“A Multidimensional Continuum Model of Fish Population Dynamics and Behaviour: Application to the Barents Sea Capelin (Mallotus Villosus)”

Authors: Mark Reed and Jens G. Balchen,
Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 1982, Vol 3, No 2, pp. 65-109.

Keywords: Capelin, fishery dynamics, fish populations, population dynamics, ecosystem modeling, fish migration, fish behaviour, behaviour modeling

Abstract: The theoretical basis for a fishery model continuous in physical, temporal, and biological dimensions is discussed. A concrete application, constructed as one component of a larger system of physical and biological dynamic models descriptive of the Barents Sea ecosystem, is presented. Some of the potentials of such an approach are demonstrated through an example simulation of population dynamics. Simple parameterizations of other components of the ecosystem (ocean currents, temperature, sea ice, cod, marine mammals, the fishing fleet, copepods, and krill) are used to provide an ersatz environment in which to perform simulation tests.

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[1] Jens G. Balchen (2000), doi:10.4173/mic.2000.1.1
[2] Mark Reed, Malcolm L. Spaulding, Ernesto Lorda, Henry Walker and Saul B. Saila (1984), doi:10.1016/0272-7714(84)90017-9
[3] Mark Reed (1983), doi:10.1016/0304-3800(83)90039-X
[4] Keith Downing and Mark Reed (1996), doi:10.1016/S0304-3800(96)00003-8
[5] A.D. Bryant, M.R. Heath, N. Broekhuizen, J.G. Ollason, W.S.C. Gurney and S.P.R. Greenstreet (1995), doi:10.1016/0077-7579(95)90055-1
[6] Ole P. Pedersen, Dag Slagstad and Kurt S. Tande (2003), doi:10.1046/j.1365-2419.2003.00267.x
[7] C. C. E. HOPKINS and E. M. NILSSEN (1991), doi:10.1111/j.1751-8369.1991.tb00671.x
[8] Kjartan G. Magnússon, Sven Th. Sigurdsson and Eva Hlín Dereksdóttir (2005), doi:10.1016/j.nonrwa.2004.12.014
[9] Harald Gjøsæter (1998), doi:10.1080/00364827.1998.10420445
[10] Ø. FIKSEN, J. GISKE and D. SLAGSTAD (1995), doi:10.1111/j.1365-2419.1995.tb00143.x
[11] Geir Huse and Jarl Giske (1998), doi:10.1016/S0165-7836(98)00134-9
[12] A. Barbaro, B. Einarsson, B. Birnir, S. Sigurthsson, H. Valdimarsson, O. K. Palsson, S. Sveinbjornsson and T. Sigurthsson (2009), doi:10.1093/icesjms/fsp067
[13] Ketil Eiane and Domenico Parisi (2001), doi:10.1080/00364827.2001.10420486
[14] Geir Huse and Ingrid Ellingsen (2008), doi:10.1007/s10584-007-9347-z
[15] Jens G. Balchen (1994), doi:10.1007/978-94-011-0962-8_24
[16] Thomas G. Hallam, Ray R. Lassiter, Jia Li and William McKinney (1992), doi:10.1007/978-1-4757-0869-1_15
[17] R. Andrew Goodwin, Yong G. Lai, David E. Taflin, David L. Smith, Jacob McQuirk, Robert Trang and Ryan Reeves (2023), doi:10.3389/fevo.2023.703946
[1] ANDERSEN, K.P., URSIN, E. (1977). A multi-species extension of the Beverton and Holt theory of fishing, with accounts of phosphorous circulation and primary production, Meddelser fro Danmarks Fiskeri og Havandersøgelser, 7, 319-434.
[2] ANONYMOUS (1981). Ressursoversikt, Fisken og Havet.Særnummer 1, 1-52.
[3] ANONYMOUS (1979). Resource overview for 1979-1980, Ressursoversikt for 1979-1980. Fisken og Havet, Havforskningsinstituttet, Bergen, Særnummer 1.
[4] ANONYMOUS (1975). Investigating on capelin and cod in the Barents Sea during the winter of 1975, Fiskets gang, 5, 69-73.
[5] ANONYMOUS (1958). Oceanographic Atlas of the Polar Seas, Part II: ARCTIC.U.S. Navy Hydrographic Office, Washington D.C.
[6] ATKINSON, D.G., CARSCADDEN, J.E. (1979). Biological characteristics of inshore capelin, Mallotus Villosus, Müller. June-July 1977. Fish. Mar. Serv. Tech. Rep. 881: iv+ 18 p. Dept. of Fisheries Envmnt Canada.
[7] BAKKE, S., BJØRKE, H. (1973). Diving observations on Barents Sea capelin at the spawning ground off northern Norway, Fisk. Dir. Sea. Havunders., 16, 140-147.
[8] BALCHEN, J.G. (1980). Modeling and identification of marine ecological systems with applications in measurement of fish resources and planning of fisheries operations, Modeling, Ident, and Control, 1, 67-68 doi:10.4173/mic.1980.2.1
[9] BALCHEN, J.G. (1979). Modeling, prediction and control of fish behavior, pp. 99-146 in Control and Dynamic Systems, edited by C.T. Leondes.Academic Press, New York.
[10] BALCHEN, J.G. (1976). Principles of migration in fishes, SINTEF Technical report nr. 81, May 1976, 33 pp.
[11] BELTESTAD, A.K., NAKKEN, O., SMEDSTAD, O. (1975). Investigations in the diel vertical migration of O-group fish in the Barents Sea, Fisk. Sir. Ser. Ser. Havunders., 16, 229-244.
[12] BENJAMINSEN, TERJE (1979). Pup production and sustainable yield of white sea harp seals, Fisk. Dir. Skr. Sea. Havunders., 16, 551-559.
[13] BERNTSEN, HANS, et al. (1981). Efficient numerical simulation of ocean hydrodynamics by a splitting procedure, Modeling, Indent., and Control, 2, 181-199 doi:10.4173/mic.1981.4.1
[14] VON BERTALANFFY, L. (1938). A quantitative theory of organic growth laws, Inquiries on Growth Laws II. Human Biology, 10, 181-213.
[15] BEYER, J.E., LAURENCE, G.C. (1979). Modelling growth and mortality of larval herring, Clupea harengus. Early Life History Symposium, Woods Hole, Mass./M:6.
[16] BJØRKE, H. (1976). Some preliminary results on food and feeding of young capelin larvae, ICES CM. 1976/H: 37, Pelagic Fish.Northern Committee.
[17] BJØRKE, J., GJØSÆTER, J., SÆTRE, R. (1972). Investigations at the spawning grounds of capelin in 1972, in Norwegian w/Engl. abstract. Fiskets Gang, 36, 710-716.
[18] BLAXTER, J.H. (1969). Development: eggs and larvae, Pp. 178-252 in Fish Physiology, Vol. III, edited by W.S. Hoar and D.J. Randall.Academic Press, New York.
[19] BLAXTER, J.H.S. (1969). Swimming speeds of fish, FAO Fish. Rep. 62, Vol. 2, 69-100.
[20] BLAXTER, J., STAINES, M. (1971). Food searching in marine fish larvae, 4th European Biology Symposium, edited by J. Crisp.Comb. Univ. Press, pp. 467-485.
[21] BLAXTER, J., HEMPEL, G. (1963). The influence of egg size on herring larvae, J. Cons. Int. Expl. Mer., 28, 211-240.
[22] BLINDHEIM, J., MONSTAD, T. (1972). The spawning migration of capelin in 1972, Fiskets gang,.22, 519-524.
[23] CHRISTENSEN, I., RØRVIK, C.J. (1980). Analysis of markings and recaptures of minke whales in the Barents Sea 1974-1979, Inst. Marine Research, Bergen SC/32/Mi 6.
[24] CHRISTENSEN, I., RØRVIK, C.J. (1981). Availability of minke whales in the Barents Sea and adjacent waters, Inst. Marine Research, Bergen SC/32/Mi 7.
[25] DAAN, N. (1979). Comparison of estimates of egg production of the Southern Bight cod stock from plankton surveys and market statistics, Mimeo. 28 pp., ICES, Early Life History Symposium, Woods Hole, Mass.
[26] DALEN, J., DOMMASNES, A. (1974). Loddeundersøkelser i Barentshavet i mai-juni 1974, Særtrykk av Fiskets Gang, Nr. 38, 669-673.
[27] DOMMASNES, A. (1978). Survival of tagged Barents Sea capelin, Mallotus villosus, Müller and estimates of the 1973, 1974 and 1975 spawning stocks from tag returns. Fisk. Dir. Skr. Ser. Havunders., 16, 339-358.
[28] DOMMASNES, A., MIDTTUN, L., MONSTAD, T. (1979). Capelin investigations in the Barents Sea During the winter 1978, Fiskens Hav.,.1, 1-16.
[29] DOMMASNES, A., OLSEN, K. (1974). Capelin investigations in the Barents Sea in November-December 1973, Fiskets Gang, nr. 13, 257-261.
[30] DRAGESUND, O., GJØSÆTER, J., MONSTAD, T. (1973). Estimates of stock size and reproduction of the Barents Sea capelin 1970-1972, Fisk. Dir. Havunders., 16, 105-139.
[31] DRAGESUND, O. (ed.) (1970). International 0-group fish surveys in the Barents Sea 1965-1968, ICES Cooperative Research Report. Series A, No. 18.
[32] EBENHÖH, W. (1980). A model of the dynamics of plankton patchiness, Modeling, Indent., and Control, 1, 69-81 doi:10.4173/mic.1980.2.2
[33] EHRLICH, K., BLAXTER, J., PEMBERTON, R. (1976). Morphological and histological changes during the growth and starvation of herring and plaice larvae, Mar. Biol., 35, 105-118 doi:10.1007/BF00390932
[34] ERVIK, LEIF K., ROMAN, R.C. (1975). The capelin population and exploration - a dynamic analysis, Chr. Michelsens Inst. Report 75056-1, Bergen, Norway, 212 pp.
[35] FALK-PETERSEN, S. (1979). Populasjonsdynamikk, Vektstrategi, Protein- og Lipidinnhold hos Krillartene Thyanoessa Intermis (Krøyer), Thysanoessa Raschii (M, Sars) and Meganyctiplanes Norwegica (M. Sars). Fra Balsfjorden Nord-Norge. Ph.D. Thesis, University of Tromsø (in Norwegian), 121 pp.
[36] FRANK, J.T., LEGGETT, W.C. (1981). Wind regulation of emergence times and early larval survival in capelin, Mallotus villosus. Can. J. Fish Quat. Sci, 38, 215-228.
[37] FRIDGEIRSSON, EYJOLFUER (1976). Observations on spawning behavior and embryonic development of the Icelandic capelin, Rit Fiskideildan, 5,36 pp.
[38] GALL, G. (1974). Influence of size of eggs and age of females on hatchability and growth in rainbow trout, Calif. Fish and Game J.,.1, 26-35.
[39] GJØSÆTER, J., MONSTAD, T. (1973). Fecundity and egg size of spring spawning Barents Sea capelin, Fisk. Dir. Havunders., 16, 98-104.
[40] GJØSÆTER, J. (1972). Recruitment of the Barents Sea capelin 1951-1961, ICES C.M. 1972/H:24.
[41] GJØSÆTER, J., MIDTTUN, MONSTAD, T., NAKKEN, O., SMEDSTAD, O., SÆTRE, R., ULLTANG, O. (1972). Investigations of fish distribution and abundance in the Barents Sea and off Spitsbergen in August-September 1972, Fiskets Gang, 51, 1010-1021.
[42] GULLAND, J.A. (1964). Survival of the youngest stages of fish and its relation to year class strength, ICNAF Spec. Publ. 6, pp. 363-372.
[43] HAMRE, J., MONSTAD, T. (1980). Capelin investigations in the Barents sea during winter 1980, Fisken Hav., (5), 3-22 (in 1979). Fisken Hav., (4), 3-17.
[44] HAMRE, J., SÆTRE, R. (1976). The spawning migration of capelin during the winter of 1976, Fisken Hav,.2, 43-51.
[45] HARDEN JONES, F.R. (1968). Fish Migration, Edward Arnold, London, 325 pp.
[46] HARVEY, J. (1964). Factors Affecting Water Temperature in the Seas North of Norway, ICNAF Spec. Publ. 6, 869-879.
[47] HIMMELBLAU, D.M., BISCHOFF, K.B. (1968). Process Analysis and Simulation in Deterministic Systems, J. Wiley and Sons, New York, 348 pp.
[48] HJORT, JOHAN (1914). Fluctuations in the Great Fisheries in Northern Europe, Viewed in the Light of Biological Research. Com. Perm. Int. Exp. Mer. Rapp. et Proc. Verb., 20, 228 pp., 137 figs.
[49] HOCHARKA, P.W., SOMERS, G.N. (1971). Biochemical adaptations to the environment, Chapter 2, pp. 100-156 in Fish Physiology, Vol. VI, edited by W. S. Hoar and D. J. Randall.Academic Press, New York.
[50] JAKOBSEN, T. (1978). Skreiinnsiget i Lofoten i 1976, Fisken Hav.,.1, 1-8.
[51] JAKOBSEN, T. (1978). Skreiinnsiget i Lofoten i 1977, Fisken Hav,.1, 9-19.
[52] JANGAARD, P.M. (1974). The capelin, Mallotus villosus: biology, distribution, exploitation, utilization, and composition. Dept. of the Environment, Fisheries and Marine Service, Ottawa, Canada.
[53] JEFFERS, C.W. (1931). The Life History of the Capelin Mallotus villosus, Ph.D. Thesis, Univ. of Toronto, Ontario, Ca., 86 pp.
[54] JOHNSTONE, R., SIMPSON, T.H., YOUNGSSON, A.F. (1977). Sex reversal in salmonid culture, Aquaculture, 13 (1978), 115-134 doi:10.1016/0044-8486(78)90106-0
[55] JONES, R. (1979). Simulation Studies of the Larval Stage and Observations on the First Two Years of Life, w/Particular Reference to the Haddock, ICES/ELH SYMP/M:l. Woods Hole ELM Symposium, April 1979, Mimeo.
[56] JONES, R., HALL, R. (1973). A simulation model for studying the population dynamics of some fish species, Pp. 35-39 in The Mathematical Theory of the Dynamics of Biological Populations, edited by Partlett and Hiorns.Academic Press, New York, 347 pp.
[57] KERR, S.R. (1971). A simulation model of lake trout growth, J. Fish. Res. Bd. Canada, 28, 815-819.
[58] LAEVASTU, T., FAVORITE, F., LARKINS, H.A. (1979). Resource assessment and evaluation of the dynamics of the fisheries resources in the NE Pacific with numerical ecosystem models, U.S. Dept. Commerce, NOAA, NMFS, North-west and Alaska Fisheries Cenls, Seattle, WA 98112, 35 pp.
[59] LARRICK, S.R., DICKSON, K.L., CHERRY, D.S., CAINS, J., JR. (1978). Determining fish avoidance in polluted waters, Hydrobiologica, 61, 257-265 doi:10.1007/BF00044451
[60] LOENG, H. (1979). A review of the sea ice conditions of the Barents Sea and the area west of Spitsbergen, Fisken Hav.,.2, 29-75.
[61] LOENG, H. (1981). Distributions of adult capelin in relation to temperature, Fisken Hav.,.6, 10-17.
[62] LUND, A. (1981). Food of capelin, Mallows Villosus (Müller) in the Barents Sea (Ernæring hos lodde, Mallotus villosus (Müller) i Barentshavet, Ph.D. Thesis, Inst. for Fisheries Biology in Bergen, 128 pp.
[63] MARR, J.C. (1955). The ´critical period´ concept in the early life history of marine fishes, Cons. Perm. Inst. Exp. Mer., Journal du Cons., 21,160-170.
[64] MARSHALL, S.M., ORR, A.P. (1972). The biology of a marine copepod, Springer-Verlag, Berlin, 195 pp.
[65] MATUDA, K., SANNOMYA, N. (1980). Computer simulation of fish behavior in relation to fishing gear - I Bull, Japanese Soc. Scientific Fisheries, 46, 689-699.
[66] MILLER, R., MCINERNEY, M. (1978). Packing Density and Swimming Speed of Schooling Capelin, Mallotus villosus. ICES C.M. 1978/B:26. Fishing Technology Committee.
[67] MILSUM, J.H., ROBERGE, F.A. (1973). Physiological regulation and control, Pp. 1-96 in Foundations of Mathematical Biology, Vol. III, edited by R. Rosen.Academic Press, N.Y., 412 pp.
[68] MONSTAD, T. (1971). Alder, vekst og utbredelse av lodde i Barentshavet og ved kysten av Nord-Norge 1968-1970, Thesis (Cand. real), Univ. i Bergen, Norge (mimeo).
[69] MONSTAD, T., KOVALYOV, S.M. (1973). Capelin investigations in the Barents Sea in November-December 1972, Fiskets Gang, 17, 350-353.
[70] MØLLER, D., OLSEN, S. (1962). Norwegian capelin investigations, ICES Distant North Seas C.M. 1962, No. 34, 10 pp. + figs.
[71] NAKKEN, O., DOMMASNES, A. (1977). Acoustic estimates of the Barents Sea, Capelin stock 1971-1976. ICES C.M. 1977/H:35; 10 pp.
[72] NOVITSKIY, V.P. (1961). Permanent Currents of the Northern Barents Sea, Trans. from Russian by U.S. Naval Oceanographic Office, Wash. D.C. 1967.
[73] OLSEN, S. (1968). Some Results of the Norwegian Capelin Investigations 1960-65, ICES Rapp. P.-v. Rena Cons. Perm. Int. Exp. Mer., 158, 18-23.
[74] PONOMORENKO, V., PONOMORENKO, I., YARAGINA, N. (1978). Consumption of the Barents Sea Capelin by Cod and Haddock in 1975-1976, .
[75] PONOMORENKO, I.Y., YARAGINA, N.A. (1978). Year to Year and Seasonal Fluctuations in the Feeding of the Barents Sea Cod on Capelin in 1947-1976, ICES Demensal Fish Committee C.M. 1978/G:24.
[76] PRIVOLNEV, T.I., GALKINA, Z.I., GALKIN, G.G. (1964). Effect of the Size of Their Eggs on the Offspring, Reported in Biological Abstracts,.48; 11215,1967.
[77] PROKHOROV, V.S. (1968). Materials on the ecology of capelin in the Barents Sea, Rapp. P.-v. Reun. Cons. Peim. Inst. Exp. Merk., 158, 23-31, 1965.
[78] PROKHOROV, V.S. (1965). Ecology of the Barents Sea capelin, Mallotus Villosus and the Prospect of its Industrial Utilization. Translated by Foreign Languages Division, Fisheries Research Board of Canada, St. John´s, Newfoundland, 1967, Transaction Series No. 813.
[79] PROKHROV, V.S. (1960). Post-spawning survival of the Barents Sea capelin, ICES C.M. 1960, no. 165.
[80] REED, M., SPAULDING, M.L., CORNILLON, P. (1981). A fishery-oilspill interaction model: simulated consequences of a blowout, pp. 99-114 in Applied Operations Research in Fishing, edited by K. B. Haley.Plenum Press, N.Y., 490 p.
[81] REED, M., SPAULDING, M.L., CORNILLON, P. (1980). An oilspill-fishery interaction model: formulation and applications, U. Rhode Island, Dept. Ocean Engineering, Kingston, RI, USA 02879, 220 pp.
[82] RØRVIK, C.J. (1981). Simulations of the northeast Atlantic stock of minke whales, Bergen, Inst. Marine Research SC/32/Mi. 8., 18 pp.
[83] RØRVIK, C.J., CHRISTENSEN, I. (1980). Considerations of factors affecting the use of catch per unit effort in the Norwegian minke fishery for stock estimates, Inst. Marine Research, Bergen Sc/32/Mi. 9, 14 pp.
[84] SANNOMIYA, N., MATUDA, K. (1981). Modeling of fish behavior in relation to fishing, 25 pp., paper submitted.presented at the IFAC VIIIth World Congress.
[85] SÆTRE, R., GJØSÆTER, J. (1975). Ecological Investigations on the spawning grounds of the Barents Sea capelin, Fiskeri Direktorat Skriv. Undersøk, 16, 203-227.
[86] SHULGA, A.D., BELUSOV, V.V. (1976). Dependence of certain biological characteristics of the Barents Sea capelin on the temperature regime, ICES, Pelagic Fish.Northern Committee C.M. 1976/H:5.
[87] SLAGSTAD, D. (1980). Modeling and simulation of physiology and population dynamics of copepods, effects of physical and biological parameters, Norwegian Technical University, Division of Engineering Cybernetics, Ph.d. Thesis, 179 pp.
[88] STEPANOV, A.S., CHURMASOV, A.V., CHERKASHIN, S. (1979). Migration Direction Finding by Chum Salmon According to the Sun, Soviet Journal of Marine Biology, 5, 92-99.
[89] STOTT, B., BUCKLEY, B.R. (1979). Avoidance experiments with shoals of minnows, Phoxinus phoxinus, in a laboratory stream channel, J. Fish. Biol., 14, 135-146.
[90] VILHJALMSON, H. (1974). Ransøknir a lodnusynum in afla veidi- og ransøknaskipa a timabilinu januar-april 1974, Lo uveidanar, 1974, Reykjavik..Reported by Fridgeirsson, 1976.
[91] VILHJALMSON, H. (1968). A contribution to the knowledge of the Icelandic capelin, ICES Rapp. Reun. Cons. Perm. exp. Mer, 158, 32-38.
[92] WEBB, P.W. (1977). Effects of size on performance and energetics of fish, In Scale Effects in Animal Locomotion.Academic Press, London, edited by J. T. Pedley, pp. 315-331.
[93] WEBB, P.W. (1975). Hydrodynamics and energetics of fish propulsion, Dept. of the Envmnt, Fisheries and Marine Center, Ottawa, Canada, 159 pp.
[94] WEIHS D. (1973). Hydrodynamics of fish schooling, Nature, 241, 290-291. Optimal cruising speed for migrating fish; ibid., 245, 48-50.
[95] WIBORG, K.F. (1954). Investigations on zooplankton on coastal and offshore waters of western and northwestern Norway, with special reference to copepods, Fiskeridirektoratets Skrifter Ser. Havunders., XI.1.
[96] WINTERS, G., CASCADDEN, J. (1978). Review of capelin ecology and estimation of surplus yield from predator dynamics, ICNAF Res. Bull., 13, 21-29.
[97] ZENKEVITCH, L. (1963). Biology of the Seas of the USSR, Academic Press, London, 931 pp.

  title={{A Multidimensional Continuum Model of Fish Population Dynamics and Behaviour: Application to the Barents Sea Capelin (Mallotus Villosus)}},
  author={Reed, Mark and Balchen, Jens G.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}