382 GENERAL DISCUSSION 



achievements which have been made by uneducated men unaided by 

 mathematics or Markov stochastic processes and allied concepts. I doubt if 

 the deviser of the wheelbarrov^ knew the theory of levers : Brindley, who 

 made vast advances in the engineering practice, was an uneducated man. 

 Does this imply that we should follow Simpson's principle of emphasizing 

 the non-quantitative observational phase of natural history as the basis of 

 research, rather than adopt Skellam's precept that we should compose a 

 mathematical model before attempting to measure any parameter ? If theory 

 is needed prior to any advances, how is it that great new advances come from 

 the work of uninformed people ? Early workers in fisheries collected vital 

 data before anybody knew how it was to be used. Intuitive mathematical 

 and mechanical models (not necessarily hydrostatic !) can be of great value. 

 But in any field of biological research one can blunder on and hit upon 

 important discoveries simply because one is blundering on in the right field 

 of investigation. 



D. H. Chitty: The transition from natural history to model does not 

 arise automatically. There is a gap only bridged by intuition, not by logic. 

 In this sense discovery parallels the invention of the wheelbarrow, but a 

 mathematical model is harder to test than a wheelbarrow. As a rule models 

 cannot be tested directly, but only used by seeing if they lead to predictable 

 results. 



G. C. Varley: The model can in fact be recognized quite easily, and 

 discarded if it is inapplicable. Nicholson & Bailey's model, for example, 

 can easily be seen to be inapplicable to fish with a long life-span, and Lotka- 

 Volterra systems to insects with a short life-span. One can achieve something 

 by blundering on — by 'trial and error' processes — but this approach is 

 uneconomical of effort. It may involve much hard work in counting and 

 assaying parameters, and these, when a model is ultimately arrived at, may 

 prove to be inapplicable — while the vital parameter was omitted from the 

 study. To have a model earlier in the process makes the whole scheme much 

 more efficient. 



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