Phytoplankton patchiness: the role of lateral stirring and mixing

Explanations for the patchy distribution of marine phytoplankton are critically reviewed with the focus on the role played by lateral advection and mixing. Generating mechanisms for what is increasingly seen as a ubiquitous feature of the oceans have been sought in biology, behaviour, population dynamics, physics and various combinations thereof. As the mesoscale and sub-mesoscale (1-500 km) contain the "weather" of the ocean--eddies and fronts capable of strong stirring and mixing of any tracers advected by them--the physical circulation in this regime may have a strong role in the generation of patchiness. As a consequence, the focus here is on the ways the turbulent currents at these scales can interact with other processes to produce the complex spatial structures in phytoplankton distributions seen in countless satellite images and cruise data. The mechanisms reviewed include patch formation (KiSS theory), filamentation, Turing and related instabilities, diffusion waves, shear effects and turbulent stirring. Parallel to this is a discussion of observations and of the techniques that have been used to analyse them, particularly spectral analysis. It will be seen that many of the limitations in extant theories stem from a paucity of data and ambiguity in its interpretation. A synthesis of recent developments in sampling, instrumentation, image analysis and turbulence theory is used to suggest alternatives to conventional approaches, to highlight important work in related fields and to motivate new lines of research.

[1]  A. Kolmogorov The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[2]  T. Platt,et al.  SCALES OF VARIABILITY IN ESTUARINE ECOSYSTEMS , 1982 .

[3]  S. Corrsin,et al.  The reactant concentration spectrum in turbulent mixing with a first-order reaction , 1961, Journal of Fluid Mechanics.

[4]  L. Prieur,et al.  Phytoplankton dynamics associated with a geostrophic front: Ecological and biogeochemical implications , 1994 .

[5]  Adrian P. Martin,et al.  Mechanisms for vertical nutrient transport within a North Atlantic mesoscale eddy , 2001 .

[6]  K. Denman The variance spectrum of phytoplankton in a turbulent ocean , 1976 .

[7]  T. Wyatt The biology of Oikopleura dioica and Fritillaria borealis in the Southern Bight , 1973 .

[8]  J. Price,et al.  Lateral mixing and the North Atlantic Tracer Release Experiment: Observations and numerical simulations of Lagrangian particles and a passive tracer , 1998 .

[9]  S. Petrovskii,et al.  Wave of chaos: new mechanism of pattern formation in spatio-temporal population dynamics. , 2001, Theoretical population biology.

[10]  Edward R. Abraham,et al.  The generation of plankton patchiness by turbulent stirring , 1998, Nature.

[11]  Mercedes Pascual,et al.  Intermittency in the plankton: a multifractal analysis of zooplankton biomass variability , 1995 .

[12]  Michel Rixen,et al.  Diagnosis of vertical velocities with the QG omega equation: an examination of the errors due to sampling strategy , 2001 .

[13]  K. Denman,et al.  Phytoplankton patchiness: inferences from particle statistics , 1985 .

[14]  A. Ōkubo,et al.  Phytoplankton Patchiness In The Central Long Island Sound , 1986 .

[15]  P. Wiebe SMALL-SCALE SPATIAL DISTRIBUTION IN OCEANIC ZOOPLANKTON† , 1970 .

[16]  Annalisa Bracco,et al.  Patchy productivity in the open ocean , 2002 .

[17]  F. Schmitt,et al.  Copepod diffusion within multifractal phytoplankton fields , 1998 .

[18]  W. R. Young,et al.  Reproductive pair correlations and the clustering of organisms , 2001, Nature.

[19]  J. Horwood Observations on Spatial Heterogeneity of Surface Chlorophyll in one and two Dimensions , 1978, Journal of the Marine Biological Association of the United Kingdom.

[20]  Rovinsky,et al.  Chemical instability induced by a differential flow. , 1992, Physical review letters.

[21]  B. Jones,et al.  Eddy stirring and phytoplankton patchiness in the subarctic North Atlantic in late summer , 1998 .

[22]  G. Taylor Dispersion of soluble matter in solvent flowing slowly through a tube , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[23]  R. Cassie Microdistribution of plankton , 1963 .

[24]  James C. McWilliams,et al.  Lagrangian accelerations in geostrophic turbulence , 1998, Journal of Fluid Mechanics.

[25]  T. Tél Fractals, Multifractals, and Thermodynamics , 1988 .

[26]  J. Horwood Variation of fluorescence, particle-size groups, and environmental parameters in the southern North Sea , 1981 .

[27]  C. Grebogi,et al.  Chaotic advection, diffusion, and reactions in open flows. , 2000, Chaos.

[28]  P. Wiebe,et al.  Fine-scale multi-species aggregations of oceanic zooplankton , 1982 .

[29]  James J. Anderson,et al.  Mathematical models for zooplankton swarms: Their formation and maintenance , 1984 .

[30]  P. Bowles,et al.  SEA DISPOSAL OF LOW ACTIVITY EFFLUENT , 1959 .

[31]  G. Hays,et al.  Individual variability in diel vertical migration of a marine copepod: Why some individuals remain at depth when others migrate , 2001 .

[32]  F. Schmitt,et al.  Turbulence intermittency, small-scale phytoplankton patchiness and encounter rates in plankton: where do we go from here? , 2001 .

[33]  G. Riley A model of plankton patchiness , 1976 .

[34]  S. Petrovskii On the plankton front waves accelerated by marine turbulence , 1999 .

[35]  N. Poulakis,et al.  Site-selective oxygen isotope effect in optimally doped YBa2Cu3O6 + x , 1994, Nature.

[36]  A. Holden,et al.  EXCITATION WAVE BREAKING IN EXCITABLE MEDIA WITH LINEAR SHEAR FLOW , 1998 .

[37]  C. L. Smith,et al.  The impact of mesoscale eddies on plankton dynamics in the upper ocean , 1996 .

[38]  M. Fasham,et al.  An investigation of the spatial pattern of zooplankton using the Longhurst-Hardy plankton recorder , 1974 .

[39]  C. Torrence,et al.  A Practical Guide to Wavelet Analysis. , 1998 .

[40]  Frederic Bartumeus,et al.  Self-organized spatial structures in a ratio-dependent predator–prey model , 2001 .

[41]  C. Lorenzen,et al.  A method for the continuous measurement of in vivo chlorophyll concentration , 1966 .

[42]  P. Holligan Patchiness in Subsurface Phytoplankton Populations on the Northwest European Continental Shelf , 1978 .

[43]  Mark R. Abbott,et al.  Plankton patchiness: biology in the physical vernacular , 1985 .

[44]  G. Kullenberg Vertical Processes and the Vertical-Horizontal Coupling , 1978 .

[45]  C Grebogi,et al.  Chemical or biological activity in open chaotic flows. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[46]  A. Solow,et al.  Microaggregations of Oceanic Plankton Observed by Towed Video Microscopy , 1992, Science.

[47]  Joaquín Tintoré,et al.  Mesoscale subduction at the Almeria-Oran front: Part 1: Ageostrophic flow , 2001 .

[48]  P J Richerson,et al.  Spatial Scales of Current Speed and Phytoplankton Biomass Fluctuations in Lake Tahoe , 1975, Science.

[49]  A. Rees,et al.  Nutrient distributions in an anticyclonic eddy in the northeast Atlantic Ocean, with reference to nanomolar ammonium concentrations , 2001 .

[50]  M. El-sabh,et al.  Phytoplankton distributions observed during a % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9 , 1980, Hydrobiologia.

[51]  S. Ellner,et al.  Crossing the hopf bifurcation in a live predator-prey system. , 2000, Science.

[52]  M. Bowman,et al.  Tidal Mixing and Plankton Dynamics , 1986, Lecture Notes on Coastal and Estuarine Studies.

[53]  D. Grünbaum,et al.  From individuals to aggregations: the interplay between behavior and physics. , 1999, Journal of theoretical biology.

[54]  J. Watson,et al.  Three‐dimensional spatial coordinates of individual plankton determined using underwater hologrammetry , 2000 .

[55]  John H. Steele,et al.  A simple model for plankton patchiness , 1992 .

[56]  K. Heywood,et al.  Tracking the PRIME eddy using satellite altimetry , 2001 .

[57]  H. Malchow Spatio-temporal pattern formation in nonlinear non-equilibrium plankton dynamics , 1993, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[58]  David Archer,et al.  Modeling the impact of fronts and mesoscale circulation on the nutrient supply and biogeochemistry of the upper ocean , 2000 .

[59]  Zoltan Neufeld,et al.  Chaotic advection of reacting substances: Plankton dynamics on a meandering jet , 1999, chao-dyn/9906029.

[60]  Frederick Armstrong,et al.  Antarctic Krill Under Sea Ice: Elevated Abundance in a Narrow Band Just South of Ice Edge , 2002, Science.

[61]  P. M. Saunders Space and time variability of temperature in the upper ocean , 1972 .

[62]  J. Steele,et al.  Spatial patterns in North Sea plankton , 1979 .

[63]  Akira Okubo,et al.  Oceanic diffusion diagrams , 1971 .

[64]  Jeffrey L. Star,et al.  Spectral-Analysis - a Caveat , 1981 .

[65]  J. Beckers,et al.  Along or across front ocean survey strategy? The estimation of quasi‐geostrophic vertical velocities and temperature fluxes , 2003 .

[66]  Zizhen Li,et al.  Population's response to environmental noise: the influence of food web structure , 2002 .

[67]  Karl K. Turekian,et al.  Encyclopedia of Ocean Sciences , 2001 .

[68]  Alignment of tracer gradient vectors in 2D turbulence , 2000 .

[69]  Satellite-sensed turbulent ocean structure , 1981, Nature.

[70]  A. Tsuda,et al.  Fractal distribution of an oceanic copepodNeocalanus cristatus in the subarctic pacific , 1995 .

[71]  Zoltán Toroczkai,et al.  Advection of active particles in open chaotic flows , 1998 .

[72]  William M. Ilamner,et al.  Long‐distance horizontal migrations of zooplankton (Scyphomedusae: Mastigias)1 , 1981 .

[73]  M. Abbott PHYTOPLANKTON PATCHINESS: ECOLOGICAL IMPLICATIONS AND OBSERVATION METHODS , 1993 .

[74]  G. Haller Finding finite-time invariant manifolds in two-dimensional velocity fields. , 2000, Chaos.

[75]  G. Evans,et al.  Biological Effects of Vertical-Horizontal Interactions , 1978 .

[76]  C. Trees,et al.  Spatial variability of the ocean color field in CZCS imagery , 1987 .

[77]  On mathematical modelling of complex ecosystems: Application to marine planktonic patchiness , 1977, Helgoländer wissenschaftliche Meeresuntersuchungen.

[78]  Zoltan Neufeld,et al.  Chaotic mixing induced transitions in reaction-diffusion systems. , 2002, Chaos.

[79]  Frank E. Hoge,et al.  Spatial Variability In Near-Surface Chlorophyll-A Fluorescence Measured By The Airborne Oceanographic Lidar (AOL) , 1993 .

[80]  A. Ōkubo,et al.  The chlorophyll fluctuation spectrum in the sea1,2 , 1977 .

[81]  Environmental Control of Phytoplankton Patchiness , 1981 .

[82]  C. G. Holladay,et al.  Mesoscale Variability of Sea Surface Temperatures , 1975 .

[83]  S. Plourde,et al.  A biophysical model of the interaction between vertical migration of crustacean zooplankton and circulation in the Lower St. Lawrence Estuary , 1999 .

[84]  A. Ōkubo A note on small organism diffusion around an attractive center: A mathematical model , 1972 .

[85]  G. E. Hutchinson,et al.  The Balance of Nature and Human Impact: The paradox of the plankton , 2013 .

[86]  D. Smeed,et al.  Real‐time forecasting of biological and physical dynamics at the Iceland‐Faeroes Front in June 2001 , 2002 .

[87]  Andreas Oschlies,et al.  Eddy-induced enhancement of primary production in a model of the North Atlantic Ocean , 1998, Nature.

[88]  T. Platt Spectral Analysis of Spatial Structure in Phytoplankton Populations , 1978 .

[89]  Patrice Klein,et al.  An exact criterion for the stirring properties of nearly two-dimensional turbulence , 1998 .

[90]  Peter Franks,et al.  Spatial patterns in dense algal blooms , 1997 .

[91]  M. Fasham The Application of Some Stochastic Processes to the Study of Plankton Patchiness , 1978 .

[92]  A. Longhurst Analysis of Marine Ecosystems , 1981 .

[93]  Shaun Lovejoy,et al.  Universal multifractal analysis as a tool to characterize multiscale intermittent patterns : example of phytoplankton distribution in turbulent coastal waters , 1999 .

[94]  J. G. Skellam Random dispersal in theoretical populations , 1951, Biometrika.

[95]  J. Brindley,et al.  Patchiness in plankton populations , 1997 .

[96]  M. Srokosz RRS Discovery Cruise 227, 15 Apr-16 May 1997. Plankton patchiness studies by ship and satellite: P2S3 , 1997 .

[97]  Balram Dubey,et al.  A predator–prey interaction model with self and cross-diffusion , 2001 .

[98]  A. Tsuda,et al.  White-noise-like distribution of the oceanic copepod Neocalanus cristatus in the subarctic North Pacific , 1993 .

[99]  P. Boyd,et al.  Importance of stirring in the development of an iron-fertilized phytoplankton bloom , 2000, Nature.

[100]  Paul Tett,et al.  Mixing and plankton: an interdisciplinary theme in oceanography , 1984 .

[101]  E. Hernández‐García,et al.  Small-scale structure of nonlinearly interacting species advected by chaotic flows. , 2001, Chaos.

[102]  Graham P. Harris,et al.  Temporal and Spatial Scales in Phytoplankton Ecology. Mechanisms, Methods, Models, and Management , 1980 .

[103]  R. W. Gilmer,et al.  Behavior of Antarctic Krill, Euphausia superba: Chemoreception, Feeding, Schooling, and Molting , 1983, Science.

[104]  D. Mason,et al.  Description and Analysis of Spatial Patterns , 1993 .

[105]  A. Watson,et al.  Mixing of a tracer in the pycnocline , 1998 .

[106]  L. Legendre,et al.  Towards Dynamic Biological Oceanography and Limnology , 1984 .

[107]  M. Estrada,et al.  Spectral analysis of spatial series of oceanographic variables , 1977 .

[108]  A. Mahadevan,et al.  Mesoscale variability of sea surface pCO2: What does it respond to? , 2004 .

[109]  D. Cushing,et al.  Studies on a Calanus Patch I. The Identification of a Calanus patch , 1963, Journal of the Marine Biological Association of the United Kingdom.

[110]  V. Garçon,et al.  Phytoplankton pigment distribution from SeaWiFS data in the subtropical convergence zone south of Africa: A wavelet analysis , 1999 .

[111]  K. Denman,et al.  Phytoplankton patchiness indicates the fluctuation spectrum of mesoscale oceanic structure , 1980, Nature.

[112]  P. Wiebe,et al.  Three-dimensional acoustic visualization of zooplankton patchiness , 1998 .

[113]  John H. Martin glacial-interglacial Co2 change : the iron hypothesis , 1990 .

[114]  R. Bainbridge THE SIZE, SHAPE AND DENSITY OF MARINE PHYTOPLANKTON CONCENTRATIONS , 1957 .

[115]  H. Malchow Nonequilibrium structures in plankton dynamics , 1994 .

[116]  J. Kittredge,et al.  CHEMICAL SIGNALS IN THE SEA: MARINE ALLELOCHEMICS AND EVOLUTION 1 , 1973 .

[117]  Satish C. Gupta System Simulation in Water Resources , 1977 .

[118]  V. Strass,et al.  Chlorophyll patchiness caused by mesoscale upwelling at fronts , 1992 .

[119]  Z. Toroczkai,et al.  A model for resolving the plankton paradox : coexistence in open flows , 2000 .

[120]  A. Ōkubo,et al.  Turbulence, diffusion and patchiness in the sea , 1994 .

[121]  L. Prieur,et al.  Biophysical aspects of Almofront-1, an intensive study of a geostrophic frontal jet , 1993 .

[122]  S. Pearre Problems of detection and interpretation of vertical migration , 1979 .

[123]  A. Provenzale,et al.  Mesoscale vortices and the paradox of the plankton , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[124]  E. Hernández‐García,et al.  Spatial patterns in chemically and biologically reacting flows , 2002, nlin/0205009.

[125]  Makoto Omori,et al.  Patchy distribution of zooplankton: Behavior, population assessment and sampling problems , 1982 .

[126]  D. Cushing,et al.  The ecology of the seas , 1978 .

[127]  C. Reynolds,et al.  Phytoplankton Productivity - Carbon assimilation in marine and freshwater ecosystems , 2002 .

[128]  M. Vargas,et al.  Hydrodynamics and the spatial distribution of plankton and TEP in the Gulf of Cádiz (SW Iberian Peninsula). , 2002 .

[129]  D. Mackas,et al.  Spectral Analysis of Zooplankton Spatial Heterogeneity , 1979, Science.

[130]  S. Piontkovski,et al.  Spatial heterogeneity, biomass and size structure of plankton of the Indian Ocean: Some general trends , 1995 .

[131]  Z Toroczkai,et al.  Chaotic flow: the physics of species coexistence. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[132]  H. Mitsudera,et al.  Chaotic Advection of the Shallow Kuroshio Coastal Waters , 2002 .

[133]  Lopez,et al.  Multifractal structure of chaotically advected chemical fields , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[134]  Rovinsky,et al.  Self-organization induced by the differential flow of activator and inhibitor. , 1993, Physical review letters.

[135]  V. Garçon,et al.  Ocean fertilization experiments may initiate a large scale phytoplankton bloom , 2002 .

[136]  T. Platt Analysis of the importance of spatial and temporal heterogeneity in the estimation of annual production by phytoplankton in a small, enriched, marine basin , 1975 .

[137]  E. Widder,et al.  Effects of a decrease in downwelling irradiance on the daytime vertical distribution patterns of zooplankton and micronekton , 2002 .

[138]  C. Folt,et al.  Biological drivers of zooplankton patchiness. , 1999, Trends in ecology & evolution.

[139]  T. D. Dickey,et al.  Influence of mesoscale eddies on new production in the Sargasso Sea , 1998, Nature.

[140]  R. Fisher THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES , 1937 .

[141]  A. Ōkubo,et al.  Diffusion-driven instability in a predator-prey system with time-varying diffusivities , 1992 .

[142]  Irad Yavneh,et al.  Anisotropy and Coherent Vortex Structures in Planetary Turbulence , 1994, Science.

[143]  Mercedes Pascual,et al.  Mechanisms of Patch Formation , 1993 .

[144]  Adrian P. Martin,et al.  Phytoplankton production and community structure in an unstable frontal region , 2001 .

[145]  A. Turing The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[146]  R. Kraichnan Inertial Ranges in Two‐Dimensional Turbulence , 1967 .

[147]  The role of diffusion in the chaotic advection of a passive scalar with finite lifetime , 2001, nlin/0111049.

[148]  J. J. O'Brien,et al.  A spatial model of phytoplankton patchiness , 1976 .

[149]  L. Seuront,et al.  Multiscale patchiness of the calanoid copepod Temora longicornis in a turbulent coastal sea , 2001 .

[150]  Z. Toroczkai,et al.  Competing populations in flows with chaotic mixing. , 2001, Theoretical population biology.

[151]  R. Wilson,et al.  Spatial variability of phytoplankton biomass in the surface waters of Long Island , 1978 .

[152]  D. Mackas Spatial autocorrelation of plankton community composition in a continental shelf ecosystem , 1984 .

[153]  Scott C. Doney,et al.  The role of mesoscale variability on plankton dynamics in the North Atlantic , 2001 .

[154]  J. Ottino The Kinematics of Mixing: Stretching, Chaos, and Transport , 1989 .

[155]  John Brindley,et al.  Ocean plankton populations as excitable media , 1994 .

[156]  R. Amann,et al.  Mesoscale distribution of dominant bacterioplankton groups in the northern North Sea in early summer , 2002 .

[157]  L. Segel,et al.  Hypothesis for origin of planktonic patchiness , 1976, Nature.

[158]  J. Zimmerman,et al.  Chaotic Stirring in a Tidal System , 1992, Science.

[159]  K. Denman,et al.  Spectral Analysis in Ecology , 1975 .

[160]  G. Rosen Effects of diffusion on the stability of the equilibrium in multi-species ecological systems. , 1977, Bulletin of mathematical biology.

[161]  T. Piatt,et al.  Spatial variability of phytoplankton turnover in relation to physical processes in a coastal environment , 1978 .

[162]  Adrian P. Martin On filament width in oceanic plankton distributions , 2000 .

[163]  Bai-lian Li,et al.  REVIEWS OF TOPICAL PROBLEMS: Spatio-temporal pattern formation, fractals, and chaos in conceptual ecological models as applied to coupled plankton-fish dynamics , 2002 .

[164]  K. Denman Covariability of chlorophyll and temperature in the sea , 1976 .

[165]  Gilreath,et al.  Experimental Evidence for Chaotic Scattering in a Fluid Wake. , 1996, Physical review letters.

[166]  John H. Steele,et al.  Some Comments on Plankton Patches , 1978 .

[167]  Daniel M. Dubois,et al.  A model of patchiness for prey—predator plankton populations , 1975 .

[168]  Adrian P. Martin,et al.  On the role of biological dynamics in plankton patchiness at the mesoscale: an example from the eastern North Atlantic Ocean , 2003 .

[169]  J. Beckers,et al.  Along or across front survey strategy? An operational example at an unstable front , 2003 .

[170]  A. P. Martin,et al.  Plankton distribution spectra: inter‐size class variability and the relative slopes for phytoplankton and zooplankton , 2002 .

[171]  Horst Malchow Nonlinear plankton dynamics and pattern formation in an ecohydrodynamic model system , 1996 .

[172]  Rovinsky,et al.  Differential flow instability in dynamical systems without an unstable (activator) subsystem. , 1994, Physical review letters.

[173]  P. Strutton,et al.  Phytoplankton patchiness: quantifying the biological contribution using Fast Repetition Rate Fluorometry , 1997 .

[174]  S. Spall,et al.  A numerical model of mesoscale frontal instabilities and plankton dynamics — I. Model formulation and initial experiments , 2000 .

[175]  R. Bainbridge Movement of Zooplankton in Diatom Gradients , 1949, Nature.

[176]  T. Platt,et al.  SPATIAL VARIABILITY OF THE PRODUCTIVITY: BIOMASS RATIO FOR PHYTOPLANKTON IN A SMALL MARINE BASIN , 1973 .

[177]  T. Piatt,et al.  Spatial heterogeneity of phytoplankton biomass and related factors in the near-surface waters of an exposed coastal embayment , 1978 .

[178]  Patrice Klein,et al.  Impact of sub-mesoscale physics on production and subduction of phytoplankton in an oligotrophic regime , 2001 .

[179]  J. A. Coil,et al.  Spatial Heterogeneity in Closed Basins , 1978 .

[180]  S. Solomon,et al.  The importance of being discrete: life always wins on the surface. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[181]  Janet Campbell,et al.  Biogeochemical patchiness at the sea surface , 2002 .

[182]  John Brindley,et al.  Plankton patchiness and its effect on larger-scale productivity , 2003 .

[183]  Cristóbal López,et al.  Smooth-filamental transition of active tracer fields stirred by chaotic advection , 1999, chao-dyn/9906019.

[184]  Excitable media in a chaotic flow. , 2001, Physical review letters.

[185]  E. Hernández‐García,et al.  Filament bifurcations in a one-dimensional model of reacting excitable fluid flow , 2003, nlin/0302040.

[186]  Sergei Petrovskii,et al.  A minimal model of pattern formation in a prey-predator system , 1999 .

[187]  V. Garçon,et al.  Rossby wave and ocean color: The cells uplifting hypothesis in the South Atlantic Subtropical Convergence Zone , 2003 .

[188]  Eric D. Barton,et al.  The influence of island-generated eddies on chlorophyll distribution : a study of mesoscale variation around Gran Canaria , 1997 .

[189]  C. Duarte,et al.  The relationship between mesoscale phytoplankton heterogeneity and hydrographic variability , 1992 .

[190]  J. Steele,et al.  Spatial Heterogeneity and Population Stability , 1974, Nature.

[191]  S. Piontkovski,et al.  Multiscale variability of tropical ocean zooplankton biomass , 1995 .

[192]  S. Levin Patchiness in marine and terrestrial systems: from individuals to populations , 1994 .

[193]  Kenneth L. Denman,et al.  Collection and Analysis of Underway Data and Related Physical Measurements , 1978 .

[194]  A. Alldredge,et al.  Direct sampling and in situ observation of a persistent copepod aggregation in the mesopelagic zone of the Santa Barbara Basin , 1984 .

[195]  M. Menzinger,et al.  Patchiness and enhancement of productivity in plankton ecosystems due to the differential advection of predator and prey , 1997 .

[196]  J. Beckers,et al.  Non-synoptic versus pseudo-synoptic data sets: an assimilation experiment , 2001 .

[197]  Adrian P. Martin,et al.  Minimum length scale for growth-limited oceanic plankton distributions , 2002 .

[198]  John W. Kanwisher,et al.  AN IN SITU PARTICLE COUNTER1 , 1965 .

[199]  C. Garrett On the initial streakness of a dispersing tracer in two- and three-dimensional turbulence , 1983 .

[200]  P. Pugh The Application of Particle Counting to an Understanding of the Small-Scale Distribution of Plankton , 1978 .

[201]  Shaun Lovejoy,et al.  Multifractal analysis of phytoplankton biomass and temperature in the ocean , 1996 .

[202]  Marina Lévy,et al.  Mesoscale variability of phytoplankton and of new production: Impact of the large-scale nutrient distribution , 2003 .

[203]  Ian Hampton,et al.  The variance spectra of phytoplankton, krill and water temperature in the Antarctic Ocean south of Africa☆ , 1986 .

[204]  M. Fasham,et al.  Observations on the horizontal coherence of chlorophyll a and temperature , 1976 .

[205]  P. Flament,et al.  Cautionary remarks on the spectral interpretation of turbulent flows , 1985 .

[206]  Simon A. Levin,et al.  Pattern Formation in Ecological Communities , 1978 .

[207]  Scott M. Gallager,et al.  High-resolution observations of plankton spatial distributions correlated with hydrography in the Great South Channel, Georges Bank , 1996 .

[208]  D. Schertzer,et al.  Universal multifractals and ocean patchiness: phytoplankton, physical fields and coastal heterogeneity , 2001 .

[209]  Adrian P. Martin,et al.  Horizontal dispersion within an anticyclonic mesoscale eddy , 2001 .

[210]  C. L. Leonard,et al.  Interannual mesoscale physical and biological variability in the North Pacific Central Gyre , 2001 .

[211]  P. Wiebe,et al.  Patterns and Processes in the Time-Space Scales of Plankton Distributions , 1978 .

[212]  M. Kahru,et al.  Size structure of planktonic particles in relation to hydrographic structure in the Skagerrak , 1991 .

[213]  B. Rothschild,et al.  Population-dynamic instability as a cause of patch structure , 1996 .

[214]  R. Pollard,et al.  Vorticity and vertical circulation at an ocean front , 1992 .

[215]  G. Griffiths,et al.  Some observations of biophysical interaction in the ocean using high frequency acoustics , 2001 .

[216]  Edward R. Abraham,et al.  Chaotic stirring by a mesoscale surface-ocean flow. , 2002, Chaos.

[217]  T. Platt Local phytoplankton abundance and turbulence , 1972 .

[218]  Andrew J. Watson,et al.  A mesoscale phytoplankton bloom in the polar Southern Ocean stimulated by iron fertilization , 2000, Nature.

[219]  F. Schmitt,et al.  Multifractal intermittency of Eulerian and Lagrangian turbulence of ocean temperature and plankton fields , 1996 .

[220]  William M. Balch,et al.  A line in the sea , 1994, Nature.

[221]  W. Kimmerer Direct measurement of the production:biomass ratio of the subtropical calanoid copepod Acrocalanus inermis , 1983 .