Marine Biology

, Volume 54, Issue 4, pp 383–394 | Cite as

Fish school density and volume

  • T. J. Pitcher
  • B. L. Partridge
Article

Abstract

All the fish in a school occupy a volume estimated as N·BL3, where N is the number of fish and BL is their mean body length. We present extensive data from our experiments on cruising schools of saithe (Pollachius virens), herring (Clupea harengus) and cod (Gadus morhua) to validate this formula. Two methods of calculating the volumes of schools are described. One method is aggregative and depends on measuring the envelope of free space around a schooling fish, whereas the other is based on the dimensions of the school as a whole. The whole-school method is more reliable since it includes lacunae between the sub-units which exist in schools. For this method, we derive a computation which eliminates bias from outliers. The most realistic theoretical aggregative packing model predicts a volume per fish of 0.6 BL3. In saithe, the envelope of free space is approximately an ellipsoid, which, although it becomes more compressed at higher swimming speeds, yields a volume close to 0.7 BL3. From the whole-school method we calculate average volumes of 1.4 BL3 for saithe and 0.7 BL3 for herring. Increase in swimming speed produces more compact schools in saithe, but changes in arousal level can generate equally large differences. Changes in volume were not adequately explained by changes in nearest neighbour distance, giving support to the whole-school method.

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Literature Cited

  1. Bateson, W.: The sense organs and perceptions of fish; with remarks on the supply of bait. J. mar. biol. Ass. U.K. 1, 225–256 (1889)Google Scholar
  2. Breder, C.M.: Equations descriptive of fish schools and other animal aggregations. Ecology 35, 361–370 (1954)Google Scholar
  3. —: Studies of social groupings in fishes. Bull. Am. Mus. nat. Hist. 117, 397–481 (1959)Google Scholar
  4. —: Fish schools as operational structures. Fish. Bull. U.S. 74, 471–502 (1976)Google Scholar
  5. Cullen, J.M., E. Shaw and H. Baldwin: Methods for measuring the 3-D structure of fish schools. Anim. Behav. 13, 534–543 (1965)Google Scholar
  6. Cushing, D.H.: Direct estimation of a fish population acoustically. J. Fish. Res. Bd Can. 25, 2349–2364 (1968)Google Scholar
  7. —: Observations on fish schools with the ARL scanner. Rapp. P.-V. Réun. Cons. perm. int. Explor. Mer 170, 15–20 (1977)Google Scholar
  8. — and F.R. Harden-Jones: Why do fish school? Nature, Lond. 218, 918–920 (1968)Google Scholar
  9. Graves, J.: Photographic method for measuring spacing and density within pelagic fish schools at sea. Fish Bull. U.S. 75, 230–233 (1977)Google Scholar
  10. Hamilton, W.D.: Geometry for the selfish herd. J. theor. Biol. 31, 295–311 (1971)Google Scholar
  11. Hewitt, R.P., P.E. Smith and J.C. Brown: Developments and use of sonar mapping for pelagic stock assessment in the California current area. Fish. Bull. U.S. 74, 281–300 (1976)Google Scholar
  12. Holliday, D.V.: Two applications of the Doppler effect in the study of fish schools. Rapp. P.-v. Réun. Cons. perm. int. Explor. Mer 170, 21–30 (1977)Google Scholar
  13. Hunter, J.R.: Procedure for analysis of schooling behavior. J. Fish. Res. Bd Can. 23, 547–562 (1966)Google Scholar
  14. Keenleyside, M.: Aspects of schooling behaviour in fish. Behaviour 8, 83–248 (1955)Google Scholar
  15. Kendall, M.G. and P.A.P. Moran: Geometrical probability, 125 pp. London: C. Griffin 1963Google Scholar
  16. Parr, E.A.: A contribution to the theoretical analysis of the schooling behavior of fishes. Occ. Pap. Bingham oceanogr. Colln 1, 1–32 (1927)Google Scholar
  17. Partridge, B.L.: Sensory aspects of schooling, 550 pp. Dissertation, University of Oxford 1978Google Scholar
  18. Partridge, B.L.: The effects of size on the 3-D structure of minnow schools. Anim. Behav. (In press). (1979)Google Scholar
  19. — and T.J. Pitcher: Evidence against the hydrodynamical function of fish schools. Nature, Lond. 279, 418–419 (1979)Google Scholar
  20. Partridge, B.L., T.J. Pitcher, J.M. Cullen and J. Wilson: The three dimensional structure of fish schools. Behavl Ecol. Sociobiol. (In press). (1979)Google Scholar
  21. Pitcher, T.J.: The 3-dimensional structure of schools in the minnow, Phoxinus phoxinus. Anim. Behav. 21, 673–686 (1973)Google Scholar
  22. —: A periscopic method for determining the 3-D positions of fish in schools. J. Fish. Res. Bd Can. 32, 1533–1538 (1975)Google Scholar
  23. —: Sensory information and the organisation of behaviour in a shoaling cyprinid fish. Anim. Behav. 27, 126–149 (1979)Google Scholar
  24. Pitcher, T.J. and B.L. Partridge: The structure, sensory basis and sociobiology of fish schools. New Scient. (In press). (1979)Google Scholar
  25. —— and C.S. Wardle: A blind fish can school. Science, N.Y. 194, 963–965 (1976)Google Scholar
  26. Radakov, D.V.: Schooling in the ecology of fish, 173 pp. New York: John Wiley & Sons 1973. (Israeli Translation Series)Google Scholar
  27. Rottingen, I.: On the relation between echo intensity and fish density. FiskDir. Skr. (Ser. Havunders.) 16, 301–314 (1976)Google Scholar
  28. Serebrov, L.I.: Relationship between school density and size of fish. J. Ichthyol. 15, 135–140 (1976)Google Scholar
  29. Shaw, E.: The development of schooling behaviour in fishes. Physiol. Zoöl. 33, 79–86 (1960)Google Scholar
  30. —: The optomotor response and the schooling of fish. Spec. Publs int. Commn NW. Atlant. Fish. 6, 753–779 (1965)Google Scholar
  31. Smith, P.E.: The horizontal dimensions and abundance of fish schools in the upper mixed layer as measured by sonar. In: Proceedings of an International Symposium on Biological Sound Scattering in the Ocean, pp 563–591 Ed. by G.B. Farquhar. Washington, D.C.: Department of the Navy 1970Google Scholar
  32. Squire, J.L.: Northern anchovy school shapes as related to problems in school size estimation. Fish. Bull. U.S. 76, 443–448 (1978)Google Scholar
  33. Symons, P.E.: Spacing and density of schooling three spine sticklebacks (Gasterosteus aculeatus) and mummichog (Fundulus heteroclitus). J. Fish. Res. Bd Can. 28, 999–1004 (1971)Google Scholar
  34. Treisman, M.: Predation and the evolution of gregariousness. I. Models of concealment and evasion. Anim. Behav. 23, 779–800 (1975)Google Scholar
  35. Truskanov, M.D. and M.N. Scherbino: Methods of direct calculation of fish concentrations by means of hydroacoustic apparatus, paper presented to the Seminar on Fishery Biology and Oceanography, Moscow (1964); [Translation as Appendix 2, pp 594–600, in Smith (1970)]Google Scholar
  36. Weihs, D.: Hydrodynamics of fish schooling. Nature, Lond. 241, 290–291 (1973)Google Scholar
  37. —: Some hydrodynamical aspects of fish schooling. In: Proceedings of a Symposium on Swimming and Flying in Nature, held at Pasadena, Calif., July, 1974, pp 297–311. Ed. by T. Wu et al. New York: Plenum Press 1975Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • T. J. Pitcher
    • 1
  • B. L. Partridge
    • 2
  1. 1.School of Biological and Environmental StudiesNew University of UlsterColeraineNorthern Ireland
  2. 2.Department of Experimental PsychologyUniversity of OxfordOxfordEngland

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