II. TECHNICAL BASIS OF MODELING 



Modelers frequently state that no model can be better than the data on 

 which it is based. However, there is more to establishing confidence in a 

 model than assuring the quality of the data set, although this is an important 

 aspect. Although ecosystem modeling is a highly technical activity, it mainly 

 proceeds by unwritten procedures. There do not exist, as yet, formal rules for 

 formulating models. The process generally occurs in stages — problem definition, 

 model conceptualization, formulation, calibration, validation, output to user — 

 but the ecological community has given very little attention to developing the 

 technical basis of each of these steps. Examples are: 



1. Problem definition . Mathematicians recognize poorly specified versus 

 well specified problems. What criteria can be developed to assure that modeling 

 activities occur in response to well specified problems? How can normal 

 procedures for testing hypotheses be engaged here? 



2. Model conceptualization . Models are supposed to be analogies which 

 organize relevant considerations about a problem into a consistent interactive 

 set. Usually, some scheme of functional taxonomy is constructed in the process. 

 How may formalisms such as set, hierarchy, and category theories contribute to 

 this process? What do such theories tell us about consequences of aggregation or 

 disaggregation for function preservation? 



Structural characteristics of a model influence model behavior. There is 

 considerable latitude in design of the basic structure of the model (i.e., 

 number of compartments, connections, feedbacks, modes of input, etc.) and equal 

 latitude in the mathematical interpretation of this structure. Little work has 

 been done that systematically explores the effect of model structure on results. 

 An appreciation of robustness of results to different model configurations is 

 needed to evaluate the reliability of a model in representing the ecosystem. 

 This knowledge is particularly important with ecosystem models because they are 

 so difficult to evaluate. 



3. Model formulation . Can formal criteria be developed to aid in the 

 choice of alternative mathematical functions? Are rules of parsimony available, 

 e.g., at what point would decisions be made to select dynamic over static, 

 nonlinear over linear, spatial over nonspatial models? In general, the criteria 

 for such decisions have been very soft in the past. For example, quite often 



an empirical, curve-fitting function is chosen because of tradition. The 

 criteria for such choices should be amenable to formalization. 



Once a model is mathematically formulated, it should not be carelessly used 

 in computer simulations. The twin mathematical properties of existence and 

 uniqueness are almost never investigated for ecological models. It may be 

 possible to generate numerical solutions of equations for which no analytical 

 solutions exist. Ecological models are usually mathematically complex, and 

 careful attention should be given to their mathematical properties before they 

 are acceptable for environmental management purposes. 



4. Model calibration . Adequate data to implement ecosystem models almost 

 never are available. Is it possible to develop mathematically sound procedures 

 for generating missing data comparable to the missing data procedures which are 



248 





