This paper is published in The Quarterly Review of Biology (Chicago University Press), available on http://www.journals.uchicago.edu/doi/pdfplus/10.1086/685301
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[en] Ant mill, caterpillar circle, bat doughnut, amphibian vortex, duck swirl, and fish torus are different names for rotating circular animal formations, where individuals turn around a common center. These “collective vortex behaviors” occur at different group sizes from pairs to several million individuals and have been reported in a large number of organisms, from bacteria to vertebrates, including humans. However, to date, no comprehensive review and synthesis of the literature on vortex behaviors has been conducted. Here, we review the state of the art of the proximate and ultimate causes of vortex behaviors.
The ubiquity of this behavioral phenomenon could suggest common causes or fundamental underlying principles across contexts. However, we find that a variety of proximate mechanisms give rise to vortex behaviors. We highlight the potential benefits of collective vortex behaviors to individuals involved in them. For example, in some species, vortices increase feeding efficiency and could give protection against predators. It has also been argued that vortices could improve collective decision making and information transfer. We highlight gaps in our understanding of these ubiquitous behavioral phenomena and discuss future directions for research in vortex studies.
Research Center/Unit :
AFFISH-RC - Applied and Fundamental FISH Research Center - ULiège
Alexander R. M. 2003. Principles of Animal Locomotion. Princeton (New Jersey): Princeton University Press.
Aoki I. 1982. A simulation study on the schooling mechanism in fish. Bulletin of the Japanese Society of Scientific Fisheries 48:1081-1088.
Batchelor G. K. 2000. An Introduction to Fluid Dynamics. Cambridge (United Kingdom): Cambridge University Press.
Bazazi S., Buhl J., Hale J. J., Anstey M. L., Sword G. A., Simpson S. J., Couzin I. D. 2008. Collective motion and cannibalism in locust migratory bands. Current Biology 18:735-739.
Bazazi S., Ioannou C. C., Simpson S. J., Sword G. A., Torney C. J., Lorch P. D., Couzin I. D. 2010. The social context of cannibalism in migratory bands of the Mormon cricket. PLOS ONE 5:e15118.
Bazazi S., Pfennig K. S., Handegard N. O., Couzin I. D. 2012. Vortex formation and foraging in polyphenic spadefoot toad tadpoles. Behavioral Ecology and Sociobiology 66:879-889.
Bearon R. N., Grünbaum D. 2006. Bioconvection in a stratified environment: experiments and theory. Physics of Fluids 18:127102.
Beckers R., Holland O. E., Deneubourg J.-L. 1994. From local actions to global tasks: stigmergy and collective robotics. Artificial Life 4:181-189.
Beebe W. 1921. Edge of the Jungle. New York: H. Holt and Company.
Beecham J. A., Farnsworth K. D. 1999. Animal group forces resulting from predator avoidance and competition minimization. Journal of Theoretical Biology 198:533-548.
Belmonte J. M., Thomas G. L., Brunnet L. G., de Almeida R. M. C., Chaté H. 2008. Self-propelled particle model for cell-sorting phenomena. Physical Review Letters 100:248702.
Ben-Jacob E. 2003. Bacterial self-organization: coenhancement of complexification and adaptability in a dynamic environment. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 361:1283-1312.
Ben-Jacob E., Levine H. 2006. Self-engineering capabilities of bacteria. Journal of the Royal Society Interface 3:197-214.
Ben-Jacob E., Cohen I., Czirók A., Vicsek T., Gutnick D. L. 1997. Chemomodulation of cellular movement, collective formation of vortices by swarming bacteria, and colonial development. Physica A: Statistical Mechanics and its Applications 238:181-197.
Bode N. W. F., Delcourt J. 2013. Individual-to-resource landscape interaction strength can explain different collective feeding behaviours. PLOS ONE 8: e75879.
Bode N. W. F., Faria J. J., Franks D. W., Krause J., Wood A. J. 2010. How perceived threat increases synchronization in collectively moving animal groups. Proceedings of the Royal Society B: Biological Sciences 277:3065-3070.
Bode N. W. F., Franks D. W., Wood A. J. 2011. Limited interactions in flocks: relating model simulations to empirical data. Journal of the Royal Society Interface 8:301-304.
Buhl J., Sumpter D. J. T., Couzin I. D., Hale J. J., Despland E., Miller E. R., Simpson S. J. 2006. From disorder to order in marching locusts. Science 312: 1402-1406.
Bumann D., Krause J. 1993. Front individuals lead in shoals of three-spined sticklebacks (Gasterosteus aculeatus) and juvenile roach (Rutilus rutilus). Behaviour 125:189-198.
Bumann D., Krause J., Rubenstein D. 1997. Mortality risk of spatial positions in animal groups: the danger of being in the front. Behaviour 134:1063-1076.
Burggren W. W., Bemis W. E. 1992. Metabolism and ram gill ventilation in juvenile paddlefish, Polyodon spathula (Chondrostei: Polyodontidae). Physiological Zoology 65:515-539.
Calovi D. S., Lopez U., Ngo S., Sire C., Chaté H., Theraulaz G. 2014. Swarming, schooling, milling: phase diagram of a data-driven fish school model. New Journal of Physics 16:015026.
Camazine S., Deneubourg J.-L., Franks N. R., Sneyd J., Theraulaz G., Bonabeau E. 2001. Self-Organization in Biological Systems. Princeton (New Jersey): Princeton University Press.
Carlson J. K., Goldman K. J., Lowe C. G. 2004. Metabolism, energetic demand, and endothermy. Pages 203-224 in Biology of Sharks and Their Relatives, edited by J. C. Carrier, J. A. Musick, and M. R. Heithaus. Boca Raton (Florida): CRC Press.
Carter A. J., Feeney W. E., Marshall H. H., Cowlishaw G., Heinsohn R. 2013. Animal personality: what are behavioural ecologists measuring? Biological Reviews of the Cambridge Philosophical Society 88:465-475.
Charabidze D., Bourel B., Gosset D. 2011. Larval-mass effect: characterisation of heat emission by necrophageous blowflies (Diptera: Calliphoridae) larval aggregates. Forensic Science International 211: 61-66.
Choi Y., Jung E., Park H., Paik S. R., Jung S., Kim S. 2004. Construction of microbial fuel cells using thermophilic microorganisms, Bacillus licheniformis and Bacillus thermoglucosidasius. Bulletin of the Korean Chemistry Society 25:813-818.
Cisneros L. H., Cortez R., Dombrowski C., Goldstein R. E., Kessler J. O. 2007. Fluid dynamics of self-propelled microorganisms, from individuals to concentrated populations. Experiments in Fluids 43:737-753.
Couzin I. D. 1999. Collective Animal Behaviour. PhD diss., University of Bath.
Couzin I. D. 2009. Collective cognition in animal groups. Trends in Cognitive Sciences 13:36-43.
Couzin I. D., Franks N. R. 2003. Self-organized lane formation and optimized traffic flow in army ants. Proceedings of the Royal Society B: Biological Sciences 270:139-146.
Couzin I. D., Krause J. 2003. Self-organization and collective behavior in vertebrates. Advances in the Study of Behavior 32:1-75.
Couzin I. D., Krause J., James R., Ruxton G. D., Franks N. R. 2002. Collective memory and spatial sorting in animal groups. Journal of Theoretical Biology 218:1-11.
Czirók A., Vicsek T. 2000. Collective behavior of interacting self-propelled particles. Physica A: Statistical Mechanics and its Applications 281:17-29.
Czirók A., Ben-Jacob E., Cohen I., Vicsek T. 1996. Formation of complex bacterial colonies via selfgenerated vortices. Physical Review E 54:1791-1801.
Delcourt J., Poncin P. 2012. Shoals and schools: back to the heuristic definitions and quantitative references. Reviews in Fish Biology and Fisheries 22: 595-619.
Delcourt J., Ylieff M. Y., Bolliet V., Poncin P, Bardonnet A. 2011. Video tracking in the extreme: a new possibility for tracking nocturnal underwater transparent animals with fluorescent elastomer tags. Behavior Research Methods 43:590-600.
Delcourt J., Denoël M., Ylieff M., Poncin P. 2013. Video multitracking of fish behaviour: a synthesis and future perspectives. Fish and Fisheries 14:186-204.
Deneubourg J.-L., Goss S., Franks N., Pasteels J. M. 1989. The blind leading the blind: modeling chemically mediated army ant raid patterns. Journal of Insect Behavior 2:719-725.
Deneubourg J.-L., Aron S., Goss S., Pasteels J. M. 1990. The self-organizing exploratory pattern of the Argentine ant. Journal of Insect Behavior 3:159-168.
Dombrowski C., Cisneros L., Chatkaew S., Goldstein R. E., Kessler J. O. 2004. Self-concentration and large-scale coherence in bacteria dynamics. Physical Review Letters 93:098103.
Dorigo M., Bonabeau E., Theraulaz G. 2000. Ant algorithms and stigmergy. Future Generation Computer Systems 16:851-871.
Dowd W. W., Brill R. W., Bushnell P. G., and Musick J. A. 2006. Standard and routine metabolic rates of juvenile sandbar sharks (Carcharhinus plumbeus), including the effects of body mass and acute temperature change. Fisheries Bulletin 104:323-331.
Dyer J. R. G., Johansson A., Helbing D., Couzin I. D., Krause J. 2009. Leadership, consensus decision making and collective behaviour in humans. Philosophical Transactions of the Royal Society B: Biological Sciences 364:781-789.
Economakis A. E., Lobel P. S. 1998. Aggregation behavior of the grey reef shark, Carcharhinus amblyrhynchos, at Johnston Atoll, Central Pacific Ocean. Environmental Biology of Fishes 51:129-139.
Fabre J.-H. 1899. Souvenirs Entomologiques. Études sur l'Instinct et les Moeurs des Insectes. Paris (France): Librairie Ch. Delagrave.
Fitzgerald T. D. 2003. Role of a trail pheromone in the foraging and processionary behavior of pine processionary caterpillars Thaumetopoea pityocampa. Journal of Chemical Ecology 29:513-532.
Foster K. W., Smydth R. D. 1980. Light antennas in phototactic algae. Microbiological Reviews 44:572-630.
Franks N. R., Gomez N., Goss S., Deneubourg J.-L. 1991. The blind leading the blind in army ant raid patterns: testing a model of self-organization (Hymenoptera: Formicidae). Journal of Insect Behavior 4:583-607.
Garnier S., Gautrais J., Theraulaz G. 2007. The biological principles of swarm intelligence. Swarm Intelligence 1:3-31.
Gautrais J., Jost C., Theraulaz G. 2008. Key behavioural factors in a self-organised fish school model. Annales Zoologici Fennici 45:415-428.
Gautrais J., Ginelli F., Fournier R., Blanco S., Soria M., Chaté H., Theraulaz G. 2012. Deciphering interactions in moving animal groups. PLOS Computational Biology 8:e1002678.
Ghorai S., Hill N. A. 1999. Development and stability of gyrotactic plumes in bioconvection. Journal of Fluid Mechanics 400:1-31.
Gooders J., Boyer T. 1986. Ducks of North America and the Northern Hemisphere. Reissue Edition. New York: Facts On File.
Gotwald W. H. 1995. Army Ants: The Biology of Social Predation. Ithaca (New York): Comstock Publishing Associates, Cornell University Press.
Grassé P.-P. 1959. La reconstruction du nid et les coordinations interindividuelles chez Bellicositermes natalensis et Cubitermes sp. La théorie de la stigmergie: essai d'interprétation du comportement des termites constructeurs. Insectes Sociaux 6:41-80.
Grossman D., Aranson I. S., Ben-Jacob E. 2008. Emergence of agent swarm migration and vortex formation through inelastic collisions. New Journal of Physics 10:023036.
Halloy J., Sempo G., Caprari G., Rivault C., Asadpour M., Tâche F., Saïd I., Durier V., Canonge S., Amé J. M., Detrain C., Correll N., Martinoli A., Mondada F., Siegwart R., Deneubourg J.-L. 2007. Social integration of robots into groups of cockroaches to control self-organized choices. Science 318:1155-1158.
Hamilton W. D. 1971. Geometry for the selfish herd. Journal of Theoretical Biology 31:295-311.
Helbing D., Molnár P. 1995. Social force model for pedestrian dynamics. Physical Review E 51:4282-4286.
Hemelrijk C. K., Reid D. A. P., Hildenbrandt H., Padding J. T. 2015. The increased efficiency of fish swimming in a school. Fish and Fisheries 16:511-521.
Herbert-Read J. E., Krause S., Morrell L. J., Schaerf T. M., Krause J., Ward A. J. W. 2013. The role of individuality in collective group movement. Proceedings of the Royal Society B: Biological Sciences 280: 20122564.
Hill N. A., Pedley T. J. 2005. Bioconvection. Fluid Dynamics Research 37:1-20.
Huth A., Wissel C. 1992. The simulation of the movement of fish schools. Journal of Theoretical Biology 156:365-385.
James R., Bennett P. G., Krause J. 2004. Geometry for mutualistic and selfish herds: the limited domain of danger. Journal of Theoretical Biology 228:107-113.
Johnsgard P. A. 1965. Handbook of Waterfowl Behavior. Ithaca (New York): Comstock Publishing Associates.
José J. V., Kadanoff L. P., Kirkpatrick S., Nelson D. R. 1977. Renormalization, vortices, and symmetrybreaking perturbations in the two-dimensional planar model. Physical Review B 16:1217-1241.
Kessler J. O. 1985a. Hydrodynamic focusing of motile algal cells. Nature 313:218-220.
Kessler J. O. 1985b. Co-operative and concentrative phenomena of swimming micro-organisms. Contemporary Physics 26:147-166.
Kils U. 1993. Formation of micropatches by zooplankton-driven microturbulences. Bulletin of Marine Science 53:160-169.
Kitsunezaki S., Komori R., Harumoto T. 2007. Bioconvection and front formation of Paracemium tetraurelia. Physical Review E 76:046301.
Krause J., Bumann D., Todt D. 1992. Relationship between the position preference and nutritional state of individuals in schools of juvenile roach (Rutilus rutilus). Behavioral Ecology and Sociobiology 30:177-180.
Krause J., Reeves P., Hoare D. 1998. Positioning behaviour in roach shoals: the role of body length and nutritional state. Behaviour 135:1031-1039.
Krause J., Hoare D., Krause S., Hemelrijk C. K., Rubenstein D. I. 2000. Leadership in fish shoals. Fish and Fisheries 1:82-89.
Kunz H., Züblin T., Hemelrijk C. K. 2006. On prey grouping and predator confusion in artificial fish schools. Pages 365-371 in Artificial Life X: Proceedings of Tenth International Conference on the Simulation and Synthesis of Living Systems, edited by L. M. Rocha, L. S. Yaeger, M. A. Bedau, D. Floreano, R. L. Goldstone, and A. Vespignani. Cambridge (Massachusetts): MIT Press.
Kuznetsov A. V. 2005. Thermo-bioconvection in a suspension of oxytactic bacteria. International Communications in Heat and Mass Transfer 32:991-999.
Lima S. L. 1995. Back to the basics of anti-predatory vigilance: the group-size effect. Animal Behaviour 49:11-20.
Lukeman R., Li Y.-X., Edelstein-Keshet L. 2009. A conceptual model for milling formations in biological aggregates. Bulletin of Mathematical Biology 71:352-382.
Mach R., Schweitzer F. 2007. Modeling vortex swarming in Daphnia. Bulletin of Mathematical Biology 69: 539-562.
Mann R. P., Perna A., Ströbom D., Garnett R., Herbert-Read J. E., Sumpter D. J. T., Ward A. J. W. 2012. Multi-scale inference of interaction rules in animal groups using Bayesian model selection. PLOS Computational Biology 8:e1002308.
Marras S., Killen S. S., Lindström J., McKenzie D. J., Steffensen J. F., Domenici P. 2015. Fish swimming in schools save energy regardless of their spatial position. Behavioral Ecology and Sociobiology 69:219-226.
Michelena P., Jeanson R., Deneubourg J.-L., Sibbald A. M. 2010. Personality and collective decisionmaking in foraging herbivores. Proceedings of the Royal Society B: Biological Sciences 277:1093-1099.
Milgram S., Toch H. 1969. Collective behaviour: crowds and social movements. Pages 507-610 in The Handbook of Social Psychology, Second Edition, edited by G. Lindzey and E. Aronson. Reading (Massachusetts): Addison-Wesley Publishing Company.
Miller N., Garnier S., Hartnett A. T., Couzin I. D. 2013. Both information and social cohesion determine collective decisions in animal groups. Proceedings of the National Academy of Sciences of the United States of America 110:5263-5268.
Mitri S., Wischmann S., Floreano D., Keller L. 2013. Using robots to understand social behaviour. Biological Reviews 88:31-39.
Mogami Y., Yamane A., Gino A., Baba S. A. 2004. Bioconvective pattern formation of Tetrahymena under altered gravity. Journal of Experimental Biology 207:3349-3359.
Morton T. L., Haefner J. W., Nugula V., Decino R. D., Mendes L. 1994. The selfish herd revisited: do simple movement rules reduce relative predation risk? Journal of Theoretical Biology 167:73-79.
Moussaïd M., Helbing D., Garnier S., Johanson A., Combe M., Theraulaz G. 2009. Experimental study of the behavioural mechanisms underlying selforganization in human crowds. Proceedings of the Royal Society B: Biological Sciences 276:2755-2762.
Moussaïd M., Helbing D., Theraulaz G. 2011. How simple rules determine pedestrian behavior and crowd disasters. Proceedings of the National Academy of Sciences of the United States of America 108:6884-6888.
Nill D., Siemers B. 2001. Fledermäuse-eine Bildreise in die Nacht. München (Germany): BLV Verlagsgesellschaft mbH.
Ochiai N., Dragiila M. I., Parker J. L. 2011. Pattern swimming of Phytophthora citricola zoospores: an example of microbial bioconvection. Fungal Biology 115:228-235.
O'Neal Campbell M. 2015. Vultures: Their Evolution, Ecology and Conservation. Boca Raton (Florida): CRC Press, Taylor & Francis.
Ordemann A., Balazsi G., Moss F. 2003. Pattern formation and stochastic motions of the zooplankton Daphnia in a light field. Physica A: Statistical Mechanics and its Applications 325:260-266.
Parr A. E. 1927. A contribution to the theoretical analysis of the schooling behavior of fishes. Occasional Papers of the Bingham Oceanographic Collection 1:1-32.
Parrish J. K., Viscido S. V., Grünbaum D. 2002. Selforganized fish schools: an examination of emergent properties. Biological Bulletin 202:296-305.
Pennycuick C. J. 2008. Modelling the Flying Bird. Burlington (Massachusetts): Academic Press.
Perna A., Granovskiy B., Garnier S., Nicolis S. C., Labédan M., Theraulaz G., Fourcassié V., Sumpter D. J. T. 2012. Individual rules for trail pattern formation in Argentine ants (Linepithema humile). PLOS Computational Biology 8:e1002592.
Platt J. R. 1961. "Bioconvection patterns" in cultures of free-swimming organisms. Science 133:1766-1767.
Rappel W.-J., Nicol A., Sarkissian A., Levine H., Loomis W. F. 1999. Self-organized vortex state in twodimensional Dictyostelium dynamics. Physical Review Letters 83:1247-1250.
Reynolds C. W. 1987. Flocks, herds, and schools: a distributed behavioural model. Computer Graphics 21:25-34.
Rieucau G., Martin J. G. A. 2008. Many eyes or many ewes: vigilance tactics in female bighorn sheep Ovis canadensis vary according to reproductive status. Oikos 117:501-506.
Robertson B. A., Rehage J. S., Sih A. 2013. Ecological novelty and the emergence of evolutionary traps. Trends in Ecology and Evolution 28:552-560.
Schneirla T. C. 1944. A unique case of circular milling in ants, considered in relation to trail following and the general problem of orientation. American Museum Novitates 1253:1-26.
Schneirla T. C. 1971. Army Ants: A Study in Social Organization. San Francisco (California): W. H. Freeman.
Shitanda I., Yoshida Y., Tatsuma T. 2007. Microimaging of algal bioconvection by scanning electrochemical microscopy. Analytical Chemistry 79:4237-4240.
Sih A., Bell A. M., Johnson J. C., Ziemba R. E. 2004. Behavioral syndromes: an integrative overview. Quarterly Review of Biology 79:241-277.
Silverberg J. L., Bierbaum M., Sethna J. P., Cohen I. 2013. Collective motion of humans in mosh and circle pits at heavy metal concerts. Physical Review Letters 110:228701.
Stuart D. 1994. Bats: Mysterious Flyers of the Night. Minneapolis (Minnesota): Carolrhoda Books.
Sumpter D. J. T. 2006. The principles of collective animal behaviour. Philosophical Transactions of the Royal Society B: Biological Sciences 361:5-22.
Sumpter D. J. T. 2010. Collective Animal Behavior. Princeton (New Jersey): Princeton University Press.
Theraulaz G., Bonabeau E. 1999. A brief history of stigmergy. Artificial Life 5:97-116.
Todd F. S. 1979. Waterfowl: Ducks, Geese and Swans of the World. New York: Sea World Press.
Tunstrøm K., Katz Y., Ioannou C. C., Huepe C., Lutz M. J., Couzin I. D. 2013. Collective states, multistability and transitional behavior in schooling fish. PLOS Computational Biology 9:e1002915.
Viscido S. V., Parrish J. K., Grünbaum D. 2004. Individual behavior and emergent properties of fish schools: a comparison of observation and theory. Marine Ecology Progress Series 273:239-249.
Vollmer J., Vegh A. G., Lange C., Eckhardt B. 2006. Vortex formation by active agents as a model for Daphnia swarming. Physical Review E 73:061924.
Wager H. 1911. On the effect of gravity upon the movements and aggregation of Euglena viridis, Ehrb. and other micro-organisms. Philosophical Transaction of the Royal Society of B: Biological Sciences 201:333-390.
Wegner N. C., Sepulveda C. A., Bull K. B., Graham J. B. 2010. Gill morphometrics in relation to gas transfer and ram ventilation in high-energy demand teleosts: scombrids and billfishes. Journal of Morphology 271:36-49.
Wheeler W. M. 1910. Ants, their Structure, Development and Behavior. New York: Columbia University Press.
Williams C. R., Bees M. A. 2011. A tale of the three taxes: photo-gyro-gravitactic bioconvection. Journal of Experimental Biology 214:2398-2408.
Wood A. J., Ackland G. J. 2007. Evolving the selfish herd: emergence of distinct aggregating strategies in an individual-based model. Proceedings of the Royal Society B: Biological Sciences 274:1637-1642.
