Abstract
We consider the spatio-temporal dynamics of a spatially-structured generalization of the phytoplankton-zooplankton-fish larvae model system proposed earlier (Biktashev et al., 2003, J. Plankton Res. 5, 21–33; James et al., 2003, Ecol. Model. 160, 77–90). In contrast to Pitchford and Brindley (2001, Bull. Math. Biol. 63, 527–546), who were concerned with small scale patchiness (i.e., 1–10m), on which the (stochastic) raptorial behaviour of individual larvae is important, we address here the much larger scale ‘patchy’ problems (i.e., 10–100 km), on which both larvae and plankton may be regarded as passive tracers of the fluid motion, dispersed and mixed by the turbulent diffusion processes. In particular, we study the dependence of the fish recruitment on carrying capacities of the plankton subsystem and on spatio-temporal evolution of that subsystem with respect to the larvae hatching site(s). It is shown that the main features found both in the nonstructured and age-structured spatially uniform models are observed in the spatially structured case, but that spatial effects can significantly modify the overall quantitative outcome.
Spatial patterns in the metamorphosed fish distribution are a consequence of quasi-local interaction of larvae with plankton, in which the dispersion of larvae by large scale turbulent eddies plays little part due to the relatively short timescale of the larvae development. As a result, in a strong phyto/zooplankton subsystem, with fast reproduction rate and large carrying capacity of phytoplankton and high conversion ratio of zooplankton, recruitment success depends only on the localization and timing of the hatching with respect to the plankton patches. In a weak phyto/zooplankton system, with slow reproduction rate and small carrying capacity of phytoplankton and low conversion ratio of zooplankton, the larvae may significantly influence the evolution of the plankton patches, which may lead to nontrivial cooperative effects between different patches of larvae. However, in this case, recruitment is very low.
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References
Abraham, E. R. (1998). The generation of plankton patchiness by turbulent stirring. Nature 391, 577–580.
Bainbridge, R. (1957). Size, shape and density of marine phytoplankton concentrations. Biol. Rev. 32, 91–115.
Biktashev, V. N., J. Brindley and J. W. Horwood (2003). Phytoplankton blooms and fish recruitment rate. J. Plankton Res. 5, 21–33.
Cushing, D. H. and J. W. Horwood (1994). The growth and death of fish larvae. J. Plankton Res. 16, 291–300.
de Roos, A. M., E. McCawley and W. G. Wilson (1998). Pattern formation and the scale of interaction between predators and their prey. Theor. Pop. Biol. 52, 108–130.
Fisher, R. A. (1937). The wave of advance of advantageous genes. Phil. Trans. Roy. Soc. Lond. B 7, 355–369.
Flierl, G. R. and C. S. Davis (1993). Biological effects of Gulf-Stream meandering. J. Marine Res. 51, 529–560.
Folt, C. L. and C. W. Burns (1999). Biological drivers of zooplankton patchiness. Trends Ecol. Evol. 14, 300–305.
Gurney, W. J. C. and R. Veitch (2000). Self-organisation, scale and stability in a spatial predator-prey intraction. Bull. Math. Biol. 62, 61–86.
Heath, M. R. and A. Gallego (1998). Bio-physical modeling of the early life stages of haddock, melanogrammus aeglefinus, in the North Sea. Fisheries Oceanography 7, 110–125.
James, A., J. W. Pitchford and J. Brindley (2003). The relationship between plankton blooms, the hatching of fish larvæ and recruitment. Ecological Modelling 160, 77–90.
Kolmogoroff, A., I. Petrovsky and N. Piscounoff (1937). Étude de l’ équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique. Moscow Univ. Bull. Math. 1, 1–25.
Martin, A. P. and K. G. Richards (2001). Mechanisms for vertical nutrient transport within a North Atlantic mesoscale eddy. Deep-Sea Res. II 48, 757–773.
Matthews, L. and J. Brindley (1997). Patchiness in plankton populations. Dyn. Stab. Syst. 12, 39–59.
McGillicuddy, D. J. Jr and A. R. Robinson (1997). Eddy-induced nutrient supply and new production in the Sargasso Sea. Deep-Sea Res. I 44, 1427–1450.
Miller, D. G. M. and I. Hampton (1989). Biology and ecology of the Antarctic krill (Euphausia superba Dana): a review, in BIOMASS 9, Cambridge, England: Scott Polar Research Institute (SCAR/SCOR), pp. 1–166.
Neufeld, Z., P. Haynes, V. Garçon and J. Sudre (2002). Ocean fertilization experiment may initiate a large scale phytoplankton bloom. Geophys. Res. Lett. 29, 1534.
Okubo, A. (1980). Diffusion and ecological problems: mathematical models, Biomathematics 10, Berlin, Heidelberg, New York: Springer.
Oschlies, A. and V. Garçon (1998). Eddie-induced enhancement of primary productivity in a model of the North Atlantic. Nature 398, 266–268.
Oschlies, A., W. Koeve and V. Garçon (2000). An eddy-permitting coupled physical biological model of the North Atlantic, 2. Ecosystem dynamics and comparison with satellite and JGOFS local studies data. Global Biogeochemical Cycles 14, 499–523.
Pitchford, J. W. and J. Brindley (2001). Prey patchiness, predator survival and fish recruitment. Bull. Math. Biol. 63, 527–546.
Siegel, D. A., D. J. McGillicuddy Jr and E. A. Fields (1999). Mesoscale eddies, satellite altimetry and new production in the Sargasso Sea. J. Geophys. Res. 104, 13359–13379.
Steele, J. H. (1978). Some comments on plankton patches, in Spatial Pattern in Plankton Communities, J. H. Steele (Ed.), New York and London: Plenum Press, pp. 1–20.
Steele, J. H. and E. W. Henderson (1981). A simple plankton model. Am. Naturalist 117, 676–691.
Steele, J. H. and E. W. Henderson (1992a). The role of predation in plankton models. J. Plankton Res. 14, 157–172.
Steele, J. H. and E. W. Henderson (1992b). A simple model for plankton patchiness. J. Plankton Res. 14, 1397–1403.
Strass, V. H. (1992). Chlorophyll patchiness caused by mesoscale upwelling at fronts. Deep-Sea Res. A 39, 75–96.
Talbot, J. W. (1976). Diffusion data, in Fisheries Research Technical Report 28, Lowestoft: MAFF Directorate of Fisheries Research.
The PRIME Community (2001). The PRIME study. Deep-Sea Res. II 48.
Truscott, J. E. and J. Brindley (1994). Equilibria, stability and excitability in a general class of plankton population models. Phil. Trans. Roy. Soc. London A 347, 703–718.
Venrick, E. L. (1990). Mesoscale patterns of Chlorophyll-A in the central North Pacific. Deep-Sea Res. A 37, 1017–1031.
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Biktashev, V.N., Brindley, J. Phytoplankton blooms and fish recruitment rate: Effects of spatial distribution. Bull. Math. Biol. 66, 233–259 (2004). https://doi.org/10.1016/j.bulm.2003.08.008
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DOI: https://doi.org/10.1016/j.bulm.2003.08.008