Small-scale spatial structure in plankton distributions

The observed filamental nature of plankton populations suggests that stirring plays an important role in determining their spatial structure. If diffusive mixing is neglected, the various interacting biological species within a fluid parcel are determined by the parcel time history. The induced spatial structure has been shown to be a result of competition between the time evolution of the biological processes involved and the stirring induced by the flow as measured, for example, by the rate of divergence of the distance of neighbouring fluid parcels. In the work presented here we examine a simple biological model based on delay-differential equations, previously seen in Abraham (1998), including nutrients, phytoplankton and zooplankton, coupled to a strain flow. Previous theoretical investigations made on a differential equation model (Hernandez-Garcia et al., 2002) imply that the latter two should share the same small-scale structure. The generalisation from differential equations to delay-differential equations, associated with the addition of a maturation time to the zooplankton growth, should not make a difference, provided sufficiently small spatial scales are considered. However, this theoretical prediction is in contradiction with the results of Abraham (1998), where the phytoplankton and zooplankton structures remain uncorrelated at all length scales. A new set of numerical experiments is performed here which show that these two regimes coexist. On larger scales, there is a decoupling of the spatial structure of the zooplankton distribution on the one hand, and the phytoplankton and nutrient on the other. On the other hand, at small enough length scales, the phytoplankton and zooplankton share the same spatial structure as expected by the theory involving no maturation time.