process or, conversely, including the decisionmaker throughout the modeling 

 process (see Section III). 



While this may seem to be a serious limitation to modeling, it is an 

 essential perspective to take when attempting to specify the state-of-the-art 

 of modeling and how models can provide useful input to management. The extent 

 and quality of scientific information about different topics varies greatly. 

 Similarly, there is a spectrum of approaches to ecosystem modeling, each with 

 its specific data requirements and each capable of contributing information at 

 different degrees of resolution to management decisions. Modelers vary widely 

 in their interests and convictions about what model types are best. Perhaps a 

 more appropriate view is to see the various modeling approaches as members of a 

 spectrum of strategies. Relatively simple empirical models are at one end of 

 the spectrum while highly detailed mechanistic models incorporating many 

 functional forms of complex cause and effect interactions are at the other end. 

 Throughout this broad spectrum there is the consideration of deterministic 

 versus stochastic modeling techniques. The deterministic approach is the 

 simpler of the two since a unique set of outputs, free of variability, results 

 from each unique set of input data. Stochastic approaches, on the other hand, 

 incorporate variability (uncertainty) in the model structure often resulting in 

 nonunique outputs which are viewed as probabilities of occurrence within the 

 natural variability of the system being modeled. 



The remainder of this section is a brief summary of a general framework 

 within which the various approaches may be viewed. 



Empirical Models 



A number of purely statistical techniques exist for describing apparent 

 relationships among or between empirical observations. In the simplest case, 

 linear regression can relate a single dependent variable (Y) to an independent 

 variable (X). Multiple linear regression relates the range of observed Y-values 

 to more than one X or independent variable. Polynomial regressions are more 

 complex, and assume that the variation in Y is related as some nonlinear function 

 of one or more X variables. 



The statistical methods are well known and readily available on most 

 computers. Thus, these methods are relatively quick and inexpensive to implement 

 if the data are available. The most serious limitation is that such regression 

 methods do not necessarily reveal anything about causal relationships, though 

 it is often tempting to suspect they do. 



Mechanistic Models 



At the other extreme of modeling strategies is the family of models that 

 attempt to represent the functional mechanisms that regulate the processes 

 taking place in the natural ecosystem. These models are based upon massive 

 amounts of data, often at the level of physiological responses of organisms to 

 important features of their environment. Such data are almost never available 

 for all or most of the species in any given system, and assumptions must be 

 made about specific features unique to each locale. The predictions of these 

 mechanistic models are usually compared to data of a fundamentally different 

 kind: synoptic observations of the standing stocks of the state variables 

 through time. Thus, this modeling approach requires the greatest amount of 



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