410 J.L. Tiwarietal. 



Finally, the model and its construction were excellent management 

 tools. The modeling procedure forced us to examine certain interactions, 

 such as the interaction of phosphate with the sediments, that proved to be 

 important keys to our eventual understanding of the controls of the 

 ecosystem. In addition the construction of the model over three years kept 

 us on a relatively narrow track and helped us avoid the innumerable 

 branch lines we could have taken. These, while interesting, could not all be 

 followed with the limits of time and manpower placed on this project. 



Overall, we conclude that the modeling effort was well worthwhile. 

 Yet, the value lies mainly in the construction and not in the output from 

 the model; this value is difficult to document here. Also, it is difficult to 

 document the interaction of the modeling with the design of experiments. 

 This difficulty is added to by the organization of this book; logical 

 development required presentation of driving variables (such as 

 temperature and light) initial conditions (such as concentrations of 

 organisms at the beginning of the year) and parameters and constants 

 (such as respiration coefficients and ^lo's) before the presentation of the 

 model. For these reasons, the modeling is presented last in this report and 

 may appear somewhat separate from the rest of the synthesis. As noted, 

 the modeling was an important part of the whole project. 



General Description 



The study of ecological systems using the formalisms of system 

 science requires an understanding of the whole system, of its living and non- 

 living component entities, and of their various relationships in abstract 

 form. Thus the structure of the system under consideration can be 

 conceptualized as a collection of "objects" coupled together by some form 

 of interactions. Each object is characterized by a finite number of 

 "attributes" which can be measured and assigned some value. In general, 

 these attributes are time-dependent quantities. Various interactions 

 between the objects and between the attributes of each object can be 

 described by mathematical formulae. (For details and rigorous definitions 

 and formulations of these concepts see Zadeh and Desoer 1963, Zadeh and 

 Polak 1969, Caswell et al. 1972, Klir 1969, Rosen 1970.) 



Thus an object is essentially a set of variables together with a set of 

 relationships between them; a time sequence of instantaneous values of 

 these attributes describes the behavior of the system. The dynamics of the 

 system are characterized by the interactions between the elements of the 

 system, for these interactions impose a set of constraints on the output 

 variables of the system. 



The objects and interactions between them provide a basis for a "state- 

 space" description of the system. Each basic entity of the system is a state 

 variable whigh is chosen by the investigator for the particular system. Over 



