浮游植物水华与鱼类补充率：空间分布的影响

Biktashev V N, Brindley J

Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK.

Bull Math Biol. 2004 Mar;66(2):233-59. doi: 10.1016/j.bulm.2003.08.008.

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., 1-10 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 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.

我们研究了先前提出的浮游植物 - 浮游动物 - 鱼幼体模型系统的空间结构广义化的时空动态（Biktashev等人，2003年，《浮游生物研究杂志》5，21 - 33；James等人，2003年，《生态模型》160，77 - 90）。与Pitchford和Brindley（2001年，《数学生物学公报》63，527 - 546）不同，他们关注的是小尺度斑块（即1 - 10米），在这个尺度上单个幼体的（随机）捕食行为很重要，我们在此处理的是大得多的尺度的“斑块状”问题（即10 - 100千米），在这个尺度上幼体和浮游生物都可被视为流体运动的被动示踪剂，通过湍流扩散过程进行分散和混合。特别地，我们研究了鱼类补充量对浮游生物子系统承载能力的依赖性，以及该子系统相对于幼体孵化地点的时空演化。结果表明，在非结构化和年龄结构化空间均匀模型中发现的主要特征在空间结构化情况下也能观察到，但空间效应可显著改变总体定量结果。变态后鱼类分布的空间格局是幼体与浮游生物准局部相互作用的结果，由于幼体发育时间尺度相对较短，大尺度湍流涡旋对幼体的扩散作用不大。因此，在一个强大的浮游植物/浮游动物子系统中，浮游植物繁殖率快、承载能力大且浮游动物转化率高，补充成功仅取决于相对于浮游生物斑块的孵化定位和时间。在一个弱小的浮游植物/浮游动物系统中，浮游植物繁殖率慢、承载能力小且浮游动物转化率低，幼体可能会显著影响浮游生物斑块的演化，这可能导致不同幼体斑块之间出现非平凡的协同效应。然而，在这种情况下，补充量非常低。