Abstract
This is work is focused on the role of diffusive interaction between separate habitats in a patchy environment in plankton pattern formation. We demonstrate that conceptual reaction-diffusion mathematical models constitute an appropriate tool for searching and understanding basic mechanisms of plankton pattern formation and complex spatio-temporal plankton dynamics.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Abbot M R and Zion P M 1985 Satellite observations of phytoplankton variability during an upwelling event;Continental Shelf Res. 4 661–680
Allen J C, Scheffer W M and Rosko D 1993 Chaos and extinction in ecological populations;Nature (London) 364 229–232
Angel M V and Fasham M J R 1983 Eddies and biological processes; inEddies in marine science (ed.) A R Robinson (New York: Springer) 492–524
Armi L, Hebert D, Oakey N, Price J, Richrdson P L, Rossby T and Ruddick B 1988 The history and decay of a Mediterranean salt lens;Nature (London) 333 649–651
Armi L and Zenk W 1984 Large lenses of highly saline Mediterranean water;J. Phys. Oceanogr. 14 1560–1576
Barenblatt G I 1996Scaling, self-similarity, and intermediate asymptotics (Cambridge: Cambridge University)
Barenblatt G I, Galerkina N I and Luneva M V 1987 Evolution of a localized turbulent burst;Inzhenerno-fizichesky J. 53 733–740
Barnard A H, Stegmann P M and Yoder J A 1997 Seasonal surface variability in the South Atlantic Bight derived from CZCS and AVHRR imagery;Continental Shelf Res. 17 1181–1206
Barth J A 1989 Stability of a coastal upwelling front. I. Model development and a stability theorem;J. Geophys. Res. 94 10844–10856
Bucklin A 1991 Population genetic responses of the planktonic copepodMetridia pacifica to a coastal eddy in the California Current;J. Geophys. Res. 96 14799–14808
Capella J E, Quetin L B, Hofmann E E and Ross R M 1992 Models of the early life history ofEuphausia superba. Part II. Lagrangian calculations;Deep-Sea Res. 39 1201–1220
Denmann K L 1976 Covariability of chlorophyll and temperature in the sea;Deep-Sea Res. 23 539–550
Fasham M J R 1978 The statistical and mathematical analysis of plankton patchiness;Oceanogr. Mar. Biol. Annu. Rev. 16 43–79
Fedorov K N 1983Physical nature and structure of the ocean fronts (Leningrad: Gidrometeoizdat)
Fedorov K N and Ginzburg A I 1988The subsurface layer in the ocean (Leningrad: Gidrometeoizdat)
Fiedler P C and Bernard H J 1987 Tuna aggregation and feeding near fronts observed in satellite imagery;Continental Shelf Res. 7 871–881
Foster T D 1974 The hierarchy of convection; inColloques Intern. Du CNRS 115.Processus de formation des eaux oceaniques profondes en particulier en Mediterranee occidentale (Paris) pp 237–241
Garfinkel A, Spano M, Ditto W and Weiss J 1992 Controlling cardiac chaos;Science 257 1230–1235
Hastings A 1993 Complex interactions between dispersal and dynamics: lessons from coupled logistic equations;Ecology 74 1362–1372
Haury L R, Simpson J J, Pelaez J, Koblinsky C J and Weisenhahn D 1986 Biological consequences of a recurrent eddy off Pont Conception, California;J. Geophys. Res. 91 12937–12956
Hayward T L and Mantyla A W 1990 Physical, chemical and biological structure of a coastal eddy near Cape Mendocino;J. Mar. Res. 48 825–850
Hofmann E E, Capella J E, Ross R M and Quetin L B 1992 Models of the early life hystory ofEuphausia superba. Part I. Time and temperature dependence during the descent-ascent cycle;Deep-Sea Res. 39 1177–1200
Hood R R, Abbott M R, Huyer A and Kosro P M 1990 Surface patterns in temperature, flow, phytoplankton biomass and species composition in the coastal transition zone off northern California, June to August 1988;J. Geophys. Res. 95 18081–18094
Huisman J and Weissing F J 1999 Biodiversity of plankton by species oscillations and chaos;Nature (London) 402 407–410
Jenkinson I R and Biddanda B A 1995 Bulk-phase viscoelastic properties of seawater: relationship with plankton components;J. Plankt. Res. 17 2251–2274
Joseph D D 1976Springer tracts in natural philosophy 27/28.Stability of fluid motion (Berlin: Springer)
Jörgensen S E 1994Fundamentals of ecological modelling (Amsterdam: Elsevier)
Kamenkovich V M, Koshlyakov M N and Monin A S 1987Synoptic eddies in the ocean (Leningrad: Godrometeoizdat)
Kostianoy A G and Belkin I M 1989 A survey of observations on intrathermocline eddies in the world ocean; inElsevier oceanography series 50Mesoscale/Synoptic coherent structures in geophysical turbulence (eds) J C J Nihoul and B M Jamart (Amsterdam: Elsevier) pp 821–841
Laurs R M, Fidler P C and Montgomery D R 1984 Albacore tuna catch distributions relative to environmental features observed from satellites;Deep-Sea Res. 31 1085–1099
Lipsitz L and Goldberger A 1992 Loss of complexity and aging: potential applications of fractals and chaos theory to senescence;J. Am. Med. Assoc. 267 1806–1809
Mackas D L, Washburn L and Smith S L 1991 Zooplankton community pattern associated with a California Current cold filament;J. Geophys. Res. 96 14781–14797
MacKenzie B R, Miller T J, Cyr S and Leggett W C 1994 Evidence for a dome-shaped relationship between turbulence and larval fish ingestion rates;Limnol. Oceanogr. 39 1790–1799
Malchow H and Shigesada N 1994 Nonequilibrium plankton community structures in an ecohydrodynamic model system;Nonlinear Processes in Geophys. 13–11
Marks-Tarlow T 1999 The self as a dynamical system;Nonlinear Dynamics Psychol. Life Sci. 3 311–345
Marrase C, Saiz E and Redondo J M (eds) 1997Scientia Marina 61 (Suppl. 1)Lectures on plankton and turbulence (Barcelona: International Centre for Coastal Resources Research)
Medvinsky A B, Petrovskii S V, Tikhonov D A, Tikhonova I A, Ivanitsky G R, Venturino E and Malchow H 2001 Biological factors underlying regularity and chaos in aquatic ecosystems: Simple models of complex dynamics;J Biosci. 26 77–108
Monin A S, Kamenkovich V M and Kort V G 1974Variability of the World Ocean (Leningrad: Gidrometeoizdat)
Monin A S and Krasitskii V P 1985Phenomena on the ocean surface (Leningrad: Gidrometeoizdat)
Monin A S and Ozmidov R V 1981Ocean turbulence (Leningrad: Gidrometeoizdat)
Nihoul J C J (ed.) 1980Elsevier oceanography Series 28.Marine Turbulence (Amsterdam: Elsevier)
Nisbet R M, Briggs C J, Gurney W, Murdoch W W and Stewart-Oaten A 1993 Two-patch metapopulation dynamics; inLecture notes in biomathematics 96Patch dynamics (eds) S A Levin, T M Powell and J H Steele (Berlin: Springer)
Njoku E G, Barnett T P, Laurs R M and Vastano A C 1985 Advances in satellite sea surface temperature measurements and oceanographic applications;J. Geophys. Res. 90 11573–11586
Okubo A 1971 Oceanic diffusion diagrams;Deep-Sea Res. 18 789–802
Okubo A 1980Biomathematics 10.Diffusion and ecological problems. Mathematical models (Berlin: Springer)
Okubo A 1986 Dynamical aspects of animal grouping: swarms, schools, flocks and herds;Adv. Biophys. 22 1–94
Ozmidov R V 1966 Scales in ocean turbulence;Oceanology 6 393–398
Ozmidov R V 1968Horizontal turbulence and turbulent exchange in the ocean (Moscow: Nauka)
Pahl-Wostl C 1993 The influence of a hierarchy in time scales on the dynamics of, and the coexistence within, ensembles of predator-prey pairs;Theor. Popul. Biol. 43 159–183
Pedlosky J 1987Geophysical fluid dynamics (Berlin: Springer)
Pedlosky J 1996Oceanic circulation theory (Berlin: Springer)
Phillips O M 1977The dynamics of the upper ocean (Cambridge: Cambridge University)
Pond S and Piskard G L 1978Introductory dynamic oceanography (Oxford: Pergamon)
Ranta E, Kaitala V and Lundberg P 1997 The spatial dimension in population fluctuations;Science 278 1621–1623
Raymont J E G 1980Plankton and productivity in the ocean (Oxford: Pergamon)
Robinson A R (ed) 1983Eddies in marine science (New York: Springer)
Rodionov V B and Kostianoy A G 1998Ocean fronts of the North-European basin seas (Moscow: GEOS)
Scheffer M 1989 Alternative stable states in eutrophic, shallow freshwater systems: a minimal model;Hydrobiol. Bull. 23 73–83
Scheffer M 1991a Fish and nutrients interplay determines algal biomass: a minimal model;Oikos 62 271–282
Skellam J G 1951 Random dispersal in theoretical populations;Biometrika 38 196–218
Steffen E, Malchow H and Medvinsky A B 1997 Effects of seasonal perturbations on a model plankton community;Environ. Model. Assess. 2 43–48
Sur H I, Ossoy E, Ilyin Y P and Unluata U 1996 Coastal/deep ocean interactions in the Black Sea and their ecological/environmental impacts;J. Mar. Syst. 7 293–320
Sverdrup H U 1938 On the process of upwelling;J. Mar. Res. 1 115–164
The Coastal Transition Zone Group 1988 The coastal transition zone program;EOS 69 669–707
The Ring Group 1981 Gulf Stream cold core rings: their physics, chemistry and biology;Science 212 1091–1100
Vozjinskaya V B 1964 Swimming algae of the West Pacific;Oceanology 4 876–883
Walsh J J, Dieterle D A, Meyers M B and Muller-Karger F E 1989 Nitrogen exchange at the continental margin: a numerical study of the Gulf of Mexico;Prog. Oceanogr. 23 245–301
West B and Deering B 1995The lure of modern science: fractal thinking (River Edge: World Scientific)
Wiebe P H, Hulbert E M, Carpenter E J, Jahn A E, Knapp G P, Boyd S H, Ortner P B and Cox J L 1976 Gulf Stream cold core rings: large-scale interaction sites for open ocean plankton communities;Deep-Sea Res. 23 695–710
Wilson D S 1992 Complex interactions in metacommunities: with implications for biodiversity and higher levels of selection;Ecology 73 1984–2000
Wroblewski J S and O’Brien J J 1976 A spatial model of phytoplankton patchiness;Mar. Biol. 35 161–175
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Medvinsky, A.B., Petrovsk, S.V., Tikhonova, I.A. et al. Chaos and regular dynamics in model multi-habitat plankton-fish communities. J Biosci 26, 109–120 (2001). https://doi.org/10.1007/BF02708984
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02708984