CHAPTER V. MATHEMATICAL MODELLING OF THE FUNCTIONING 

 OF A PELAGIC ECOSYSTEM 



Analysis of the environment and its population as a single, 

 interconnected system has been one of the most fruitful ideas of modern 

 ecology, opening broad doors for the systems approach to the study of 

 biologic processes in the biosphere. From this standpoint, the ocean 

 and its population can also be looked upon as a single, dynamic system 

 (Lebedev et al., 1974). 



The systems approach has allowed the ideas, methods and apparatus 

 of such mathematical disciplines as cybernetics, information theory, 

 game theory and decision theory to be applied to the study of biologic 

 phenomena. However, in order to actualize the capabilities of these 

 disciplines, information on the structure and functioning of biologic 

 objects, communities in the present case, must be summarized and 

 formalized, and used as the basis for the construction of a model. This 

 requires that only the basic, definitive, parameters and connections of 

 the system be used, ignoring many interesting details. Unavoidably, 

 this leads to some internal protest among researchers who have spent a 

 great deal of time and effort in the study of details. 



Depending on the nature of the task at hand, the degree of 

 development and specifics of the mathematical apparatus used for its 

 performance and the completeness of the information available on the 

 object of study, various models can be used: for example, description 

 of processes by differential equations (deterministic models), analysis 

 of random processes (stochastic models) or the development of algorithms 

 of self organization (self-organizing models). However, in any case, a 

 model should describe the complete set of elements present in the system 

 and their interactions, and should allow evaluation of certain 

 situations arising in the actual systems which either cannot be directly 

 measured or can be measured only with great difficulty. 



Obviously, so-called "simulation models," allowing the use of 

 computerized numerical models to draw conclusions concerning the 

 behavior of a system as its various parameters change, and even allowing 

 decisions to be made concerning the most effective methods for more 

 traditional study of the system (Menshutkin, 1972), are of particular 

 prognostic value. Furthermore, the construction of such models is an 

 important means for testing the agreement of individual experimentally- 

 observed facts. Simulation models are closely related to imitation 

 models, differing in that they do not include a portrait description of 

 the object due to the insufficiency of initial data on the object. 

 These models can describe both the functioning of biologic systems and 

 their structural peculiarities, for example the regularities of 

 formation of horizontal (Wroblewski et al . , 971; Wroblewski, O'Brien, 



320 



