Pattern formation in models of plankton dynamics. A synthesis

Abbott, 1993, Phytoplankton patchiness: ecological implications and observation methods, vol. 96, 37 Abraham, 1998, The generation of plankton patchiness by turbulent stirring, Nature, 391, 577, 10.1038/35361 Allee, 1931 Allee, 1949 Alt, 1990, Biological Motion, vol. 89 Ascioti, 1993, Is there chaos in plankton dynamics?, J. Plankton Res., 15, 603, 10.1093/plankt/15.6.603 Bain, 1968, Predicting DO variations caused by algae. Journal of the Sanitary Engineering Division, 867 Behrenfeldt, 1997, A consumer's guide to phytoplankton primary productivity models, Limnol. Oceanogr., 42, 1479, 10.4319/lo.1997.42.7.1479 Beltrami, 1989, A mathematical model of the brown tide, Estuaries, 12, 13, 10.2307/1351445 Beltrami, 1996, Unusual algal blooms as excitable systems: The case of “brown-tides”, Environ. Model. Assess., 1, 19, 10.1007/BF01874843 Ben-Jacob, 1992, Adaptive self-organization during growth of bacterial colonies, Physica, A87, 378, 10.1016/0378-4371(92)90002-8 Boerlijst, 1993, Evolutionary consequences of spiral waves in a host parasitoid system, Proc. R. Soc. Lond., B253, 15, 10.1098/rspb.1993.0076 Charlson, 1987, Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate, Nature, 326, 655, 10.1038/326655a0 Costantino, 1995, Experimentally induced transitions in the dynamic behaviour of insect populations, Nature, 375, 227, 10.1038/375227a0 Costantino, 1997, Chaotic dynamics in an insect population, Science, 275, 389, 10.1126/science.275.5298.389 Cushing, 1975 Daly, 1993, Physical-biological interactions influencing marine plankton production, Annu. Rev. Ecol. Syst., 24, 555, 10.1146/annurev.es.24.110193.003011 Davidson, 1998, Chaotic wakes and other wave-induced behavior in a system of reaction-diffusion equations, Int. J. Bifurcation Chaos, 8, 1303, 10.1142/S0218127498001005 DeAngelis, 1992 Denman, 1976, Covariability of chlorophyll and temperature in the sea, Deep-Sea Res., 23, 539 Dennis, 1995, Nonlinear demographic dynamics: Mathematical models, statistical methods, and biological experiments, Ecol. Monogr., 65, 261, 10.2307/2937060 Doveri, 1993, Seasonality and chaos in a plankton-fish model, Theor. Pop. Biol., 43, 159, 10.1006/tpbi.1993.1008 Droop, 1983, 25 years of algal growth kinetics, Bot. Mar. XXVI, 99, 10.1515/botm.1983.26.3.99 Dubois, 1975, A model of patchiness for prey-predator plankton populations, Ecol. Model., 1, 67, 10.1016/0304-3800(75)90006-X Duinker, 1994, Das CO2-Problem und die Rolle des Ozeans, Naturwissenschaften, 81, 237, 10.1007/BF01131574 Ebeling, 1980, Nonequilibrium phase transitions and nucleation in reacting systems, 95 Evans, 1985, A model of annual plankton cycles, Biol. Oceanogr., 3, 327 Fasham, 1978, The statistical and mathematical analysis of plankton patchiness, Oceanogr. Mar. Biol. Ann. Rev., 16, 43 Field, R.J., Burger, M. (Eds.), 1985. Oscillations and Travelling Waves in Chemical Systems. Wiley, New York Fisher, 1937, The wave of advance of advantageous genes, Ann. Eugen., 7, 355, 10.1111/j.1469-1809.1937.tb02153.x Fleming, 1939, The control of diatom populations by grazing, J. Cons. Perm. Int. Explor. Mer, 14, 210, 10.1093/icesjms/14.2.210 Franks, 1997, Spatial patterns in dense algal blooms, Limnol. Oceanogr., 42, 1297, 10.4319/lo.1997.42.5_part_2.1297 Gerisch, 1968, Cell aggregation and differentiation in Dictyostelium, vol. 3, 157 Gerisch, 1971, Periodische Signale steuern die Musterbildung in Zellverbänden, Naturwissenschaften, 58, 430, 10.1007/BF00624616 Godfray, 1997, Chaotic beetles, Science, 275, 323, 10.1126/science.275.5298.323 Greene, 1992, The migration behavior, fine structure, and bioluminescent activity of krill sound-scattering layer, Limnol. Oceanogr., 37, 650, 10.4319/lo.1992.37.3.0650 Gulland, 1977, Fish Population Dynamics Haken, 1977, Synergetics. An Introduction, vol. 1 Hallegraeff, 1988 Hensen V. (Ed.), 1892. Ergebnisse der in dem Atlantischen Ocean von Mitte Juli bis bis Anfang November 1889 ausgeführten Plankton-Expedition der Humboldt-Stiftung. Kiel und Leipzig Höfer, 1995, Cellular pattern formation during Dictyostelium aggregation, Physica, D85, 425 Holling, 1959, Some characteristics of simple types of predation and parasitism, Can. Entomol., 91, 385, 10.4039/Ent91385-7 Holmes, 1994, Partial differential equations in ecology: Spatial interactions and population dynamics, Ecology, 75, 17, 10.2307/1939378 Huisman, 1999, Biodiversity of plankton by species oscillations and chaos, Nature, 402, 407, 10.1038/46540 Ikegami, 1995, Chemotaxis toward inorganic phosphate in the red tide alga Chattonella antiqua, J. Plankton Res., 17, 1587, 10.1093/plankt/17.7.1587 Ivanitsky, 1994, From the dynamics of population autowaves generated by living cells to neuroinformatics, Physics - Uspekhi, 37, 961, 10.1070/PU1994v037n10ABEH000049 Ivlev, 1945, Biologicheskaya produktivnost' vodoemov, Usp. Sovrem. Biol. XIX, 98 Jørgensen, 1994 Kawasaki, 1995, A mathematical model of pattern formation in a bacterial colony, Control Measurement, 34, 811 Kawasaki, 1995, Modeling spatio-temporal patterns generated by Bacillus subtilis, J. Theor. Biol., 188, 177, 10.1006/jtbi.1997.0462 Keller, 1970, Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol., 26, 399, 10.1016/0022-5193(70)90092-5 Keller, 1971, Model for chemotaxis, J. Theor. Biol., 30, 225, 10.1016/0022-5193(71)90050-6 Keller, 1971, Travelling bands of chemotactic bacteria: A theoretical analysis, J. Theor. Biol., 30, 235, 10.1016/0022-5193(71)90051-8 Kierstead, 1953, The size of water masses containing plankton blooms, J. Mar. Res. XII, 141 Kolmogorov, 1937, Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, Bull. Univ. Moscou Sér. Int. Section, A1, 1 Kuznetsov, 1992, Bifurcations and chaos in a periodic predator-prey model, Int. J. Bifurcation Chaos, 2, 117, 10.1142/S0218127492000112 Leibovich, 1993, Spatial aggregation arising from convective processes, vol. 96, 110 Levin, 1976, Hypothesis for origin of planktonic patchiness, Nature, 259, 659, 10.1038/259659a0 Lewis, 1993, Allee dynamics and the spread of invading organisms, Theor. Popul. Biol., 43, 141, 10.1006/tpbi.1993.1007 Lotka, 1925 Ludwig, 1978, Qualitative analysis of insect outbreak systems: the spruce budworm and forest, J. Anim. Ecol., 47, 315, 10.2307/3939 Luther, 1906, Räumliche Ausbreitung chemischer Reaktionen, Z. Elektrochem., 12, 596, 10.1002/bbpc.19060123208 Mackas, 1979, Spectral analysis of zooplankton spatial heterogeneity, Science, 204, 62, 10.1126/science.204.4388.62 Malchow, 1993, Spatio-temporal pattern formation in nonlinear nonequilibrium plankton dynamics, Proc. R. Soc. Lond., B251, 103, 10.1098/rspb.1993.0015 Malchow, 1994, Nonequilibrium structures in plankton dynamics, Ecol. Model., 75/76, 123, 10.1016/0304-3800(94)90012-4 Malchow, 1995, Flow- and locomotion-induced pattern formation in nonlinear population dynamics, Ecol. Model., 82, 257, 10.1016/0304-3800(94)00095-Y Malchow, 1996, Nonlinear plankton dynamics and pattern formation in an ecohydrodynamic model system, J. Mar. Syst., 7, 193, 10.1016/0924-7963(95)00012-7 Malchow, 1998, Flux-induced instabilities in ionic and population-dynamical interaction systems, Z. Phys. Chem., 204, 35, 10.1524/zpch.1998.204.Part_1_2.095 Malchow, 1985, Noise and Diffusion in Bistable Nonequilibrium Systems, vol. 5 Malchow, 1994, Nonequilibrium plankton community structures in an ecohydrodynamic model system, Nonlinear Processes Geophys., 1, 3, 10.5194/npg-1-3-1994 Malin, 1997, Sulphur, climate and the microbial maze, Nature, 387, 857, 10.1038/43075 Matsushita, 1990, Diffusion-limited growth in bacterial colony formation, Physica, A168, 498, 10.1016/0378-4371(90)90402-E May, 1974, Biological populations with nonoverlapping generations: stable ponts, stable cycles and chaos, Science, 186, 645, 10.1126/science.186.4164.645 Mayzaud, 1978, The importance of the time factor in the response of zooplankton to varying concentrations of naturally occurring particulate matter, Limnol. Oceanogr., 23, 1144, 10.4319/lo.1978.23.6.1144 Merkin, 1996, Wave-induced chemical chaos, Phys. Rev. Lett., 76, 546, 10.1103/PhysRevLett.76.546 Michaelis, 1913, Die Kinetik der Invertinwirkung, Biochem. Z., 49, 333 Mimura, 1978, On a diffusive prey-predator model which exhibits patchiness, J. Theor. Biol., 75, 249, 10.1016/0022-5193(78)90332-6 Monod, 1961, General conclusions: Teleonomic mechanisms in cellular metabolism, growth and differentiation, Cold Spring Harbor Symp. Quant. Biol., 26, 389, 10.1101/SQB.1961.026.01.048 Nakata, 1975, Fluctuation of local phytoplankton abundance in coastal waters, Jpn. J. Ecol., 25, 201 Newell, 1983, Attraction and adhesion in the slime mold Dictyostelium, vol. 43, 43 Nicolis, 1977 Nitzan, 1974, Nucleation in systems with multiple stationary states, Faraday Symp. Chem. Soc., 9, 241, 10.1039/fs9740900241 O'Brien, 1973, On advection in phytoplankton models, J. Theor. Biol., 38, 197, 10.1016/0022-5193(73)90235-X Odum, 1956, Primary production in flowing waters, Limnol. Oceanogr., 1, 102, 10.4319/lo.1956.1.2.0102 Okubo, 1980, Diffusion and Ecological Problems: Mathematical Models, vol. 10 Pascual, 1993, Diffusion-induced chaos in a spatial predator-prey system, Proc. R. Soc. Lond., B251, 1, 10.1098/rspb.1993.0001 Pedley, 1992, Hydrodynamic phenomena in suspensions of swimming microorganisms, Annu. Rev. Fluid Mech., 24, 313, 10.1146/annurev.fl.24.010192.001525 Petrovskii, 1994, Approximate determination of the magnitude of the critical size in the problem of the evolution of an ecological impact, J. Eng. Phys. Thermophys., 66, 346, 10.1007/BF00853455 Petrovskii, 1999, A minimal model of pattern formation in a prey-predator system, Math. Comp. Model., 29, 49, 10.1016/S0895-7177(99)00070-9 Petrovskii, 2001, Wave of chaos: new mechanism of pattern formation in spatiotemporal population dynamics, Theor. Pop. Biol., 59, 157, 10.1006/tpbi.2000.1509 Platt, 1961, Bioconvection patterns in cultures of free-swimming organisms, Science, 133, 1766, 10.1126/science.133.3466.1766 Platt, 1972, Local phytoplankton abundance and turbulence, Deep-Sea Res., 19, 183 Popova, 1997, Chaotic behaviour of an ocean ecosystem model under seasonal forcing, J. Plankton Res., 19, 1495, 10.1093/plankt/19.10.1495 Porep, 1970, Der Physiologe und Planktonforscher Victor Hensen (1835-1924) Powell, 1994, Turbulence, diffusion and patchiness in the sea, Proc. R. Soc. Lond., B343, 11 Powell, 1975, Spatial scales of current speed and phytoplankton biomass fluctuations in Lake Tahoe, Science, 189, 1088, 10.1126/science.189.4208.1088 Raymont, 1980 Riley, 1946, Factors controlling phytoplankton populations on Georges Bank, J. Mar. Res., 6, 54 Riley, 1963, Theory of food-chain relations in the ocean, vol. 2, 438 Rinaldi, 1993, Conditioned chaos in seasonally perturbed predator-prey models, Ecol. Model., 69, 79, 10.1016/0304-3800(93)90050-3 Rinaldi, 1993, Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities, Bull. Math. Biol., 55, 15, 10.1007/BF02460293 Ritschard, 1992, Marine algae as a CO2 sink, Water Air Soil Pollut., 64, 289, 10.1007/BF00477107 Rovinsky, 1992, Chemical instability induced by a differential flow, Phys. Rev. Lett., 69, 1193, 10.1103/PhysRevLett.69.1193 Ryabchenko, 1997, What causes short term oscillations in ecosystem models of the ocean mixed layer?, J. Mar. Syst., 13, 33, 10.1016/S0924-7963(96)00110-8 Scheffer, 1991, Fish and nutrients interplay determines algal biomass: a minimal model, Oikos, 62, 271, 10.2307/3545491 Scheffer, 1991, Should we expect strange attractors behind plankton dynamics - and if so, should we bother?, J. Plankton Res., 13, 1291, 10.1093/plankt/13.6.1291 Scheffer, 1998, Ecology of Shallow Lakes, vol. 22 Scheffer, 1997, Seasonal dynamics of Daphnia and algae explained as a periodically forced predator-prey system, Oikos, 80, 519, 10.2307/3546625 Schlögl, 1972, Chemical reaction models for nonequilibrium phase transitions, Z. Phys., 253, 147, 10.1007/BF01379769 Segel, 1977, A theoretical study of receptor mechanisms in bacterial chemotaxis, SIAM J. Appl. Math., 32, 653, 10.1137/0132054 Segel, 1972, Dissipative structure: an explanation and an ecological example, J. Theor. Biol., 37, 545, 10.1016/0022-5193(72)90090-2 Segel, 1972, Instability of a layer of chemotactic cells, attractant and degrading enzyme, J. Theor. Biol., 37, 561, 10.1016/0022-5193(72)90091-4 Shapiro, 1989, Escherichia coli K-12 cell-cell interactions seen by time-lapse video, J. Bacteriol., 171, 5963, 10.1128/jb.171.11.5963-5974.1989 Shapiro, 1991, Sequential events in bacterial colony morphogenesis, Physica, D49, 214 Sherratt, 1995, Ecological chaos in the wake of invasion, Proc. Natl. Acad. Sci. USA, 92, 2524, 10.1073/pnas.92.7.2524 Sherratt, 1997, Oscillations and chaos behind predator-prey invasion: mathematical artifact or ecological reality?, Phil. Trans. R. Soc. Lond., B352, 21, 10.1098/rstb.1997.0003 Siegert, 1991, Analysis of optical density wave propagation and cell movement in the cellular slime mold Dictyostelium discoideum, Physica, D49, 224 Skellam, 1951, Random dispersal in theoretical populations, Biometrika, 38, 196, 10.1093/biomet/38.1-2.196 Sommer, 1994 Sommer, 1996, Algen, Quallen, Wasserfloh Steele, 1974 Steele, 1977, Fisheries Mathematics Steele, 1978, Spatial Pattern in Plankton Communities, vol. 3 Steele, 1981, A simple plankton model, Am. Nat., 117, 676, 10.1086/283752 Steele, 1992, The role of predation in plankton models, J. Plankton Res., 14, 157, 10.1093/plankt/14.1.157 Steele, 1992, A simple model for plankton patchiness, J. Plankton Res., 14, 1397, 10.1093/plankt/14.10.1397 Steffen, 1996, Chaotic behaviour of a model plankton community in a heterogeneous environment, 331 Steffen, 1996, Multiple equilibria, periodicity, and quasiperiodicity in a model plankton community, Senckenberg. Marit., 27, 137 Steffen, 1997, Effects of seasonal perturbations on a model plankton community, Environ. Model. Assess., 2, 43, 10.1023/A:1019096924487 Steinbock, 1991, Quantitative analysis of periodic chemotaxis in aggregation patterns of Dictyostelium discoideum, Physica, D49, 233 Stommel, 1948, Trajectories of small bodies sinking slowly through convection cells, J. Mar. Res., 8, 24 Timm, 1994, Gyrotaxis: A plume model for self-focusing micro-organisms, Bull. Math. Biol., 56, 187, 10.1007/BF02460639 Truscott, 1995, Environmental forcing of simple plankton models, J. Plankton Res., 17, 2207, 10.1093/plankt/17.12.2207 Truscott, 1994, Ocean plankton populations as excitable media, Bull. Math. Biol., 56, 981, 10.1007/BF02458277 Truscott, 1994, Equilibria, stability and excitability in a general class of plankton population models, Phil. Trans. R. Soc. Lond., A347, 703, 10.1098/rsta.1994.0076 Turing, 1952, On the chemical basis of morphogenesis, Phil. Trans. R. Soc. Lond., B237, 37, 10.1098/rstb.1952.0012 Vasiev, 1994, Simulation of Dictyostelium discoideum aggregation via reaction-diffusion model, Phys. Rev. Lett., 73, 3173, 10.1103/PhysRevLett.73.3173 Vinogradov, 1977, The modelling of open-sea ecosystems, vol. 6, 891 Volterra, 1926, Variazioni e fluttuazioni del numero d'individui in specie animali conviventi, Mem. Acad. Lineei, III 6, 31 Weber, 1986, The variance spectra of phytoplankton, krill and water temperature in the Antarctic ocean south of Africa, Deep-Sea Res., 33, 1327, 10.1016/0198-0149(86)90039-7 Williamson, 1991, How plankton change the climate, New Scientist 16 March, 48 Winet, 1972, On the origin of bioconvection fluid instabilities in Tetrahymena culture systems, Biorheology, 9, 87, 10.3233/BIR-1972-9206 Wissel, 1989 Witten, 1981, Diffusion-limited aggregation, a kinetic critical phenomenon, Phys. Rev. Lett., 47, 1400, 10.1103/PhysRevLett.47.1400 Wroblewski, 1976, A spatial model of phytoplankton patchiness, Mar. Biol., 35, 161, 10.1007/BF00390938 Wroblewski, 1975, On the physical and biological scales of phytoplankton patchiness in the ocean, Mém. Soc. R. Sci. Liège VII, 43 Wyatt, 1971, Production dynamics of Oikopleura dioica in the Southern North Sea, and the role of fish larvae which prey on them, Thalassia Jugosl., 7, 435 Wyatt, 1973, The biology of Oikopleura dioica and Fritillaria borealis in the Southern Bight, Mar. Biol., 22, 137, 10.1007/BF00391778 Yoder, 1994, A line in the sea, Nature, 371, 689, 10.1038/371689a0 Yodzis, 1994, The trophodynamics of whole ecological communities, vol. 100, 443