[...]... zooplankton is an important loss term for phytoplankton The most simply way to include this top down control on phytoplankton is the inclusion of the grazing effects in the phytoplankton mortality However, the dynamical variations of zooplankton, and hence their effect on phytoplankton, can better be accounted for by means of a new state variable referring to zooplankton biomass Phytoplankton is a... than the much older study of marine biology This is perhaps partly due to the complexities of the material More important, however, is the fact that physical oceanography has aroused the interest of a number of men of considerable mathematical ability, while on the other hand marine biologists have been largely unaware of the growing field of bio-mathematics, or at least they have felt that the synthetic... modelers to address the right questions and to develop theoretical descriptions of the processes to be modelled The development of the interdisciplinary dialogue is a process which should start at the universities where students of marine biology should acquire some theoretical and mathematical background to be able to model marine ecosystems or to cooperate closely with modelers The main goal of this... use the term 'model' synonymously for theoretical descriptions in terms of sets of differential equations which describe the food web dynamics of marine systems The food webs are relatively complex systems, which can sketched simply as a flux of material from nutrients to phytoplankton to zooplankton to fish and recycling paths back to nutrients Phytoplankton communities consist of a spectrum of microscopic... by the mass of one of the chemical elements needed by the plankton cells and most often the Redfield ratio is used to estimate the other constituents Typical choices are, for example, carbon or nitrate used as a 'model currency' to quantify the amount of plankton biomass and detritus (i.e., the state variables which refer to living and non-living elements of the ecosystem) The fact that changes of. .. and have to take the memory effects of the ecosystem into account The integration of 'bottom-up' modelling into models used in fishery management and stock assessment is a difficult task and poses a modelling challenge which needs further research Today it seems to be feasible to involve those aspects 8 CHAPTER1 INTRODUCTION of environmental control into fisheries models, which act directly on the trophic... However they do not define the mathematical formulations needed for modelling First we have to identify a clear goal in order to define what we wish to describe with the model The example we are going to use in this chapter aims at the description of the seasonal cycle of phytoplankton in mid-latitudes We wish to formulate models that help to quantify the transfer of inorganic nutrients through parts of the. .. by the dynamics of the flow field and the individual motion, as well as the growth of 10 CHAPTER 1 INTRODUCTION the individuals Let v(r, t) be the resulting vector of the water motion and the individual's motion relative to the water and let ~(t) be the turbulent fluctuations, then it follows that the location of an individual is specified by ri(t) - ~0t dt'(v(ri, t') + ~(t')) (1.3) To describe the. .. considered by Laplace in the context of the physics of many-particle systems Assuming that there is a superhuman ghost (Laplace's demon) who knows all initial conditions for every single particle of a many particle system, such as an ideal classical gas, then by integration of the equations of motion the future state of the many-particles system could be predicted The analysis of this problem had shown... zooplankton growth Let Z be the zooplankton biomass per unit of volume Then the zooplankton growth obeys a relation described by d d~Z ~ g(P)Z, (2.21) where g(P) is a grazing rate which quantifies the ingestion of phytoplankton Similarly as for the uptake of nutrients by phytoplankton we expect that a relationship exists which becomes independent of the food if the food is abundant but is proportional to the . and mathemati- cal background to be able to model marine ecosystems or to cooperate closely with modelers. The main goal of this book is to help to facilitate. that a textbook giving a systematic introduction to the modelling of marine ecosystem is not available and, therefore, it is timely to write a book that