, Volume 148, Issue 3, pp 538–546 | Cite as

Plankton motility patterns and encounter rates

  • André W. Visser
  • Thomas Kiørboe
Behavioural Ecology


Many planktonic organisms have motility patterns with correlation run lengths (distances traversed before direction changes) of the same order as their reaction distances regarding prey, mates and predators (distances at which these organisms are remotely detected). At these scales, the relative measure of run length to reaction distance determines whether the underlying encounter is ballistic or diffusive. Since ballistic interactions are intrinsically more efficient than diffusive, we predict that organisms will display motility with long correlation run lengths compared to their reaction distances to their prey, but short compared to the reaction distances of their predators. We show motility data for planktonic organisms ranging from bacteria to copepods that support this prediction. We also present simple ballistic and diffusive motility models for estimating encounter rates, which lead to radically different predictions, and we present a simple criterion to determine which model is the more appropriate in a given case.


Ballistic Diffusion Predator–prey interactions Random walk Reaction distance Swimming behaviour 



This study was supported by Danish Research Agency grants, 98-01-391 to AWV and KT, and 21-03-0299 to AWV. The authors also wish to thank Hans Jackobsen, Espen Bagøien and Marja Koski for data and carrying out valuable lab work.


  1. Alexander RM (2005) Models and the scaling of energy costs for locomotion. J Exp Biol 208:1645–1652CrossRefPubMedGoogle Scholar
  2. Bartumeus F, Peters F, Pueyo S, Marrasé C, Catalan J (2003) Helical Lévy walks: adjusting searching statistics to resource availability in microzooplankton. Proc Natl Acad Sci USA 100:12771–12775CrossRefPubMedGoogle Scholar
  3. Berg HC (1992) Random walks in biology. Princeton University Press, Princeton, NJGoogle Scholar
  4. Berg HC, Brown DA (1977) Chemotaxis in Escherichia coli analysed by three-dimensional tracking. Nature 239:500–504CrossRefGoogle Scholar
  5. Boudreau BP (1989) The diffusion and telegraph equations in diagenetic modelling. Goechim Cosmochim Acta 53:1857–1866CrossRefGoogle Scholar
  6. Broglio E, Johansson M, Jonsson PR (2001) Trophic interactions between copepods and ciliates: effects of prey swimming behavior on predation risk. Mar Ecol Prog Ser 220:179–186CrossRefGoogle Scholar
  7. Buskey EJ (1984) Swimming pattern as an indicator of the roles of copepod sensory systems in the recognition of food. Mar Biol 79:165–175CrossRefGoogle Scholar
  8. Buskey EJ, Stoecker DK (1988) Locomotory patterns of the planktonic ciliate Favella sp.: adaptations for remaining within food patches. Bull Mar Sci 43:783–796Google Scholar
  9. Buskey EJ, Coulter C, Strom S (1993) Locomotory patterns of microzooplankton: potential effects on food selectivity of larval fish. Bull Mar Sci 53:29–43Google Scholar
  10. Carslaw HS, Jaeger JC (1959) Conduction of heat in solids. Oxford University Press, OxfordGoogle Scholar
  11. Charnov EL (1976) Optimal foraging: the marginal value theorem. Theor Popul Biol 30:45–75Google Scholar
  12. Csanady GT (1963) Turbulent diffusion of heavy particles in the atmosphere. J Atmos Sci 20:201–208CrossRefGoogle Scholar
  13. Doall MH, Colin SP, Yen J, Strickler JR (1998) Locating a mate in 3D: the case of Temora longicornis. Phil Trans R Soc Lond B 353:681–687CrossRefGoogle Scholar
  14. Doall MH, Strickler JR, Fields DM, Yen J (2002) Mapping the free-swimming attack volume of a planktonic copepod, Euchaeta rimana. Mar Biol 140:871–879CrossRefGoogle Scholar
  15. Evans GT (1989) The encounter speed of moving predator and prey. J Plankton Res 11:415–417CrossRefGoogle Scholar
  16. Fenchel T, Blackburn N (1999) Motile chemosensory behaviour of phagotrophic protists: mechanisms for and efficiency in congregating at food patches. Protist 150:325–336PubMedGoogle Scholar
  17. Gerritsen J (1980) Adaptive response to encounter problems. In: Kerfoot WC (ed) Evolution and ecology of zooplankton communities. University Press of New England, Hanover, NH, pp 52–62Google Scholar
  18. Gerritsen J, Strickler JR (1977) Encounter probabilities and community structure in zooplankton: a mathematical model. J Fish Res Board Can 34:73–82Google Scholar
  19. Goldstein S (1963) On diffusion by discontinuous movements, and on the telegraph equation. Q J Mech Appl Math 4:129–155CrossRefGoogle Scholar
  20. Hamner WM (1990) Design developments in the planktonkreisel: a plankton aquarium for ships at sea. J Plankton Res 12:397–402CrossRefGoogle Scholar
  21. Hansen B, Bjornsen PK, Hansen PJ (1994) The size ratio between planktonic predators and their prey. Limnol Oceanogr 39:385–403CrossRefGoogle Scholar
  22. Jackson GA (1987) Simulating chemosensory responses of marine microorganisms. Limnol Oceanogr 32:1253–1266Google Scholar
  23. Jackson GA (1989) Simulation of bacterial attraction and adhesion to falling particles in an aquatic environment. Limnol Oceanogr 34:514–530Google Scholar
  24. Jakobsen HH, Halvorsen E, Hansen B, Visser AW (2005) Effects of prey motility and concentration on feeding in Acartia tonsa and Temora longicornis: the importance of feeding modes. J Plankton Res 27:763–774CrossRefGoogle Scholar
  25. Jetz W, Carbone C, Fulford J, Brown JH (2004) The scaling of animal space use. Science 306:266–268CrossRefPubMedGoogle Scholar
  26. Jonsson PR, Tiselius P (1990) Feeding behaviour, prey detection and capture efficiency of the copepod Acartia tonsa feeding on planktonic ciliates. Mar Ecol Prog Ser 60:35–44CrossRefGoogle Scholar
  27. Kamykowski D, Reed RE, Kirkpatrick GJ (1992) Comparison of sinking velocity, swimming velocity, rotation and path characteristics among six marine dinoflagellates. Mar Biol 113:319–328Google Scholar
  28. Kiørboe T, Bagøien E (2005) Motility patterns and mate encounter rates in planktonic copepods. Limnol Oceanogr 50:1999–2007Google Scholar
  29. Kiørboe T, Grossart HP, Ploug H, Tang K (2002) Mechanisms and rates of bacterial colonization of sinking aggregates. Appl Environ Microbiol 68:3996–4006CrossRefPubMedGoogle Scholar
  30. Kiørboe T, Grossart HP, Ploug H, Tang K, Auer B (2004) Particle-associated flagellates: swimming patterns, colonization rates, and grazing on attached bacteria. Aquat Microb Ecol 35:141–152CrossRefGoogle Scholar
  31. Levandowsky M, Klafter J, White BS (1988) Feeding and swimming behavior in grazing microzooplankton. J Protozool 35:243–246Google Scholar
  32. Lima S, Dill LM (1990) Behavioral decisions made under the risk of predation: a review and prospectus. Can J Zool 68:619–640CrossRefGoogle Scholar
  33. Mann J, Ott S, Pécseli HL, Trulsen J (2005) Turbulent particle flux to a perfectly absorbing surface. J Fluid Mech 534:1–21CrossRefGoogle Scholar
  34. Mitchell JG, Pearson L, Bonazinga A, Dillon S, Khouri H, Paxinos R (1995) Long lag times and high velocities in the motility of natural assemblages of marine bacteria. Appl Environ Microbiol 61:877–882PubMedGoogle Scholar
  35. Okubo A (1986) Dynamical aspects of animal grouping: swarms, schools, flocks and herds. Adv Biophys 22:1–94CrossRefPubMedGoogle Scholar
  36. Rothschild BJ, Osborn TR (1988) Small-scale turbulence and plankton contact rates. J Plankton Res 10:465–474CrossRefGoogle Scholar
  37. Saiz E, Kiørboe T (1995) Predatory and suspension feeding of the copepod Arcartia tonsa in turbulent environments. Mar Ecol Prog Ser 122:147–158CrossRefGoogle Scholar
  38. Schmitt FC, Seuront L (2001) Multifractal random walk in copepod behavior. Physica A 301:375–396CrossRefGoogle Scholar
  39. Seuront L, Hwang JS, Tseng LC, Schmitt F, Soussi S, Wong CK (2004) Individual variability in the swimming behavior of the sub-tropical copepod Oncaea venusta (Copepoda: Poecilostomatoida). Mar Ecol Prog Ser 283:199–217CrossRefGoogle Scholar
  40. Svensen C, Kiørboe T (2000) Remote prey detection in Oithona similis: hydromechanical versus chemical cues. J Plankton Res 22:1155–1166CrossRefGoogle Scholar
  41. Taylor GI (1921) Diffusion by continuous movements. Proc Lond Math Soc 20:196–212CrossRefGoogle Scholar
  42. Tiselius P (1992) Behavior of Acartia tonsa in patchy food environments. Limnol Oceanogr 37:1640–1651CrossRefGoogle Scholar
  43. Titelman J, Kiørboe T (2003) Motility of copepod nauplii and implications for food encounter. Mar Ecol Prog Ser 247:123–135CrossRefGoogle Scholar
  44. Turchin P (1998) Quantitative analysis of movement. Sinauer Press, SunderlandGoogle Scholar
  45. Uchaikin VV, Saenko VV (2001) On the theory of classical mesodiffusion. Theor Math Phys 46:139–146Google Scholar
  46. Viswanathan GM, Buldyrev SV, Havlin S, da Luz MGE, Raposo EP, Stanley HE (1999) Optimizing the success of random searches. Nature 401:911–914PubMedCrossRefGoogle Scholar
  47. Woodward G, Ebenman B, Emmerson M, Montoya JM, Olesen JM, Valido A, Warren PH (2005) Body size in ecological networks. Trend Ecol Evol 20:402–409CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Marine Ecology and AquacultureDanish Institute for Fisheries ResearchCharlottenlundDenmark

Personalised recommendations