M 



I 



E 

 u 



9 



E 



20 



40 



Time, days 



Major Findings 17 



60 



FIGURE 1-12. Model simulation of epipelic algal 

 biomass. The lines represent the deterministic model 

 (D), the mean of nine runs of the stochastic version of 

 the same model (SM), and the standard deviation of 

 the stochastic mean (SD). (After Tiwari et al. 1978.) 



some of these. Therefore, the result shown in Figure 1-11 can be easily 

 changed in an extremely drastic way by changing the algal respiration 

 coefficient from 0.25 to 0.30. Even if we did have a good way of measuring 

 algal respiration, in the field it would not distinguish between these two 

 values. In a similar fashion, if the rate of maximum photosynthesis is 

 changed from 0.05 to either 0.04 or 0.06, the algal biomass rapidly 

 approaches zero. Yet we know that this maximum photosynthesis rate 

 does change over the year in our pond. 



The next step was to see what would happen to the model if all the 

 coefficients and parameters were varied slightly. This stochastic model is 

 probably more realistic, as variability is a property of every biological 

 measurement and interaction. Unfortunately, we did not have the data on 

 the mean and standard deviation of every measurement that would be 

 necessary to implement this approach. However, when we incorporated 

 reasonable variability into the benthic model, the mean values (Figure 1- 

 12) were quite different from the deterministic model values. 



In only a few cases could the model be used to test hypotheses. For 

 example, we did examine the hypothesis that the mixing of the sediments 

 was an important control of the growth of benthic algae. This mixing 

 could not be measured directly in the field or laboratory but the modeling 

 exercise helped to put reasonable limits on this rate. 



Our conclusions from the modeling effort were that we knew too 

 much about the pond ecosystem to be satisfied with fine-tuning a model 



