Journal of Bioeconomics

, Volume 12, Issue 2, pp 119–143 | Cite as

Economic models of fish shoal (school) size: a near comprehensive view of single species shoaling strategy



This paper extends theory of shoaling presented by Landa (1998), which uses the economic theory of clubs (Buchanan 1965). The findings include that non-patchy feeding shoals formed for defense increase in size with increased predation and decline in size with increased food concentration. There is strong evidence for the former and a piece of evidence for the latter. The size of shoals formed to find patches of food is unaffected by food availability. When defense is also involved, increasing predation increases shoal size and increasing food availability decreases shoal size. The optimum size of migrating schools—synchronized and polarized swimming shoals—is often the whole population migrating, explaining the mammoth size of some schools. Further, mergers of schools are forecast along the migration route with larger schools at the end of the route than at the beginning. When there is no defense motive for shoaling, non-patchy feeders may form large schools under low food density and be solitary under high food density. Small schools might not be found. When there is also a defense motivation for shoaling, small schools are possible. For schools formed among patchy feeders, increased food availability decreases school size. The same finding holds for schooling among patchy feeders where an added shoal benefit is defense. Also under these circumstances, increased predation increases shoal size.


Flock Herd Optimum shoal size Defense Food patches Collective good Free-riding Comparative static analysis Marginal 

JEL Classification



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Amesbury S. S., Myers R. F. (1982) The fishes, guide to the coastal resources of Guam (Vol. 1). University of Guam Press, Mangilao, GuamGoogle Scholar
  2. Anderson J. J. (1981) A stochastic model for the size of fish schools. Fisheries Bulletin 79(2): 315–323Google Scholar
  3. Barber, I., & Huntingford, F. A. (1996). Parasite infection alters schooling behavior: Deviant positioning of helminth-infected minnows in conspecific groups. Proceedings of Royal Society, London, 263, 1095–1102.Google Scholar
  4. Berner T. O., Grubb T. C. Jr. (1985) An experimental analysis of mixed-species flocking in birds of deciduous woodland. Ecology 66: 1229–1236CrossRefGoogle Scholar
  5. Bleckmann H. (1993) Role of the lateral line in fish behavior. In: Pitcher T. J. (eds) The behavior of teleost fishes, 2nd ed. Chapman and Hall, London, pp 211–246Google Scholar
  6. Breder C. M. Jr. (1967) On the survival value of fish schools. Zoologica 52: 25–40Google Scholar
  7. Brown G. E. (2003) Learning about danger: Chemical alarm cues a local risk assessment in prey fishes. Fish and Fisheries 4(3): 227–234CrossRefGoogle Scholar
  8. Brown C., Laland K. N. (2003) Social learning in fishes: A review. Fish and Fisheries 4(3): 280–288CrossRefGoogle Scholar
  9. Buchanan J. M. (1965) An economic theory of clubs. Economica 32: 1–14CrossRefGoogle Scholar
  10. Caraco T., Wolf L. L. (1975) Ecological determinants of group sizes of foraging lions. The American Naturalist 109(967): 343–352CrossRefGoogle Scholar
  11. Clark C. W. (1987) The lazy, adaptable lions: A Markovian model of group foraging. Animal Behaviour 35: 361–368CrossRefGoogle Scholar
  12. Clark C. W., Mangel M. M. (1984) Foraging and flocking strategies: Information in an uncertain environment. The American Naturalist 123: 625–641CrossRefGoogle Scholar
  13. Clark C. W., Mangel M. M. (1986) The evolutionary advantages of group foraging. Theoretical Population Biology 30: 45–75CrossRefGoogle Scholar
  14. Cosmides L., Tooby J. M. (1994) Better than rational: Evolutionary psychology and the invisible hand. The American Economic Review 84: 327–332Google Scholar
  15. Davis M. W., Olla B. L. (1994) The role of visual cues in the facilitation of growth in a schooling fish. Environmental Biology of Fishes 34(4): 421–424CrossRefGoogle Scholar
  16. Dawkins R. (1989) The selfish gene. Oxford University Press, OxfordGoogle Scholar
  17. Dawkins R., Krebs J. R. (1979) Arms races between and within species. Proceedings of the Royal Society of London Series B 205: 489–511CrossRefGoogle Scholar
  18. Deng, J., & Shao, X. M. (2006). Hydrodynamics in a diamond-shaped fish school. Journal of Hydrodynamics Series B, 18(3, Supplement 1), 438–442.Google Scholar
  19. Dill L. M. (1987) Animal decision making and its ecological consequences: The future of aquatic ecology and behavior. Canadian Journal of Zoology 65: 803–811CrossRefGoogle Scholar
  20. Duffy D. C., Wissel C. (1988) Models of fish school size in relation to environmental productivity. Ecological Modeling 40: 201–211CrossRefGoogle Scholar
  21. Eggers D. M. (1976) Theoretical effect of schooling by planktivorous predators on rate of prey consumption. Journal of Fish Resource Board Canada 33: 1964–1971Google Scholar
  22. Flierl G., Grűnbaum D., Levin S., Olson D. (1999) From individuals to aggregations: The interplay between behavior and physics. Journal of Theoretical Biology 196: 397–454CrossRefGoogle Scholar
  23. Foster W. A., Treherne J. E. (1981) Evidence for the dilution effect in the selfish herd from fish predation on a marine insect. Nature 293: 466–467CrossRefGoogle Scholar
  24. Griffiths S. W. (2003) Learned recognition by conspecifics by fishes. Fish and Fisheries 4(3): 256–268CrossRefGoogle Scholar
  25. Grubb T. C. Jr. (1987) Changes in the flocking behaviour of wintering English titmice with time, weather and supplementary food. Animal Behaviour 35: 794–806CrossRefGoogle Scholar
  26. Hamilton W. D. (1971) Geometry for the selfish herd. Journal of Theoretical Biology 31: 295–311CrossRefGoogle Scholar
  27. Hara T. J. (1993) Role of olfaction in fish behavior. In: Pitcher T. J. (eds) The behavior of teleost fishes, 2nd ed. Chapman & Hall, London, pp 171–197Google Scholar
  28. Hart P. J. B. (1993) Teleost foraging: Facts and theories. In: Pitcher T. J. (eds) The behavior of teleost fishes, 2nd ed. Chapman & Hall, London, pp 253–284Google Scholar
  29. Helfman G. S. (1993) Fish behavior by day, night and twilight. In: Pitcher T. J. (eds) The behavior of teleost fishes, 2nd ed. Chapman & Hall, London, pp 479–512Google Scholar
  30. Huntington F. A. (1993) Development of behavior in fish. In: Pitcher T. J. (eds) The behavior of teleost fishes, 2nd ed. Chapman & Hall, London, pp 57–93Google Scholar
  31. Kelly J. L. (2003) Learning predator recognition and antipredator responses. Fishes 4(3): 216–226Google Scholar
  32. Krause J., Godin J.-G. J., Brown David (1996) Phenotypic variability within and between fish shoals. Ecology 77(5): 1586–1591CrossRefGoogle Scholar
  33. Krause J., Hoare D.J., Croft D., Lawrence J., Ward A., Ruxton G.D., Godin J.-G. J., James R. (2000) Fish shoal composition: Mechanisms and constraints. Proceedings the Royal Society 267: 2011–2016CrossRefGoogle Scholar
  34. Laland K. N., Brown C. (2003) Learning in fishes: From three-second memory to culture. Fish and Fisheries 4(3): 199–204CrossRefGoogle Scholar
  35. Landa J. T. (1998) Bioeconomics of schooling fishes: Selfish fish, quasi-free riders, and other fishy tales. Environmental Biology of Fishes 53: 353–364CrossRefGoogle Scholar
  36. Liao J. C., Beal D. N., Lauder G. V., Triantafyilou M. S. (2003) Fish exploiting vortices decrease muscle activity. Science 302: 1566–1569CrossRefGoogle Scholar
  37. Lobban C. S., Schefter M. (1997) Tropical pacific island environments. University of Guam Press, Mangilao, GuamGoogle Scholar
  38. Magurran A. E., Pitcher T. J. (1983) Foraging, timidity and shoal size in Minnows and goldfish. Behavioral Ecology and Sociobiology 12: 147–152CrossRefGoogle Scholar
  39. Mangel M. M., Clark C. W. (1986) Towards a unified foraging theory. Ecology 67(5): 1137–1138CrossRefGoogle Scholar
  40. Mayer, P. C. (2005). Property Rights and resource management among nonhuman species. In American Law & Economics Association 15th annual meeting, Working Paper 47. or search ‘Peter C. Mayer’ Property Rights.
  41. McNamara J. M., Houston A. I. (1986) The currency for behavioral decisions. The American Naturalist 127(3): 358–378CrossRefGoogle Scholar
  42. Mikheev V. N., Pasternak A. F. (2006) Defense behavior of fish against predators and parasites. Journal of Ichthyology 46(Supplement 2): S173–S179CrossRefGoogle Scholar
  43. Milinski M. (1993) Predation risk and feeding behavior. In: Pitcher T. J. (eds) The behavior of teleost fishes, 2nd ed. Chapman & Hall, London, pp 285–305Google Scholar
  44. Morocha P., Lauffer R. (1994) Look again, animal disguises. Compass Productions, Long Beach, CAGoogle Scholar
  45. Partridge B. L. (1982) The structure and function of fish schools. Scientific American 246(2): 114–123CrossRefGoogle Scholar
  46. Pitcher T. J. (1983) Heuristic definition of fish shoaling behaviour. Animal Behaviour 31(2): 611–613CrossRefGoogle Scholar
  47. Pitcher T. J. (1986) Functions of shoaling behavior in teleosts. In: Pitcher T. J. (eds) The behavior of teleost fishes, 1st ed. Johns Hopkins University Press, Baltimore, pp 204–337Google Scholar
  48. Pitcher T. J., Magurran A. E., Winfield I. J. (1982) Fish in larger shoals find food faster. Behavioral Ecology and Sociobiology 10: 149–151CrossRefGoogle Scholar
  49. Pitcher T. J., Parrish J. K. (1993) Functions of shoaling behavior in teleosts. In: Pitcher T. J. (eds) The behavior of teleost fishes, 2nd ed. Chapman & Hall, London, pp 363–427Google Scholar
  50. Pool R. (1995) Putting game theory to the test. Science 267: 1591–1593CrossRefGoogle Scholar
  51. Pulliam H. R., Caraco T. (1984) Living in groups: Is there an optimal group size?. In: Krebs J. R., Davies N. B. (eds) Behavioral ecology, 2nd ed. Blackwell, Oxford, pp 122–147Google Scholar
  52. Ripley. (5, November 1995). Ripley’s believe it or not. In Pacific Sunday News, Vol. 26, p. 277. Agana, Guam. from United Feature Syndicates, Inc.Google Scholar
  53. Roare D. J., Krause J. (2003) Social organization, shoal structure and information transfer. Fish and Fisheries 4(3): 269–279CrossRefGoogle Scholar
  54. Ryer C. H., Olla B. L. (1991) Agonistic behavior in a schooling fish: Form, function and ontogeny. Environmental Biology of Fishes 31: 355–363CrossRefGoogle Scholar
  55. Shaw E. (1978) Schooling fish. American Scientist 66: 166–175Google Scholar
  56. Sibly R. M. (1983) Optimal group size is unstable. Animal Behaviour 31: 947–948CrossRefGoogle Scholar
  57. Taylor R. J. (1984) Predation. Chapman and Hall, New York/LondonGoogle Scholar
  58. The Economist. (December 25, 1993–January 7, 1994). Evo-economics: Biology meets the dismal science, pp. 93–95.Google Scholar
  59. Treisman M. (1975) Predation and the evolution of gregariousness. I. Models for concealment and evasion. Animal Behaviour 23: 779–800CrossRefGoogle Scholar
  60. Warburton K. (2003) Learning of foraging skills by fish. Fish and Fisheries 4(3): 203–215CrossRefGoogle Scholar
  61. Ward, A. J. W., Botham, M. S., Hoare, D. J., James, R., Broom, M., Godin, J.-G. J., & Krause, J. (2002). Association patterns and shoal fidelity in the three-spined stickleback. Proceedings Royal Society, 269, 2451–2455.Google Scholar
  62. Weihs D. (1973) Hydromechanics of fish schooling. Nature 241: 290–291CrossRefGoogle Scholar
  63. Weihs D. (1975) Some hydrodynamical aspects of fish schooling. In: Wu T. Y. T., Brokaw C. J., Brennen C. (eds) Swimming and flying in nature. Plenum Press, New York, pp 703–718Google Scholar
  64. Weihs D., Webb P. M. (1983) Optimization of locomotion. In: Weihs D., Webb P. W. (eds) Fish biomechanics. Praeger Press, New York, pp 339–371Google Scholar
  65. Wilson M. (2006) Acoustic-waveguide sonar finds enormous fish shoals. Physics Today 59(4): 20–26CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  1. 1.Mangilao ConsultingGuamUSA

Personalised recommendations