Modeling 431 



of carbon to and from these variables. The square boxes in the diagram 

 represent the state variables and the arrows describe the dynamic 

 processes which are adding and removing carbon from the variables. A list 

 of all the equations describing the system is given in Table 10-3. The k's in 

 these equations are the parameters which are defined in Table 10-4. 



Primary Producers 



Although the benthic population of the sediment is distributed over 5 

 cm of depth, photosynthesis is limited to the top 3 mm. The algal cells of 

 the bottom 4.7 cm are not exposed to the light and hence are not 

 photosynthesizing. For this reason we have separated the total algal 

 biomass into two groups: surface algae (which are photosynthesizing) and 

 buried algae (which are not photosynthesizing). These two types of algal 

 populations are treated as two separate state variables. The loosely packed 

 sediment of these ponds is continuously disturbed by the movements and 

 the activities of chironomids and tadpole shrimp {Lepidurus arcticus). This 

 continual mixing contributes towards the burial (RB3) of algal cells. This 

 exchange mechanism transfers the algal biomass between the two 

 compartments and is a very important control on the exponential growth 

 of the surface algal population. 



Algal photosynthesis is modeled as a function of its biomass, of light 

 intensity, of temperature, and of the concentration of phosphorus in the 

 sediment. Experimental evidence from these ponds suggests that 

 phosphorus is in limited supply and acts as a limiting factor (Chapter 5, 

 Prentki 1976). As outlined earlier, the relationships between both light 

 intensity and phosphorus and the rate of photosynthesis are of the 

 Michaelis-Menten type. The loss terms in the differential equations 

 describing the dynamics of the algal populations are respiration (RB2 and 

 RB7), death (RB5 and RBIO), and excretion of U-DOC (RB4 and RBI 1). 

 It is assumed that the rate of excretion of U-DOC is proportional to the 

 algal biomass; a constant fraction of the primary productivity is also 

 excreted as U-DOC. 



Decomposers 



Bacteria are the only microbial decomposers included in this model. 

 Their growth rate is proportional to their biomass and to the 

 concentrations of U-DOC and R-DOC in the sediment (RBlOl and 

 RB102). The rate of uptake of U-DOC and R-DOC is assumed to follow a 

 Michaelis-Menten type of kinetics. In addition to the uptake of U-DOC 

 and R-DOC, these organisms are also obtaining some food by hydrolyzing 



