V.N. Biktashev, J. Brindley
Submitted to BMB: Dec. 5, 2002. Accepted: Aug. 4, 2003. Published online: Oct 21, 2003. Published: Bull. Math. Biol. 66(2): 233-259, March 2004
We consider the spatio-temporal dynamics of a spatially-structured generalisation of the phytoplankton-zooplankton-fish larvae model system proposed earlier (Biktashev, Brindley & Horwoord 2003, James, Pitchford & Brindley 2003). In contrast to Pitchford and Brindley (2001), who were concerned with small scale patchiness (i.e. 1--10\,m), 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 spatiotemporal evolution of that subsystem with respect to the larvae hatching site(s). It is shown that the main features found both in the non-structured 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 time scale 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 localisation 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 non-trivial cooperative effects between different patches of larvae. However, in this case, recruitment is very low.
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