Modeling 447 

 RESULTS AND DISCUSSION 



Deterministic Framework 



The primary objective of the modeling effort was to provide a 

 framework around which the ideas and experimental work of a group of 

 investigators could be organized. Thus, the structure of the model reflected 

 our current biological and ecological understanding of this particular 

 aquatic system. These ideas and the results of a number of experiments 

 carried out by the investigators were used to construct the forms of 

 mathematical equations of rate processes and dynamics of biomasses. The 

 results obtained from the computer simulation studies of these equations 

 are indicative of general seasonal changes in the biological processes and 

 species of organisms (measured as the amount of carbon per unit area or 

 volume). We do not claim to have formulated a model capable of 

 predicting everything about the system; it can only be construed as a first 

 step towards a model capable of describing the structure and function of 

 such an ecosystem. When that goal is achieved, perhaps we will have a 

 model which can be used as a powerful tool in management policy 

 decisions involving ecosystems. 



The equations used to describe the component processes (e.g. 

 photosynthesis, feeding rate of consumers, nutrient uptake, etc.) are not 

 specific to this tundra aquatic system; their general validity is supported by 

 published results from a wide range of aquatic systems. Wherever detailed 

 knowledge of some process was lacking, the functional form for that 

 process was assumed to be simply a constant multiplied by the biomass 

 (e.g. death rate, excretion rate, etc.). This can be considered a first 

 approximation. 



The basic structure of the model is specified by a set of nonlinear 

 differential equations, and a computer simulation analysis of the model 

 involves the numerical integration of these equations. Thus in a simulation 

 study it is necessary to specify the numerical value of all the parameters, 

 initial conditions,and also appropriate functional forms or tabular forms 

 of data for the effects of input variables, such as light and temperature. 

 Once these quantities are specified in the computer program the model is 

 run for a period of 60 days (the active life of tundra ponds). The model 

 output consists of the time-dependent behavior of system variables and 

 rate processes. Data collected over a 3-year period produced the values of 

 the parameters and the initial conditions of the state variables; this single 

 set of parameter values was used to obtain the simulation results. For light 

 and temperature, tables of recorded data were supplied to the program. 

 Thus the results of the computer simulation reflect the behavior of the 

 model (variables) with fixed initial conditions and parameters and variable 



