Discrete and continuous models of the dynamics of pelagic fish: Application to the capelin

Mathematics and Computers in Simulation

Volumn 79, Issue 12, 2009, Pages 3397-3414

  Barbaro, Alethea B T ^a   Taylor, Kirk ^c   Trethewey, Peterson F ^a,b   Youseff, Lamia ^b   Birnir, Björn ^d  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b University of California   (United States)

^c San Marcos High School   (United States)

^d UNIVERSITY OF ICELAND   (Iceland)

Author keywords

Capelin; Fish schooling; Interacting particle model; Migration; Swarming

Indexed keywords

CAPELIN; COLLECTIVE BEHAVIOR; COLLECTIVE MOTIONS; CONTINUOUS MODELS; DISCRETE MODELS; DISCRETE SYSTEMS; INTERACTING PARTICLE MODEL; INTERACTING PARTICLES; LONG-TERM BEHAVIOR; MIGRATION; PELAGIC FISH; PHYSICAL REVIEW; SELF-DRIVEN; SELF-PROPELLED PARTICLES; STATISTICAL PHYSICS; SWARMING; SWARMING BEHAVIOR;

BIOLOGY; FISH; MEATS; ORDINARY DIFFERENTIAL EQUATIONS; PHASE TRANSITIONS; STATISTICAL MECHANICS;

MATHEMATICAL MODELS;

EID: 67651146401     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2008.11.018     Document Type: Article

References (29)

1. A.B.T. Barbaro, P.F. Trethewey, L.M. Youseff, B. Birnir, J. Gilbert, Parallel modeling of fish interaction, in preparation.
2. Birnir B. An ODE model of the motion of pelagic fish. Journal of Statistical Physics 128 1/2 (2007) 535-568
3. Chuang Y.-L., D'Orsogna M.R., Marthaler D., Bertozzi A.L., and Chayes L.S. State transitions and the continuum limit for a 2D interacting, self-propelled particle system. Physica D 232 (2007) 33-47
4. Couzin I., Krause J., James R., Ruxton G., and Franks N. Collective memory and spatial sorting in animal groups. Journal of Theoretical Biology 218 (2002) 1-11
5. Czirók A., Stanley H., and Vicsek T. Spontaneously ordered motion of self-propelled particles. Journal of Physics A: Mathematical General 30 (1997) 1375-1385
6. Czirók A., and Vicsek T. Collective behavior of interacting self-propelled particles. Physica A 281 (2000) 17-29
7. Flierl G., Grünbaum D., Levin S., and Olson D. From individuals to aggregations: the interplay between behavior and physics. Journal of Theoretical Biology 196 (1999) 397-454
8. Gurney W.S.C., and Nisbet R.M. Ecological Dynamics (1998), Oxford University Press, New York
9. Hemelrijk C.K., and Kunz H. Density distribution and size sorting in fish schools: an individual-based model. Behavioral Ecology 16 (2005) 178-187
10. Hubbard S., Babak P., Sigurdsson S., and Magnússon K. A model of the formation of fish schools and migrations of fish. Ecological Modelling 174 (2004) 359-374
11. Kooijman S.A.L.M. Dynamic Energy and Mass Budgets in Biological Systems (2000), Cambridge University Press, Cambridge
12. Kunz H., and Hemelrijk C.K. Artificial fish schools: collective effects of school size, body size, and body form. Artificial Life 9 (2003) 237-253
13. Kunz H., Züblin T., and Hemelrijk C.K. On prey grouping and predator confusion in artificial fish schools. Proceedings of the Tenth International Conference of Artificial Life (2006), MIT Press, Cambridge, MA
14. H. Levine, W.J. Rappel, I. Cohen, Self-organization in systems of self-propelled particles, Physical Review E 63 (017101), 2000.
15. K.G. Magnússon, S. Sigurdsson, B. Einarsson, A discrete and stochastic simulation model for migration of fish with application to capelin in the seas around Iceland, Tech. Re RH-20-04, Science Institute, University of Iceland, 2004.
16. Magnússon K.G., Sigurdsson S.T., and Dereksdóttir E.H. A simulation model for capelin migrations in the north atlantic. Nonlinear Analysis: Real World Applications 6 (2005) 747-771
17. Nisbet R.M., Muller E.B., Lika K., and Kooijman S.A.L.M. From molecules to ecosystems through dynamic energy budget models. Journal of Animal Ecology 69 (2000) 913-926
18. Partridge B.L. The structure and function of fish schools. Scientific American 246 2 (1982) 114-123
19. Partridge B.L., and Pitcher T.J. The sensory basis of fish schools: relative roles of lateral line and vision. Journal of Comparitive Physiology 135 (1980) 315-325
20. Ross A.H., and Nisbet R.M. Dynamic models of growth and reproduction of the mussel Mytilus edulis l. Functional Ecology 4 (1990) 777-787
21. C.M. Topaz, A.L. Bertozzi, Swarming dynamics of a model for biological groups in two dimensions, arXiv:nlin.AO/0306030 v1 (17 June 2003).
22. Topaz C.M., and Bertozzi A.L. Swarming patterns in a two-dimensional kinematic model for biological groups. SIAM Journal of Applied Mathematics 65 1 (2004) 152-174
23. Vicsek T., Czirók A., Ben-Jacob E., Cohen I., and Shochet O. Novel type of phase transition in a system of self-driven particles. Physical Review Letters 75 6 (1995) 1226-1229
24. Vicsek T., Czirók A., Farkas I., and Helbing D. Application of statistical mechanics to collective motion in biology. Physica A 274 (1999) 182-189
25. H. Vilhjálmsson, The Icelandic capelin stock: capelin, Mallotus villosus (Müller) in the Iceland-Greenland-Jan Mayen area, Hafrannsóknastofnunin, Reykjavík, 1994.
26. Vilhjálmsson H. Capelin (Mallotus villosus) in the Iceland-East Greenland-Jan Mayen ecosystem. ICES Journal of Marine Science 59 (2002) 870-883
27. Vilhjálmsson H., and Carscadden J.E. Assessment surveys for capelin in the Iceland-East Greenland-Jan Mayen area, 1978-2001. ICES Journal of Marine Science 59 (2002) 1096-1104
28. Viscido S.V., Parrish J.K., and Grünbaum D. Individual behavior and emergent properties of fish schools: a comparison of observation and theory. Marine Ecology Progress Series 273 (2004) 239-249
29. Viscido S.V., Parrish J.K., and Grünbaum D. The effect of population size and number of influential neighbors on the emergent properties of fish schools. Ecological Modelling 183 (2005) 347-363