Modeling 451 



24 30 36 42 



Time, days 



48 54 60 



FIGURE 10-8. Field measurements (solid line) and 

 the model simulation (dashed line) of the biomass 

 of bacteria in the water of Pond B. 



add nothing to our understanding, however, so we have not bothered to 

 improve the simulation. 



In a computer simulation type of modeling scheme for a complex 

 ecosystem, the manipulation of the initial conditions and parameter values 

 is known as tuning and calibration of the model. The objective of such 

 procedures is to arrive at a set of curves almost identical and consistent 

 with the observed data. This model with tuned parameters and initial 

 conditions is used to predict or verify the results of a different year. The 

 major difficulty with this procedure is that for a new set of input variables 

 the "retuned" model does not produce a behavior of the variable similar to 

 the one observed in the field or during experimental investigations. Thus a 

 new cycle of tuning and calibration is required. This model is justified on 

 the premise that experimental and field data for parameters and initial 

 conditions do indeed show a range of values and so it is logical and 

 acceptable to manipulate the parameters within the observed range to 

 produce the desired behavior from the model. Even simple models of 

 ecosystems include dozens of parameters, all of which can be manipulated 

 within the given range. Thus, although it is relatively simple to produce a 

 set of desired curves by tuning and calibration, the inherent danger in such 

 a procedure is that one is liable to get the right results for the wrong 

 reasons. This is a serious problem and it also imposes a severe restriction 

 on the utility of these models for applied problems in ecology and resource 

 management. 



Stochastic Framework: Toward a More Realistic and General Model 



One possible and potentially very powerful approach to the analysis 

 of these complex ecological systems is to formulate the dynamics of the 

 system in terms of stochastic differential equations. The computer 



