430 J. L. Tiwari et al. 



of nutrients follows Michaelis-Menten types of curves (Hobbie and 

 Crawford 1969, Wright and Hobbie 1966, Crawford et al. 1974). The data 

 of Chisholm et al. (1975) on the feeding rates of arctic Daphnia also imply 

 that the ingestion rates can be approximated by Michaelis-Menten type 

 equations. 



It is further assumed that excretion, secretion, and death rates can be 

 represented by the following simple functional relationship: 



x.=xM^ (12) 



Xj 



where 



!x; = process representing excretion, secretion or death, 

 X, =biomass, and 

 k, = a constant. 



Wherever it is appropriate this relationship was multiplied by a^io 

 type of function to include the effect of temperature. 



Computer Simulations 



The sets of differential equations describing the benthic and 

 planktonic models were simulated on an IBM computer using CSMP III 

 (Continuous System Modeling Program). CSMP allows us to simulate the 

 dynamic behavior of a continuous system expressed as a set of ordinary 

 differential equations or a set of partial differential equations. It provides 

 considerable flexibility in the choice of integration methods and has 

 powerful capabilities for handling input and output and their 

 specifications. The program automatically sorts user-supplied structure 

 statements to establish a correct execution sequence. This sorting of 

 structure statements of the program is very important, for an incorrect 

 sequence would introduce a phase lag that could seriously affect the 

 accuracy and stability of the solution. Complex problems involving non- 

 linear and time-varying elements can be easily handled, for it is possible to 

 incorporate FORTRAN statements into CSMP III programs. The fourth- 

 order Runge-Kutta method was used for numerical integration. (For a 

 detailed description of CSMP III see IBM manual SH19-7001-2.) 



All the rates in the equations are expressed in units of hours. The 

 models were simulated for a period of 1440 hours to cover our 

 experimental observations recorded from 15 June to 15 August. 



BENTHIC CARBON FLOW MODEL 



The state variables of the benthic system and their initial conditions 

 are given in Table 10-1. The block diagram of Figure 10-1 depicts the flow 



