454 J. L. Tiwari et al. 



make predictions in terms of a range rather than a single value. It is 

 interesting that all the sample values from the field data were well within 

 the confidence interval obtained from the stochastic model. 



Although a stochastic model is more realistic and results are closer to 

 the experimental observations than those from the deterministic model, 

 some difficulty in formulating such models remains. For this model, we 

 assumed that parameters and initial conditions in the model are random 

 variables with Gaussian probability distributions. Though these equations 

 are variables, the nature of the distribution cannot usually be determined 

 from the available data because usually only five or six sample values are 

 available; this is not enough to decide the type of distributions. Thus it 

 seems that we need a method by which we can make the best use of the 

 available data without making explicit assumptions about the distribution. 

 This can be accomplished by the formalisms of Information Theory 

 (Tiwari and Hobbie 1976b). If and when more data are available, that 

 information can be utilized to modify the shape of the distribution. This 

 method can help us formulate a general realistic model based on the 

 maximum amount of information that can be extracted from a given set of 

 data. 



In spite of our use of models, the discrepancies between model results 

 and experimental and field observations on natural systems signify that 

 there are some unresolved yet fundamental problems in biology. For 

 example, what are the behavioral features of large, complex systems and 

 what are the underlying causes responsible for these properties? 

 Furthermore, the properties associated with the structures and functions 

 of biological systems have been shaped by the forces of natural selection 

 over thousands and millions of years. Some recent works in this area 

 suggest that modes of behavior of large, complex systems can be 

 influenced by the number of elements in the systems, the degree of 

 connectance between the elements, the degree of non-linearity in the 

 system, the hierarchical structure, and the magnitude of the entropy (May 

 1973, Gardner and Ashby 1970, Kauffman 1969, Siljak 1974, McMurtrie 

 1975). Perhaps the observed behavior of our models reflects the 

 cumulative effect of all these and even more factors. During the last few 

 years some progress has been made in this direction but much research is 

 needed before we can understand the behavior of models; even more is 

 needed before the models will effectively simulate real systems or 

 ecosystems. 



Conclusion 



From the preceding sections, it is evident that the modeling effort did 

 not produce predictive models or even models from which we gained new 

 insights. It became obvious that we really did not know enough about the 



