Relationships between individual- and population-based plankton models

Abstract

Two simulations of plankton dynamics are combined: an N/P/Z model and an optimal foraging strategy dependent on variable vertical migration. We show that there is no optimal individual strategy consistent with a copepod population that has two generations and is a significant grazer on its limiting food supply. Alternative roles for diel vertical migration are considered. Introduction The purpose of this paper is to combine two different approaches to plankton modelling: one from the population perspective, the other from that of the individual. The interactions and inconsistencies between these two models will be considered in terms of their underlying assumptions as well as the technical methods used. Traditional nutrient, phytoplankton, zooplankton (N/P/Z) simulations treat P and Z as single entities. Usually there is no formal optimizing procedure, but a process of first defining the physical context, then selecting functional relationships and finally choosing parameter values. The results are judged by comparison with observations of, say, chlorophyll or zooplankton biomass. 'Tuning' is done by varying the least known (or knowable) parameters, such as predation rate (e.g. Fasham et ai, 1990). A previous paper (Steele and Henderson, 1998) used this approach in a vertically structured model with diel migration dependent on vertically varying light and food concentration, and on predator density. The responses were assessed in terms of reproductive success at diapause. Different patterns of vertical migration did not appear to produce significant changes at diapause after two generations. An alternative approach is to define explicitly an optimal strategy that the individual plankter should follow. The favoured criteria involve life-time reproductive success for strategies such as acquiring food and avoiding predation. A popular method, dynamic programming, involves back calculation over the life cycle of the selected species (Mangel and Clark, 1988). This 'backward' method is necessary when the optimal condition, maximum reproductive output, is only defined at the end of the forward simulation. Each type of simulation will be used, with the common critical variable being the diel vertical migration (DVM) of a calanoid copepod species. The population model will be run forward in time to determine food and predator concentrations. The individual-based model can be run backwards using these concentrations to define the optimal migration strategy. This strategy can then be used for a further run of the population model. Should this iterative process lead to convergence? If not, is this due to technical inadequacies in the models, or does it arise from © Oxford University Press 1403 J.H.Steele and C.W.Clark inconsistencies in the underlying assumptions on which these two types of model are based? A plankton population model The basis for defining functions and choosing parameter values for population models should be the behaviour of individuals in the population—in acquiring food or avoiding predators. However, certain functions and parameter values are very poorly defined, or essentially unknown. This is apparent for the closure terms at the level of the 'predation mortality' on the Z. This effect becomes more obvious if the Z is decomposed into life cycle components: