(1–2):153–165. doi: 10.1016/j.ecolmodel.2007.03.042 CrossRefGoogle Scholar
  80. Ward CR, Gobet F, Kendall G (2001) Evolving collective behavior in an artificial ecology. Artif Life 7(2):191–209. doi: 10.1162/106454601753139005 PubMedCrossRefGoogle Scholar
  81. Wood AJ, Ackland GJ (2007) Evolving the selfish herd: emergence of distinct aggregating strategies in an individual-based model. Proc R Soc B-Biol Sci 274(1618):1637–1642. doi: 10.1098/rspb.2007.0306 CrossRefGoogle Scholar
  82. Zheng M, Kashimori Y, Hoshino O, Fujita K, Kambara T (2005) Behavior pattern (innate action) of individuals in fish schools generating efficient collective evasion from predation. J Theor Biol 235(2):153–167PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Christophe Lett
    • 1
  • Magali Semeria
    • 1
    • 2
  • Andréa Thiebault
    • 2
  • Yann Tremblay
    • 2
  1. 1.UMI IRD 209 UPMC UMMISCOCentre de Recherche Halieutique Méditerranéenne et Tropicale (CRH)Sète cedexFrance
  2. 2.UMR EME 212, IRDCentre de Recherche Halieutique Méditerranéenne et Tropicale (CRH)Sète cedexFrance

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