GENERAL DISCUSSION 381 



7. MATHEMATICAL MODELS 

 G. C. Varley: Even those who have Uttle mathematical understanding 

 must inevitably use some type of model, directly or indirectly. In this 

 context I feel that we have not heard enough about the use of such models 

 in plamiing research. In fact, there is a kind of sequence of processes in the 

 study of a problem: 



Natural history Theoretical Test of Interpretation. 



observations. > model. > assumptions. > Prediction. 



Measurement 

 of parameters 

 in field. 



J. G. Skellam: There is a feature of Varley' s diagram which deserves 

 emphasis. Between the observation of nature on the one hand and the 

 estimation of population parameters on the other, there stands a model. 

 For the estimation of parameters it is logically necessary to have a model, 

 even if this is only a set of common-sense assumptions scarcely deserving 

 the epithet 'mathematical'. The testing of models against observations rarely 

 takes place directly. More commonly we compare the logical consequences 

 expected from the operation of the model against observation. There is 

 here a deductive phase which is the real province of the biometrician, but 

 it is up to the biologist to provide him with at least the outlines of a model 

 on which to work. 



G. C. Varley: The biologist's main problem is often the choice between 

 a profusion of models. 



A. C. Simpson: The natural history' phase in Varley's scheme should 

 be divided into two subsections. Firstly, there is a qualitative process of 

 observation on stocks, spawning areas and the like. Secondly, there is a 

 quantitive element in which parameters are assessed. 



W. H. Pearsall: I am not happy about Skellam's approach. Surely the 

 basis of modern studies is a preHminary qualitative description, a subsequent 

 quantitative assay, and then the formulation of a model based on these data, 

 from which deductions can be drawn. The model thus follows, not precedes, 

 the estimation of population parameters. 



E. D. Le Cren: An important key to success in research is the ability to 

 ask the right questions of nature. Even at the natural history' stage one 

 must look for the right things and when measurements are made, measure 

 the right things. For this some theoretical 'model', even if an unwritten one, 

 is essential. 



M. Graham: I am becoming more and more impressed with the 



