Abstract
The mathematician and the biologist have an almost inevitable confrontation in the formulation of a model for any biological situation, for, whereas the biologist will plobably begin with the actual and complex set of facts that he has observed or otherwise become aware of, the mathematician is likely to be looking for an idealized model capable of theoretical investigation. This kind of dilemma has become more obvious as the use of mathematics has moved from the physical to the biological (and also to the social) sciences, and 1 do not believe that there is a facile answer. It is quite natural for an experimental or observational scientist to list a large collection of facts that should be taken into account in any comprehensive theoretical formulation; but the purpose of the latter is to understand and interpret the facts, and the mathematician is sometimes able to give insight by a study of idealized and over-simplified models, which are more complicated in their behaviour than is often realized. Until we can understand the properties of these simple models, how can we begin to understand the more complicated real situations? There is plenty of scope for variety of approach, but I would urge that critical criteria of success be employed wherever possible. These include the extent to which:
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(i)
known facts are accounted for;
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(ii)
greater insight and understanding are achieved of the biological situation being studied;
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(iii)
the theory or model can correctly predict the future pattern, even under different conditions from those pertaining to the current observed data.
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Bartlett, M.S. (1975). Equations and models of population change. In: Probability, Statistics and Time. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5889-0_8
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DOI: https://doi.org/10.1007/978-94-009-5889-0_8
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